operations mgmt

Reduced project completion time is

"crashing"

A company's holding cost is 16% per year. Its annual inventory turns are 12. The company buys an item for $39. What is the average cost (in $s) to hold each unit of this item in inventory?

$0.52 $39 purchase / 12 turns = $3.25 average inventory. Holding cost = $3.25 × 16% = $0.52

Expected profit=

(Price×Expected sales)+ (Salvage value ×Expected inventory ) − (Cost per unit×𝑄)

Crash cost/time period =

(crash cost-normal cost)/(normal time - crash time)

Why have inventory?

- Balance supply and demand of WIP - Balance supply and demand of finished goods. - Balancing supply and demand: decouples differences in supply and demand requirements - Buffers against uncertainties: variation in supply and demand are managed with buffer (safety) stock - Enabling economies of buying: price discounts or reduced shipping costs - Enabling geographic specialization: supply and demand locations vary

Safety Inventory

- Inventory needed to buffer against demand uncertainty. Also called Safety stock. Safety inventory can be raw materials, WIP or finished goods.

holding costs include

- Opportunity cost of capital - rent and maintenance of the building - warehouse cost

Earliest start time (EST)

- The earliest time an activity can begin, which is given by the earliest time all predecessor activities have been completed. EST(A_𝑖 )=Max{ECT(A_𝑗)} where〖 A〗_𝑗 are all activities providing input to〖 A〗_𝑖

Raw material

- has not been "worked on"

Work-in-process (WIP)

- inventory that is inside the process has been "started on"

Using the newsvendor model, we need

- the critical ratio - information about the distribution of the demand data -->Empirical distribution OR -->Normal with mean and standard deviation

Finished goods

- the process is complete and does not require additional processing

difference between the periodic inventory review and continuous review

A major difference between the periodic inventory review and continuous review is, periodic reviews involve keeping track and documetation of inventory at specific times. This could mean a review weekly, monthly depending on the firm. The difference is continuous inventory review, requires a system that keeps track every item that is removed from inventory and also updates inventory count each time.

MSE

A measure of evaluating the quality of a forecast by looking at the average squared error. Errors are squared so that large positive errors do not simply cancel out large negative errors

What impact do quantity constraints have on the order quantity?

A quantity discount can be used as a motivator to order larger quantities Larger quantities increases the sum of ordering and holding costs (above minimum) but the discount reduces the purchasing cost A very large quantity may be optimal even if the discount appears to be small Firms are more price sensitive than consumers quantity discounts.

Seasonality -

A significant demand change that constitutes a repetitive fluctuation over time.

Stockout -

A stockout occurs when a customer demands an item that is not available in inventory.

Quick response -

A strategy that increases supply flexibility to allow a response to updated information about demand. For example with quick response a firm can obtain additional supply for products that are selling above expectation, thereby reducing the number of stockouts.

Project -

A temporary (and thus nonrepetitive) operation. Projects have a limited time frame, one or more specific objectives, and a temporary organizational structure, and thus often are operated in a more ad-hoc, improvised management style.

Limitations of product pooling/universal design

A universal design may not provide key functionality to consumers with special needs: - High end road bikes need to be light, high end mountain bikes need to be durable. It is hard to make a single bike that performs equally well in both settings. A universal design may be more expensive to produce because additional functionality may require additional components. But a universal design may be less expensive to produce/procure because each component is needed in a larger volume. A universal design may eliminate brand/price segmentation opportunities: - There may be a need to have different brands (e.g., Lexus vs Toyota) and different prices to cater to different segments.

Double exponential smoothing -

A way of forecasting a demand process with a trend that estimates the trend using exponential smoothing and then also uses exponential smoothing to estimate the demand rate net of the trend.

Crashing Projects is done by

Accelerating a project by committing more resources than initially planned

Which of the following is not an example of inventory? Bags of flour waiting to used in the making of bread An motorcycle that is being built. A line of cars waiting at a carwash. A container of TVs being shipped to another country. All are examples of inventory.

All are examples of inventory.

Which statement is true? Holding costs go up as Q gets bigger. Order costs go down as Q gets bigger. The total order and holding costs are minimized when the total holding costs equal the total order costs. All of the above are true.

All of the above are true. not sure

Choose the statement that is not true The term "seasonal" includes patterns that can happen throughout a day, week, month or year. Cyclic and irregular components to time series are difficult to forecast. Sports injuries follow a seasonal pattern. All of the statements are true.

All of the statements are true

Which of the following statements is correct with respect to a Gantt chart? The x-axis of a Gantt chart shows a time line. The y-axis shows the activities of a project. The Gantt chart itself does not show all dependencies among activities. The Gantt chart is named after 19th century industrialist Henry Gantt. All of these statements are correct.

All of these statements are correct.

Which of the following statements is correct with respect to slack time? The slack time of an activity is the latest completion time of the activity minus the earliest completion time. The slack time of an activity is the latest start time of the activity minus the earliest start time. The slack time of an activity determines by how much an activity can be delayed without impacting the overall completion of the project. All of these statements are correct.

All of these statements are correct.

Momentum-based forecasting -

An approach to forecasting that assumes that the trend in the future will be similar to the trend in the past.Regression of the time series

Which statement is not true? A unbiased forecast can have large positive or negative forecasting errors. The accuracy of a forecast tells how well it fits historic data. An unbiased forecast will have a mean error of 0. A positive mean error value indicates that your forecasting method tends to forecast higher than the actual values.

An unbiased forecast will have a mean error of 0.

Annual turns =

Annual cost of goods sold/Inventory

Critical Path

Any path going from the start to the finish with slacks of 0 is a critical path. Activities on this path must be started and completed on time or the project is delayed.

Assumptions

Assume that the durations of activities on the critical path are independent. Variance of project completion time = sum of variances of the activity durations on the critical path. The project completion time is normally distributed. - Normal distribution assumption is reasonable if there are many activities on the critical path (Central Limit Theorem). Non-critical activities will not become critical in spite of their uncertain durations.

Time Series Models

Assumes information needed to generate a forecast is contained in a time series of data Assumes the future will follow same patterns as the past Forecaster looks for data patterns as

Formulas

Average inventory during the unit of time=𝑄/2 Holding cost per unit of time=1/2 ×ℎ ×𝑄 Number of orders per unit of time=𝑅/𝑄 Ordering cost per unit of time= 𝐾 × 𝑅/𝑄 Total ordering and holding costs per unit of time=𝐶(𝑄)=(𝐾× 𝑅/𝑄 )+(1/2 + ℎ ×𝑄) 𝐸𝑐𝑜𝑛𝑜𝑚𝑖𝑐 𝑜𝑟𝑑𝑒𝑟 𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦=𝑄∗=√((2 ×𝐾 ×𝑅)/ℎ)

Projects have all of the following characteristics except: A.Temporary B.Set beginning and end C.Repetitive D.Projects have all of the above characteristics

C.Repetitive

Which is true? The cost of spoilage increases with lower levels of inventory. Companies consider the opportunity cost of holding inventory when determining how much inventory to hold. Obsolesce cost is a reason to increase inventory levels. A stockout cost is incurred when there is not enough room in the warehouse to hold all of inventory and extra space must be contracted out of the facility.

Companies consider the opportunity cost of holding inventory when determining how much inventory to hold.

Spoilage and Shrinkage Costs -

Costs associated with theft or product deterioration over time.

If we order Q and demand is D, then our cost is:

Cu * (D - Q) if Q <= D Co * (Q - D) otherwise

Burger Prince buys top-grade ground beef for $3 per kg. A large sign over the entrance guarantees that the meat is fresh daily. Any leftover meat is sold to the local high school cafeteria for $2 per kg. Eight hamburgers can be prepared from each kilogram of meat. Burgers sell for $2 each. Labor, overhead, meat, buns and condiments cost $1 per burger. Demand is normally distributed with a mean of 400 kg per day and a standard deviation of 50 kg per day. What daily order quantity is optimal? Cu =Co =Critical Ratio =Z = Q* =

Cu = 16 - 8 -3 = 5Co = 3 - 2 = 1Critical Ratio = 5 / (1 + 5) = 0.833Z = 0.97 (From standard normal table)Q* = 400 + 0.97 * 50 = 448.5

Expected gain on the Qth unit =`

Cu x (1-F(Q))

what are the metrics for inventory mgmt?

Days-of-Supply - The average amount of time (in days) it takes for a unit to flow through the system. Inventory Turns - The number of times the average inventory flows through a process in a designated interval of time. Service Level - The percent of time of being able to meet customer demand with available stock. Stock outs: Number of times there is no inventory is available to meet a customer's needs.

If the order quantity doubles, what happens to the frequency of orders (i.e., the number of orders submitted per unit of time)? Decreases by more than 50% Decreases by 50% Remains unchanged Increases by 50% Increases by more than 50%

Decreases by 50% The number of orders per unit of time is R / Q, where R is the flow rate and Q is the order quantity. So if Q doubles, then the number of orders per unit of time decreases by 50%.

Which statement is not true about the Newsvendor problem? There is only one opportunity to order. Demand is known. The cost of buying too many can include disposing of the items or selling them at a discount. The cost of buying too few includes lost sales. All are true about the newsvendor problem.

Demand is known.

Economic Order Quantity

EOQ is (under some fairly strict assumptions) ◦the most economical number of units to order (or produce) when an order is placed or when a production run is started. EOQ seeks the best tradeoff between annual holding cost and annual cost to place an order (or to set up production).

Differences between MA and ES

ES carries all past history (forever!) MA eliminates "bad" data after n periods MA requires all n past data points to compute new forecast estimate while ES only requires last forecast and last observation of 'demand' to continue

Newsvendor Performance Measures

Expected inventory Expected sales Expected profit In-stock probability Stockout probability Stockout

A newsvendor faces normally distributed demand and the critical ratio is 0.8. If the profit maximizing quantity is ordered, which of the following statements is true? Expected sales is less than expected demand; Expected sales is greater than expected demand; Expected sales is exactly equal to expected demand; Expected sales could be less than, equal to, or greater than expected demand.

Expected sales is less than expected demand; Expected sales is always less than expected demand, i.e., no matter the critical ratio or the demand distribution.

To maximize expected profit order Q units so that the expected loss on the Qth unit equals the expected gain on the Qth unit: (formula)

F(Q) = Cu/(Co+Cu)

Firms in the same industry will have the same inventory turns. True False

False There can be variation in inventory turns among the same firms within an industry.

Tablets and laptops would be categorized as which type of inventory by an electronics retailer? Raw materials inventory Work-in-process inventory Finished goods inventory Seasonal inventory

Finished goods inventory

A sales organization creates a new sales forecast by simply taking the average of demand forecasts that each sales manager generated individually. What type of subjective forecasting approach best describes this? Forecast combination Forecast with consensus building Prediction market Time-series forecasting

Forecast combination

Moving Average

Good for short term forecasts - 1 to 2 periods in the future Requires at n periods of data minimum to use. Must have stable time series - no trend, no seasonality Lags behind changes in the data patterns

Newsvendor applications

Goods sold seasonally - Halloween costumes - Christmas trees - Ski equipment Goods/services that have short shelf lives - High fashion goods - Certain electronics - Books??

Both PERT and CPM

Graphically display the precedence relationships & sequence of activities on an activity network Estimate the project's duration Identify critical activities that cannot be delayed without delaying the project Estimate the amount of slack associated with non-critical activities

Disadvantages of Inventory

Higher costs Difficult to control (due to "variability" in demand, production and logistics factors, quality etc.) Hides production and quality problems

The EOQ minimizes the sum of the ordering cost and which of the following costs? Stockout cost Holding cost Purchasing cost Quality cost

Holding cost

Choose the true statement Consumers are more sensitive to quantity discounts than companies. If the EOQ is feasible at the lowest price level, you do not have to calculate the other price levels and will use this quantity for your order. After calculating the total cost for each price, choose the Q with the lowest price. All of these statements are false.

If the EOQ is feasible at the lowest price level, you do not have to calculate the other price levels and will use this quantity for your order.

Which of the following statements are correct with respect to an AON graph of a project? In an AON graph, the activities are on the edges of a graph. In an AON graph, the activities are on the nodes of a graph. AON stands for the American Operations Norm. None of these statements are correct.

In an AON graph, the activities are on the nodes of a graph.

If the order quantity doubles but the flow rate remains constant, what happens to the sum of ordering and holding costs? Decreases by 50% Decreases by less than 50% Remains unchanged Increases by less than 50% Increases by 50%

Increases by less than 50% The ordering cost will decrease by 50%, and the holding cost will double. Together, this results in an increase of less than 50%.

Holding costs

Inventory costs [per unit of time] = 1/2 Order Quantity x h (1/2Qxh)

For which of the following products is there the highest probability that demand is within 50% of the mean of the demand forecast? Mean = 1,000, standard deviation = 200 Mean = 1,000, standard deviation = 300 Mean = 2,000, standard deviation = 300 Mean = 2,000, standard deviation = 500 Mean = 4,000, standard deviation = 1,600 Mean = 4,000, standard deviation = 2,000

Mean = 2,000, standard deviation = 300 The product with the lowest coefficient of variation will have the highest probability of demand being within 50% of the mean of the demand forecast.

MAE and MAPE

Mean absolute deviation (MAD) or mean absolute error (MAE): average of forecast errors, irrespective of direct Mean absolute percentage error (MAPE): the MAD adjusted to meaasure how large errors are relative to the actual demand quantities

𝐼(z)=

NORM.DIST(𝑧, 0, 1, 0)+(𝑧 ×NORM.DIST(𝑧))

𝑧=

NORM.S.INV

The critical path in a project is the sequence of activities that: has the shortest time. has the smallest number of activities. has the shortest budget. None of these statements are correct.

None of these statements are correct.

Computers lose value as they are stored in inventory. This is an example of which component of a firm's inventory holding cost? Opportunity cost of capital Storage cost Spoilage cost Obsolescence cost

Obsolescence cost

Newsvendor assumptions

One production or procurement opportunity Stochastic demand D during selling season - If D>Q, then sell out - If D<Q, then inventory leftover Fixed cost per unit ordered/made (c) Fixed price per unit sold during regular selling season (s) Leftover inventory sold for a fixed salvage value (v) 0 Positive Negative

calculation summary

Optimal order quantities and performance measures with the EOQ model: Average inventory during the unit of time=𝑄/2 Holding cost per unit of time=1/2 ×ℎ ×𝑄 Number of orders per unit of time=𝑅/𝑄 Ordering cost per unit of time=𝐾 × 𝑅/𝑄 Total ordering and holding costs per unit of time=𝐶(𝑄)=(𝐾× 𝑅/𝑄 )+(1/2 + ℎ ×𝑄) 𝐸𝑐𝑜𝑛𝑜𝑚𝑖𝑐 𝑜𝑟𝑑𝑒𝑟 𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦=𝑄∗=√((2 ×𝐾 ×𝑅)/ℎ)

Fixed-order quantity

Order a predetermined amount each time an order is placed

Order n periods

Order enough to satisfy demand for the next n periods

Lot-for-lot

Order exactly what is needed for the next period

The expected completion time is 23 days. The variance along the critical path is 2. The standard deviation along the critical path is 1.41. What is the probability that the product development will be completed in 21 days? What is the probability that the product development will be done in 24 days?

P(T ≤ 21) = P((T - 23)/1.41 ≤ (21 - 23)/1.41) = P( z ≤ -1.41) = 0.0793

Which statement is true? PERT assumes that the activity time for each activity is dependent on another activity. PERT uses a normal distribution to calculate the mean and variance for each activity. PERT assumes that the project completion time is normally distributed. All of the above are false.

PERT assumes that the project completion time is normally distributed.

Periodic inventory Review Systems

Periodic inventory review involves counting and documenting inventory at specified times. A target inventory level is set and orders are placed to bring the inventory up to this level. Reduces the time spent analyzing inventory counts Not as accurate for businesses with high-volume sales. Inventory levels uncertain between inventory review periods. This can make it difficult to ascertain when reordering items is necessary and can make accounting less accurate.

How to calculate seasonal index

Pick time period (number of years) Pick season period (month, quarter) Calculate average price for season Calculate average price over time Divide season average by over time average price

Choose the false statement. A.Moving average and exponential smoothing work best with stationary data. B.Exponential smoothing with aequal to 0 gives the same forecast as the Naïve method. C.A bad data point will leave a moving average forecast faster than it will leave an exponential smoothing forecast. D.All are true.

B.Exponential smoothing with aequal to 0 gives the same forecast as the Naïve method

Crashing is when a company fails to meet a project deadline. A.True B.False

B.False

Removing the impact of the season from the demand is called Seasonalization. A.True B.False

B.False

The activity with the lowest crash cost per unit time should be crashed first. A.True B.False

B.False The critical activity with the lowest crash cost should be crashed first.

Goal of Inventory Management:

Balance inventory costs and customer service level.

Which reason for holding inventory enables a firm to reduce the impact of large fixed costs that the firm incurs whenever it places an order to a supplier? Seasonality Uncertain demand Buffers Batching

Batching

What Is Forecasting?

Process of predicting a future event Underlying basis of all business decisions ◦Production ◦Inventory ◦Personnel ◦Facilities

A newsvendor orders the quantity that maximizes expected profit for two products, A and B. The critical ratio for both products is 0.8. The demand forecast for both products is 9,000 units and both are normally distributed. Product A has more uncertain demand in the sense that it has the larger standard deviation. Of which of the two products does the newsvendor order more? Product A, because it has less certain demand. Product B, because it has more certain demand. The order quantities are the same because they have the same critical ratio. More information is needed to determine which has the higher order quantity.

Product A, because it has less certain demand. Product A has a higher standard deviation of demand, and therefore its optimal order quantity is greater given the same mean and critical ratio.

Which is not true? Product pooling is also known as universal design. Product pooling is an attempt to reduce uncertainty in demand by aggregating the demand of several products into a single product. Product pooling is most effective when the demand for products is positively correlated. Product pooling is a form of risk pooling.

Product pooling is most effective when the demand for products is positively correlated.

Project Management Objectives

Project Cost - Planning for time and money. ◦Project Budget - Outline of the main expenses associated with the project. Project Scope - Description of what must be accomplished in order for the project to be complete. Project management triangle - The tension between the three objectives of a project: time, budget, and scope.

3 costs of the model

Purchase costs (cost of goods produced/ordered) Setup or ordering costs (K) (costs paid each time goods are ordered) Holding costs (h) (Cost of holding one unit of inventory for a period of time. Accounts for cost of capital, storage, obsolescence. Usually based on purchase costs, given for one year)

inventory profile

Q is the Y-axis Time is the X-axis when the line shoots up, that is SHIPMENT ARRIVING Average inventory - the middle dotted line (=Q/2)

total costs =

Q/2(h) + KR/Q combo of holding and order

If a firm wanted to reduce the annual EOQ cost as a percentage of the annual purchase cost by 50%, how would the demand rate have to change? Decrease by 50% Remain unchanged Increase by 50% Double Quadruple

Quadruple

types of forecasting

Qualitative and Quantitative

EOQ Example Weekly demand = 240 units No. of weeks per year = 52 Ordering cost = $50 Unit cost = $15 Annual carrying charge = 20% Lead time = 2 weeks

R = 52 x 240 = 12,480 units/year h = .2x15 = $3 per unit per year Q = √((2x50x12,480)/3) = 644.98 = 645 units TC = [(12,480/645)x50] +[(645/2)x3] = 1934.94

R = d = L =

R = Demand per year d = Demand per day L = Lead time in days

Inventory Types

Raw material Work-in-process (WIP) Finished goods Safety Inventory

A delivery truck from a food wholesaler has just delivered fresh meat and produce to a local restaurant. This meat and produce would be categorized as which type of inventory by the restaurant? Raw materials inventory Work-in-process inventory Finished goods inventory Seasonal inventory

Raw materials inventory

Consider two projects that have the same activities and the same dependencies. In the first project, the activity times are expected outcomes. The actual times will vary. In the second project, the activity times are always as expected. On average (in expectation), which project will be completed first? The first The second Cannot be determined

The first

Mary, Susan, and Sarah are running a beach boutique on the board walk of Ocean City. Their favorite product is a red lifeguard hoody. Mary believes it will sell 348 times next season. Susan forecasts sales of 524, and Sarah forecasts 219. What would be the result of a simple forecast combination?

The forecast combination is simply the average of the three forecasts. In this case, 363.67.

Opportunity Cost of Capital -

The income not earned on the amount

Latest start time (LST) -

The latest possible start time of an activity that still allows for an on-time completion of the overall project.

Late start schedule -

The latest possible timing of all activities that still allows for an on-time completion of the overall project

Inventory

The number of flow units within the process. Inventory is found in all stages of processes

What is Inventory Management?

The practice of regulating the quantity, location, and type of inventory in a process. Critical for the success of the organization

In-stock probability -

The probability that all demand was able to purchase a unit.

Stockout probability -

The probability that some demand was not able to purchase a unit; demand experienced a stockout.

Evaluating the Quality of a Forecast

The quality of a forecast can only be assessed after the real outcomes have been observed. The forecast should be: Unbiased - that is correct on average Close to the real outcomes as measured by either the mean squared error (MSE) or the mean absolute error (MAE)

A change in which of the following does not result in a change in the mismatch costs incurred by a newsvendor? The quantity ordered The revenue received from salvaging inventory The regular selling price of the product The coefficient of variation of the demand forecast The quality of the product

The quality of the product Mismatch costs include the loss on inventory that is salvaged and the opportunity cost of demand that is not satisfied due to stockouts. Those are influenced by all of the items except the quality of the product.

Chose the true statement Use a qualitative method of forecasting when you have very little data to analyze. Use caution with the Delphi method so that one person's opinion does not dominate. Quantitative methods are based on human judgement. None of these statements are true.

Use a qualitative method of forecasting when you have very little data to analyze.

Exponential Smoothing Method best used for

Used for short term forecasts - 1 to 2 periods in the future Involves little record keeping of past data When a = 1, simple exponential smoothing is the same as the Naïve method.

Objective: Economic Order Quantity

We want to minimize the cost of holding inventory and ordering inventory without running out of inventory

activity nodes

We will use a special node with seven sections. Center section contains the activity name. Top center box contains the activity duration time.

Min-max system

When on-hand inventory falls below a predetermined minimum level, order enough to refill up to maximum level

Three-time estimate approach For each activity, estimate the following times:

a = the optimistic time (min duration) b = the pessimistic time (max duration) m = the most likely time (normal duration)

Exponential Smoothing Method

a forecasting method that predicts the next value will be a weighted average between the last realized value and the old forecast

Key driver of product pooling

coefficient of variation

which assumption is at the heart of the saw-toothed inventory pattern

constant demand rate, reliable lead time

EOQ is a _________ review model. This type of model is used with the _____ in an ABC inventory system.

continuous, A's

The critical ratio incorporates the

costs of having too many and too few of an item.

The ratio Cu / (Co + Cu) is called the

critical ratio

The _______ and_________ components are hard to predict.

cyclical, irregular

Weekly demand = 240 units No. of weeks per year = 52(5 day work weeks) Ordering cost = $50 Unit cost = $15 Annual carrying charge = 20% Lead time = 2 weeks R = 12,480 units per year Q* = 645 units d = ? Reorder point = ?

d = 12480/(52)(5) = 48 units/day Reorder Point = 48 * 10 = 480 units

As more units are ordered, the expected benefit from ordering one unit

decreases while the expected loss of ordering one more unit increases.

Can reduce by combining or pooling the

demand across products.

Risk pooling reduces

demand uncertainty by aggregating demand from one or more products or regions

EOQ can be used for

determining batch size or order size.

A MA4 forecast would be smoother than a MA12 forecast true false

false

A company wants to use regression analysis to forecast the demand for the next quarter. In such a regression model, demand would be the independent variable. True False

false

EOQ is a periodic review system. True False

false

The seasonality index is based on demand fluctuations that are additive. True False

false

The seasonality index is based on demand fluctuations that are additive. True False

false

n an AON graph of a project, there only exists one path from the first to the last activity. True False

false

More safety stock means

greater service level and smaller risk of stockout

If your forecasting method has a tendency to forecast too high, the mean error will be

greater than 0.

lower demand =

higher percent of costs for ordering and holding

for large quantities, the ___________ cost dominates

holding

holding costs vs order costs

holding costs - as you increase Q, the cost increases Ordering costs - at you increase Q, the cost goes down

Graphing data is important because it can help us

identify patterns in the data including non-linear trends.

as you increase order quantity, the EOQ

increases

ABC Classification (ABC inventory system)

is a method for determining level of control and frequency of review of inventory items A - extremely important B - moderately important C - relatively unimportant

The reorder point

is the inventory level at which we place a new order.

Order-cycle service level

is the probability that demand during lead time won't exceed on-hand inventory.

Lead time

is the time between placing an order and receiving it.

To reduce the length of the project (crashing), we need to

know the critical path of the project and the cost of reducing individual activity times. Crashing activities that are not on the critical path typically do not reduce project completion time.

Mean Error (ME) is not often used because of

large positive errors can be offset by large negative errors. However, mean error is useful for checking for bias in the forecasts.

to maximize profit, choose Q such that demand is

less than or equal to Q with a probability that equals the critical ratio

An equation for linear trend can be formulated using

linear regression of the variable of interest against the time period.

Each day QBlitz, a Seattle based startup, offers a single product through its website. The product is available for order only on one day and no other product is available during that day. To add to this odd selling strategy, QBlitz does not post prices for its products. Instead, for each product there is a reserve price. On the day a product is available, customers can submit bids. All of the bids that exceed the reserve price are told at the end of the day that they "won" the product and they pay the price they bid. QBlitz then adds up all of the winning bids and submits an order to a supplier for the needed quantity, which is shipped to customers when the product arrives. The QBlitz system is best described as: make-to-stock. make-to-order. assemble to order. mass customization.

make-to-order. QBlitz submits its order after learning demand. It doesn't assemble the product and customers do not receive unique products.

A project network can be constructed to

model the precedence of the activities. ◦The nodes of the network represent the activities. ◦The arcs of the network reflect the precedence relationships of the activities.

A quick response strategy is a modification of the

newsvendor problem where the company has contracted to place a second order if demand turns out to be high.

Using the exponential smoothing based forecast, is it possible to forecast a demand that is bigger than any previously observed demand? Yes No

no

Using the moving average based forecast, is it possible to forecast a demand that is bigger than any previously observed demand? Yes No

no

products with low demand, could become unprofitable based on what cost

ordering cost

EOQ model balances

ordering costs and holding costs to seek the overall lowest inventory cost

Co =

overage cost

Project Management Triangle

project scope, project time, project budget

To maximize the expected profits, buy the

quantity for which the service level (probability of having demand less than or equal to that quantity) is equal to the critical ratio.

The capacity used in the second order is sometimes called

reactive capacity.

Reduce the coefficient of variation you

reduce mismatched costs

Negative correlation in demand for the individual products is best for

reducing COV

The more periods in a moving averages method, the

smoother the forecast.

Smoothing methods of forecasting are good for

stationary data.

Ordering one more unit increases the chance of overage, but

the benefit/gain of ordering one more unit is the reduction in the chance of underage

The key measure of demand uncertainty is

the coefficient of variation

The project completion time is

the maximum of the ECT.

smoothing parameter

the parameter that determines the weight new realized data have in creating the next forecast with exponential smoothing. this smoothing is called α

The smaller the smoothing constant in exponential smoothing

the smoother the forecast.

lead time for an order is

the time between when an order is placed with the supplier and it is received by the customer

The key objectives of a project are given by: time, scope, and budget. cost, Quality, Location. customers, suppliers, employees. efficiency, effectiveness, and success.

time, scope, and budget.

The intuition behind the MAE metric to evaluate old forecasts is: to sum up the forecast errors. to sum up the squared forecast errors. to sum up the absolute values of the forecast errors. to average the squared forecast errors. to average the absolute values of the forecast errors.

to average the absolute values of the forecast errors.

The intuition behind the MSE metric to evaluate old forecasts is: to sum up the forecast errors. to sum up the squared forecast errors. to sum up the absolute values of the forecast errors. to average the squared forecast errors. to average the absolute values of the forecast errors.

to average the squared forecast errors.

A negative mean error indicates a tendency to forecast

too low.

Newsvendor model based on

tradeoffs of overage and underage costs

time series components

trend cyclical seasonal irregular

Double exponential smoothing is like regular exponential smoothing with the addition of a

trend component.

A start-up has a demand that goes up by 50% each year. This demand increase is multiplicative. True False

true

PERT assumes that non-critical activities will never become critical True False

true

The Critical Ratio tells us the service level we should try to provide. true false

true

The newsvendor problem finds the order quantity where the expected gain from one more unit equals the expected loss. true false

true

All else being equal, a larger item is likely to have a higher annual holding cost percentage than a smaller item. True False

true A larger item requires more storage space, which is costly and this contributes to higher holding costs.

A Items -

typically 20% of the items accounting for 80% of the inventory value-use Q system 70-80% if cash volume, about 10-20% of total items

B Items -

typically an additional 30% of the items accounting for 15% of the inventory value-use Q or P 15-25% of cash volume, 30% of total items

Cu =

underage cost

Product pooling is the creation of a

universal design that replace 2 or more current products thus aggregating their demand into a single product.

Delayed customization is a form of product pooling that

uses an identical base product that is customized later when the demand for the products made from it is known.

The newsvendor model is used when

we have just one time to order and just one selling period.

EOQ occurs where?

where ordering costs and holdings costs cross (or equal each other)

Using the double exponential smoothing based forecast, is it possible to forecast a demand that is bigger than any previously observed demand? Yes No

yes

expected sales from 2nd order =

µ - Expected sales from 1st

Project completion times may need to be shortened because:

◦Different deadlines ◦Penalty clauses ◦Need to put resources on a new project ◦Promised completion dates

Principal methods for crashing

◦Improving existing resources' productivity ◦Changing work methods ◦Increasing the quantity of resources

Forecast Effect of Smoothing Coefficient (a)

◦Most recent data weighted most ◦Weights decline exponentially ◦Weights decline faster with a larger a

what can you forecast

◦Production (How many cars?) ◦Inventory (How many pounds of salmon, octopus, sea weed should I order?) ◦Personnel (How many should report for work this weekend?) ◦Facilities (How many plants should stay open next year?)

Crashing a project needs to balance

◦Shorten a project duration ◦Cost to shorten the project duration

Adjusted total cost equation

〖𝑇𝐶〗_𝑄𝐷=(𝑅/𝑄 𝐾)+(𝑄/2 ℎ)+𝑃𝑅 Same as the EOQ, except: Unit price depends upon the quantity ordered

In"−" stock probability=

𝐹(𝑄)

Expected sales=

𝑄 −Expected inventory

𝐸𝑐𝑜𝑛𝑜𝑚𝑖𝑐 𝑜𝑟𝑑𝑒𝑟 𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦=

𝑄∗=√((2 ×𝐾 ×𝑅)/ℎ)

Demand per day: d =

𝑅/(𝑊𝑜𝑟𝑘𝑖𝑛𝑔 𝑑𝑎𝑦𝑠/𝑌𝑒𝑎𝑟)

Reorder Point=

𝑑∗𝐿

Q=

𝜇+(𝑧 × 𝜎)

Expected inventory=

𝜎×𝐼(𝑧)

C Items -

Typically the remaining 50% of the items accounting for only 5% of the inventory value-use P 5-10% oof cash volume, 50% of total items

A desirable mean error is .

0

If an item costs $50. and the firm assigns a holding cost percentage of 30%, then it costs the firm ________ to hold that item in inventory for an entire year.

0.3 X $50 = $15

Risk of a stockout =

1 - (service level)

Necessary assumptions for EOQ to work

1. Demand rate is uniform and constant at R units per year. 2. Delivery lead time is zero (instant deliveries). 3. Unit purchase (or variable production) cost is unaffected by order size. 4. Annual cost to place orders (or to set-up for production) is proportional to the number of orders (or set-ups) needed. 5. Annual inventory holding cost is proportional to the average inventory level during the year.

Objectives of Inventory Management

1. Provide acceptable level of customer service (on-time delivery) 2. Buffer mismatches between supply and demand 3. Allow cost-efficient operations 4. Minimize inventory investment

Qualitative 1. characteristics 2. Strengths 3. Weakness

1. based on human judgement, opinions; subjective and nonmathmatical 2. can incorporate latest changes in th environments and "inside information" 3. can bias the forecast and reduce forecast accuracy

Quantitative 1. characteristics 2. Strengths 3. Weakness

1. based on mathematics; quantitative in nature 2. Consistent and objective; able to consider much information and data at one time 3. often quantifiable data are not available. Only as good as the data on which they are based

A manufacturing company producing medical devices reported $63 million in sales over the last year. At the end of the same year, the company had $21 million worth of inventory of ready-to-ship devices. Assuming that units in inventory are valued (based on cost of goods sold) at $1250 per unit and are sold for $2250 per unit, what is the company's annual inventory turnover?

1.7 turns COGS = $1250 COGS/unit * 28000.00 units sold * 1,000,000. $63 sales/Turns = $35.0 million COGS / $21 million inventory = 1.7 turns

A police station had to deploy a police officer for an emergency multiple times in the last four evenings. The table below shows the number of emergencies each evening. Weekday Number of calls each day Forecast for tomorrow (calls) 12 Monday 5 Tuesday 2 Wednesday 8 Thursday 13 a. Complete the "Forecast for tomorrow" column in the table above. Use an exponential smoothing forecasting approach, with α=0.1 and a forecast for Monday of 12. b. What would be their forecast for Friday using the same exponential smoothing forecasting approach?

10.420 With the exponential smoothing method, we cannot just forecast for Friday. Instead, we have to start at the beginning and first forecast for Tuesday. We can then, day by day, update our forecast for the next day. This gives us a forecast for Friday: 0.1 × 13 + (1 - 0.1) × 10.133 = 10.420. Each day's forecast follows the same pattern: 0.1*the number of calls that day + (1-0.1*the forecasted number of calls for that day.

A police station had to deploy a police officer for an emergency multiple times in the last four evenings. The table below shows the number of emergencies each evening. Weekday Number of calls each day Monday 6 Tuesday 2 Wednesday 8 Thursday 12 What would be their forecast for Friday using a naïve forecasting approach?

12 The naive forecast for Friday would be 12, as this corresponds to the last observed demand.

A police station had to deploy a police officer for an emergency multiple times in the last four evenings. The table below shows the number of emergencies each evening. Weekday Number of calls each day Monday 5 Tuesday 6 Wednesday 12 Thursday 13 What would be their forecast for the emergencies on Friday using a two-day moving average approach?

12.5 With a two-day moving average, we would forecast the demand for Friday as the average of the demand of Wednesday and Thursday. That would be: Forecast for Friday = (12 + 13) / 2 = 12.5.

Daily demand is 40 units. Lead time is 4 days. What is your reorder point?

160 ?

Stockout probability=

1−In−stock probability

A manufacturer of farm equipment has annual turns of 2, and its Cost of Goods Sold (COGS) is $59 billion. What is the average inventory it holds? (in billion $s)

29.5 b Average inventory = $59 billion COGS / 2 turns = $29.5 billion

Days-of supply =

365 X Inventory/Annual cost of goods sold

Suppose a retailer's annual inventory turns is 8.4. What is its days-of-supply of inventory? (Assume 365 days per year.)

43.5 days Days-of-supply of inventory = 365 days / 8.4 turns = 43.5 days

My App is a small but growing start-up that sees demand for several of its apps increasing quickly. The table below shows the last six months of downloads. Use a forecast for the first month of 240000, an initial trend forecast of 35000, and smoothing parameters of 0.2 for both demand smoothing and trend smoothing. Month (t) Monthly Application Downloads Forecast for Next Month Trend 240,000.00 35,000.00 1 235,000 2 250,010 3 339,000 4 390,000 5 415,000 6 494,000 a. Complete the table above, filling in the "Forecast for next month" and "Trend" columns, using double exponential smoothing. b. Month 7's forecast is:

481,952.30 The "Forecast for next month" column uses the exponential smoothing method with alpha = 0.2. In the Month 1 row, the Forecast(month 2) = 0.2(235000) + (1 - 0.2) (240000) + 35000 = 274000.00; Trend(month2) = 0.2(274000.00 - 240000) + (1 - 0.2) (35000) = 34800.00. In the Month 2 row, the Forecast(month 3) = 0.2(250010) + (1 - 0.2) (274000.00) + 34800.00 = 304002.00; Trend(month 3) = 0.2(304002.00 - 274000.00) + (1 - 0.2) (34800.00) = 33840.40. For the last row, we have a forecast = 0.2 × 494000 + (1 − 0.2) × 431337.78 + 38082.08 = 481952.30

Expected loss on the Qth unit

= Co x F(Q)

Co Formula

= Cost - Salvage value = c - v

Cu formula

= Price - Cost = p - c

coefficient of variation of pooled demand

= √1/2(1+COREELATION)x(σ/µ)

Which are good methods for data with trend? A.Moving Averages B.Regression C.Simple Exponential Smoothing D.Double Exponential Smoothing

??

Choose the true statement A. Exponential smoothing is a qualitative forecasting method. B.The larger the a, the smoother the forecast. C.The value for a is between 0 and 1

?? look at powerpoint

The Gantt Chart

A chart on which project tasks or events are displayed against time. On the left of the chart is a list of the activities and along the top is a suitable time scale. Each activity is represented by a bar; the position and length of the bar reflects the start date, duration and end date of the activity. This allows you to see at a glance: What the various activities are When each activity begins and ends How long each activity is scheduled to last Where activities overlap with other activities, and by how much The start and end date of the whole project

Trend -

A continuing increase or decrease in a variable that is consistent over a long period of time.

Naïve Forecasting Method

A forecasting method that predicts that the next value will be like the last realized value Simple to use Virtually no cost Quick and easy to prepare Data analysis is nonexistent Easily understandable Cannot provide high accuracy But, Can be a standard for accuracy

Moving Average Forecasting Method -

A forecasting method that predicts that the next value will be the average of the most recent observed values. Simple moving averages may mimic some data better than more complicated functions. The average is "moving" because an ever-new average is calculated by adding a more recent time series value to the group and dropping the oldest one.The larger the number of time periods included in the moving

Delayed Customization

A form of product pooling Prepare a stock item and customize it when the order comes in Examples Making 3/2 wetsuits and sewing on the emblem when ordered. Canning fruit or vegetables without labels and putting on labels when a chain orders them. HP Printers - power cord, labels, and correct language manual combined after country of destination is determined.

A retailer has two merchandizers, Sue and Bob, who are responsible for setting order quantities for the products they manage. For all of their products the critical ratio is 0.7 and the coefficient of variation of their demand forecasts are 0.35. At the end of the season, Sue is proud to report that she sold the entire inventory she purchased. Bob, on the other hand, sold out only about a third of his products. Who is more likely to be choosing quantities that maximize expected profit? Sue, because she doesn't incur the cost of salvaging inventory. Sue, because she must have sold more units than Bob. Bob, because even leftover inventory generates some additional revenue. Bob, because he is probably ordering more than the mean of the demand forecast.

Bob, because he is probably ordering more than the mean of the demand forecast.

Which statement is true? Both PERT and CPM use activity networks in their analysis. PERT cannot give an estimate of the project completion time. CPM is preferred when activity times are uncertain (probabilistic.) Only CPM gives an estimate of the slack for non-critical activities.

Both PERT and CPM use activity networks in their analysis.

Similarities between MA and ES

Both methods are appropriate for stationary series Both methods depend on a single parameter Both methods lag behind a trend

Which reason for holding inventory guards against a reduction in the flow rate when one assembly station is disrupted in a production line? Seasonality Uncertain demand Buffers Batching

Buffers

Expected profit -

The expected profit earned from the product, which includes leftover inventory.

Product A's demand is normally distributed with mean 150 and standard deviation 50. Product B's demand is also normally distributed with mean 150 and standard deviation 50. The sum of demand for these two products is normally distributed with a mean of 300 and a standard deviation of 50. Which of the following results is most likely? Demands for these products are negatively correlated Demands for these products are positively correlated Demands for these products are independent It is not possible to determine with this information the correlation of these products.

Demands for these products are negatively correlated If the products were independent then the standard deviation of total demand would be sqrt(2) x 50. Given that the actual standard deviation of total demand, 50, is less than what it would be if the demands were independent, sqrt(2) x 50, the demands must be negatively correlated.

The Purpose of ABC Analysis is to: Gauge the level of literacy in the work force. Reduce the level of inventory. Already Been Counted: indicate which items have been inventoried already. Determine which items in inventory should be monitored with the most intensity.

Determine which items in inventory should be monitored with the most intensity.

Critical Path Method (CPM):

Developed to coordinate maintenance projects in the chemical industry (DuPont, 1957) A complex undertaking, but individual tasks are routine (tasks' duration = deterministic)

Program Evaluation & Review Technique (PERT):

Developed to manage the Polaris missile project (1958) Many tasks pushed the boundaries of science & engineering (tasks' duration = probabilistic)

F(Q) =

Distribution function of demand = Prob{Demand <= Q)

in regards to ops: Why have Inventory? (think flow)

Inventory exists for a number of reasons and in any situation there may be multiple reasons present: Flow time - it takes time to move something from one place to another Seasonality - predictable periods of high or low demand Batching - fixed ordering costs Buffers - to deal with variability within a process Uncertain demand - unpredictable variations in demand Pricing - quantity discounts Production Smoothing Strategy - A strategy for scheduling production such that the rate of output remains relatively stable over time even though demand varies predictably over the same period. Inflation - Holding stock against anticipated increases in prices price fluctuation - build up inventory bc of expected rising profit levels in the future

which of the following is not true about the function distribution for a normal distribution? it ranges from 0 to 1 it increases as the quantity increases it generally has a bell shape when graphed it generally has a bell shape when graphed it returns the probability that the outcome from the normal distribution is a certain quantity or lower

It generally has a bell shape when graphed. The density function has a bell shape, but the distribution function is always increasing, so it never has a bell shape.

A project has four activities that take 4, 3, 6, and 7 days respectively. What is the total completion time for the project? 3 days, as this is the minimum time 7 days, as this is the maximum time 20 days, as this is the sum of the times It is not possible to determine the total completion time from the given information

It is not possible to determine the total completion time from the given information This really depends on the precedence relationships between the activities.

Which of the following is NOT an assumption of the EOQ model? It is possible to receive a purchase discount if the order quantity is sufficiently large. There is a fixed cost to submit each order that is independent of the amount ordered. Demand occurs at a constant rate per unit of time. There is a cost to hold each unit of inventory per unit of time.

It is possible to receive a purchase discount if the order quantity is sufficiently large.

Parameters for EOQ problems

K: ordering or setup cost R: flow rate (demand) h: holding cost, same unit as flow rate (both typically annual) - If initially provided as percentage of purchase/production price, need to convert to $$ Q: represents a particular order quantity

How big is the effect of statistical noise on the naïve forecast? Large Medium Small

Large

What should you do if your supplier offers a discount for large orders

Larger quantities increases the sum of ordering and holding costs (above minimum) but the discount reduces the purchasing cost A very large quantity may be optimal even if the discount appears to be small

Variations of the EOQ Model

Lead time Uncertain lead times Uncertain demand (safety stock) Service levels

Which of the following possible responses by a customer who is faced with a stockout is the most costly to the firm? Lose the sale and lose the customer Lose the sale Lose the sale of one item, but the customer purchases another item Customer waits for the item to become available

Lose the sale and lose the customer

Order Quantity Strategies

Lot-for-lot Fixed-order quantity (EOQ) Min-max system Order n periods

A firm evaluates its EOQ quantity to equal 180 cases but it chooses an order quantity of 200 cases. Relative to the order quantity of 180 cases, the order quantity of 200 cases has: Higher ordering cost and higher holding cost Higher ordering cost and lower holding cost Lower ordering cost and higher holding cost Lower ordering cost and lower holding cost

Lower ordering cost and higher holding cost The ordering cost decreases with the order quantity and the holding cost increases with the order quantity.

Mean Error

ME is not often used because of large positive errors can be offset by large negative errors. However, mean error is useful for checking for bias in the forecasts.

Independent -

Two events are independent (Their correlation is 0) when the outcome of one event has no relationship to the outcome of the other event

Sarah is a buyer for department store. A supplier offers her a 5% discount if she triples her usual order quantity. Which of the following best explains why Sarah should take the deal? Even though the increase in the operating costs is likely to exceed the benefit of the 5% discount, Sarah feels that her customers expect the lowest possible price. Sarah hopes that customers are likely to purchase more if they see an increase in the inventory in the store. Sarah knows that even though she may triple her order quantity, this would increase her operating costs by far less than a factor of three. Sarah knows that the sum of operating costs is probably less than 5% of the purchase cost, so an increase in the operating cost is unlikely to be a concern.

Sarah knows that even though she may triple her order quantity, this would increase her operating costs by far less than a factor of three. Choice A suggests that the store would lose money on the deal, which is not a good justification for the deal. Choice B is too speculative. Choice D is incorrect - even if operating costs are small relative to the purchase cost, they should not be ignored. Choice C is correct - large changes in the order quantity generally do not create large changes in operating costs.

Setup costs

Set-up costs [per unit of time]= Set-up cost / length of order cycle (KxR/Q)

Types of Forecasts by Time Horizon

Short-range forecast ◦Up to 1 year; usually < 3 months ◦Job scheduling, worker assignments ◦(What do we forecast to make cambus driver shift schedules? office petty cash level?) Medium-range forecast ◦3 months to 3 years ◦Sales & production planning, budgeting ◦(State's K1-K12 teacher salary budget?) Long-range forecast ◦3+ years ◦New product planning, facility location ◦(Develop new prostate cancer drug?)

Days-of-supply =

T = Flow time

Which statement is true? Ordering costs are more important than holding costs. Holding costs are more important than ordering costs. Purchase costs have a large impact on the quantity ordered an in EOQ system. The EOQ model can used to determine the best batch size.

The EOQ model can used to determine the best batch size. not sure

Slack time -

The amount of time an activity can be delayed without affecting the overall completion time of the project.

Activity time -

The amount of time it takes a resource to complete the activity once it has started to work on it. The concept of an activity time is the same as the processing time in a process analysis.

A company has an unbiased forecast for their demand. What does that mean? All forecast errors are equal to zero All forecast errors are less than 1% The average of all forecast errors is zero The standard deviation of forecast errors is zero

The average of all forecast errors is zero

The Newsvendor Model represents one of the canonical (recognized) challenges faced in operations:

The combination of uncertain demand with inflexible supply. Choses an order quantity that either fails to satisfy all demand or leaves some units left over Can make smart tradeoffs too much (overage) - too little (underage)

Obsolescence -

The cost associated with losing value over time because of either technological change or shifts in fashion.

Inventory Storage Cost -

The cost incurred to properly store, maintain, and insure inventory.

underage cost

The cost of ordering one fewer unit than what you would have ordered had you known demand. In other words, suppose you had lost sales (i.e., you under ordered). Cu is the increase in profit you would have enjoyed had you ordered one more unit.

overage cost

The cost of ordering one more unit than what you would have ordered had you known demand. In other words, suppose you had left over inventory (i.e., you over ordered). Co is the increase in profit you would have enjoyed had you ordered one fewer unit.

The Gantt Chart is useful for identifying

The critical path Important deficiencies Slack time

Precedence relationship -

The dependency of activities on each other.

Earliest completion time (ECT) -

The earliest time an activity can be completed, which is given by the earliest time all predecessor activities have been completed plus the activity time. ECT(A_𝑖 )=EST(A_𝑖 )+Activity time〖(A〗_𝑖)

Seasonality Index (SI)

The estimated multiplicative adjustment factor that allows us to move from the average overall demand to the average demand for a particular season.

Stockout -

The event in which one or more customers are unable to purchase a unit because inventory was not available

Expected inventory -

The expected number of units not sold at the end of the season and that are therefore salvaged.

Expected sales -

The expected number of units sold during the season at the regular price.

Consider two products A and B that have identical cost, retail price and demand parameters and the same short selling season (the summer months from May through August). The newsvendor model is used to manage inventory for both products. Product A is to be discontinued at the end of the season this year, and the leftover inventory will be salvaged at 75% of the cost. Product B will be re-offered next summer, so any leftovers this year can be carried over to the next year while incurring a holding cost on each unit left over equal to 20% of the product's cost. The quantity of each product is selected to maximize expected profit. How do those quantities compare? The quantity of product A is higher. The quantity of product B is higher. The quantities are equal. The answer cannot be determined from the data provided.

The quantity of product B is higher. The salvage value of product A is 75% of its cost. The overage cost, Co, is the difference between product A's cost and its salvage value, which is then 100% - 75% = 25% of cost. Product B's overage cost is 20% of its cost. Both products have the same underage cost, Cu, so product A has the higher overage cost, which means it has the lower critical ratio, Cu / (Co + Cu). Given they have the same demand distribution, product A's optimal order quantity must be lower, or product B's stocking quantity is higher.

Holding Cost Percentage -

The ratio of the cost to hold an item in inventory during a designated time period relative to the cost to purchase the item

A change in which of the following results in a change in the maximum profit in a newsvendor setting? The revenue received from salvaging inventory The regular selling price of the product The standard deviation of the demand forecast The coefficient of variation of the demand forecast

The regular selling price of the product The maximum profit depends on the profit earned per unit and the mean of the demand forecast. The profit earned per unit depends on the selling price.

Product pooling -

The strategy to reduce the variety offered to customers by combining, or pooling, similar products

A company uses the newsvendor model to manage its inventories and faces normally distributed demand with a coefficient of variation = 0.75. The company decides to order a quantity that exactly equals the mean of its demand forecast. Which of the following is true regarding this company's performance measures? There is a 0.50 probability that there is enough inventory to serve all demand. Expected inventory equals 50% of the mean of the demand forecast The stockout probability is 0.25. Expected inventory is 0

There is a 0.50 probability that there is enough inventory to serve all demand. If the mean of the demand forecast is ordered and demand is normally distributed, then there is a 0.50 probability that all demand is served because there is a 0.50 probability that demand is less than the mean of the forecast.

Vetox sells industrial chemicals and one of their inputs can be purchased either in jugs or barrels. A jug contains 1 gallon while a barrel contains 55 gallons. The price per gallon is the same with either container. Vetox is charged a fixed amount per order whether they purchase using jugs or barrels. The inventory holding cost per gallon per month is the same with either jugs or barrels. Vetox chooses an order quantity to minimize ordering and holding costs per year. Would Vetox purchase a greater number of gallons with each order if they purchase with jugs or if they purchase with barrels? With barrels They would order the same number of gallons with either container With jugs They might order a greater number of gallons with jugs or with barrels, depending on various factors like the demand rate, ordering cost and holding cost.

They might order a greater number of gallons with jugs or with barrels, depending on various factors like the demand rate, ordering cost and holding cost. Vetox is likely to be able to order close to the EOQ with jugs. With barrels, Vetox should order close to the EOQ, but might order more or less than the EOQ. Hence, it is not possible to determine whether it orders more with jugs or with barrels.

Which is not a reason to have inventory? To level production for anticipated increases in demand. To increase the utilization of expensive machines. To qualify for a quantity discount on an order. All are reasons to hold inventory.

To increase the utilization of expensive machines.

Reseasonalize -

To reduce the seasonal effect to the forecasted data

Deseasonalizing a Series

To remove seasonality from a series, simply divide each observation in the series by the appropriate seasonal factor. The resulting series will have no seasonality and may then be predicted using an appropriate method. Once a forecast is made on the deseasonalized series, one then multiplies that forecast by the appropriate seasonal factor to obtain a forecast for the original series.

Deseasonalize -

To remove the seasonal effect from the past.

Continuous Inventory Review Systems

Track each item and update inventory counts each time an item is removed from inventory Order Q items when inventory reaches the reorder point, r. Real-time updates of inventory counts Facilitates accurate accounting Higher cost of implementation -- bar code scanners, inventory software and computer systems are all necessary to maintain perpetual (continuous) inventory review.

The newsvendor problems seeks to find the quantity where the expected gain from Qth unit equals the expected loss from it. true false

True

If two firms have the same annual inventory turns, they also have the same days-of-supply. True False

True If two firms have the same annual inventory turns, then they have the same years-of-supply because years-of-supply = 1 / annual inventory turns. If they have the same years-of-supply, then they must have the same days-of-supply as well because Days-of-supply = Years-of-supply × 365.

Suppose the newsvendor model describes a firm's operations decision. Is it possible to have positive stockout probability and positive expected leftover inventory? Choose the best answer. No - if there is left over inventory then a stockout doesn't occur. No - if the stockout probability is positive, then expected inventory must be negative. No - actual demand can differ from sales. Yes - a firm does not stockout and have leftover inventory at the same time, but the stockout probability can be positive even though there is positive expected leftover inventory. Yes - as long as the underage cost is greater than the overage cost.

Yes - a firm does not stockout and have leftover inventory at the same time, but the stockout probability can be positive even though there is positive expected leftover inventory. It is not possible to stockout and have leftover inventory at the same time, but either one is possible, which is why there is a positive probability of a stockout and a positive expectation for leftover inventory.

Millennium Liquors is a wholesaler of sparkling wines. Their most popular product is the French Bete Noire which is shipped directly from France. Weekly demand is for 40 cases. Millennium purchases each case for $125, there is a $300 fixed cost for each order (independent of the quantity ordered) and their annual holding cost is 15 percent. a. What order quantity minimizes Millennium's annual ordering and holding costs? b. If Millennium chooses to order 300 cases each time, what is the sum of their annual ordering and holding costs? c. If Millennium chooses to order 100 cases each time, what is the sum of the ordering and holding costs incurred by each case sold? d. If Millennium is restricted to order in multiples of 50 cases (e.g., 50, 100, 150, etc.) how many cases should they order to minimize their annual ordering and holding costs? e. Millennium is offered a 5.00% discount if they purchase at least 1,000 cases. If they decide to take advantage of this discount, what is the sum of their annual ordering and holding costs?

a. 257.99. Sqrt (2 × 300 × 2080) / (125 × 0.15) = 257.99 b. 4892.50. Orders per year = 2080 annual cases / 300 = 6.93 orders. Annual order cost = 6.93 × $300 = $2080.00. Annual holding cost = .5 (300 × 125 × 0.15) = $2812.50. c. 3.45. Orders per year = 2080 annual cases / 100 = 20.80 orders. Annual order cost = 20.80 × $300 = $6240.00. Annual holding cost = .5 (100 × 125 × 0.15) = $937.50. Annual order + holding costs = 6240.00 + 937.50 = $7177.50. Annual order + holding costs per case = $7177.50 / 2080 cases = $3.45 d. 250. The order size of 250 is the quantity that is the multiple of 50 that leads to the lowest cost. e. $9530.25. Orders per year = 2080 annual cases / 1000 = 2.08 orders. Annual order cost = 2.08 × $300 = $624.00. Annual holding cost = .5 (1000× 118.75 × 0.15) = $8906.25. Annual order + holding costs = 624.00 + 8906.25 = $9530.25.

Bruno Fruscalzo decided to start a small production facility in Sydney to sell gelato to the local restaurants. His local milk supplier charges $0.50 per kg of milk plus a $15 delivery fee (that is independent of the amount ordered). Bruno's holding cost is $0.03 per kg per month. He needs 9250 kgs of milk per month. a. Suppose Bruno orders 9750 kgs each time. What is his average inventory (kgs)? b. Suppose Bruno orders 6250 kgs each time. How many orders does he place with his supplier each year? c. How many kgs should Bruno order from his supplier with each order to minimize the sum of ordering and holding costs? d. If Bruno's storage vessel can hold only 2000 kgs of milk, what would be Bruno's annual ordering and holding costs? e. If Bruno's storage vessel can hold only 5750 kgs of milk, what would be Bruno's annual ordering and holding costs? f. Bruno's supplier's truck can carry 20,000 kgs of milk. The supplier does not want to deliver to more than 3 customers with each truck. Thus, the supplier requires a minimum order quantity of 6,500 kgs. If Bruno orders the minimum amount, what would be the sum of his annual ordering and holding costs? Assume he has a storage vessel large enough to hold 6,500 kgs. g. Bruno's supplier offers a 4.00% discount when a customer orders a full truck, which is 20,000 kgs. Assume Bruno can store that quantity and the product will not spoil. If Bruno orders a full truck, what would be the inventory holding and ordering cost incurred per kg of milk?

a. 4875.00. Average inventory = 9750 / 2 = 4875.00. b. 17.76. Annual orders = (9250 per month × 12) / 6250 per order = 17.76 orders c. 3041.38. EOQ = Sqrt (2 × 15 order cost × 9250 monthly demand × 12) / (0.03 holding cost per month × 12) = 3041.38 d. $1192.50. Annual order cost = (9250 × 12)/2000) orders × $15 = $832.50. Annual holding cost = .5 (2000 × 0.03 × 12) = $360.00 832.50 Annual order + 360.00 holding costs = 1192.50 e. $1324.57. Annual order cost = (9250 × 12)/5750) orders × $15 = $289.57. Annual holding cost = .5 (5750 × 0.03 × 12) = $1035.00 289.57 Annual order + 1035.00 holding costs = 1324.57 f. $1426.15. Annual order cost = (9250 × 12)/6500) orders × $15 = $256.15. Annual holding cost = .5 (6500 × 0.03 × 12) = $1170.00 256.15 Annual order + 1170.00 holding costs = 1426.15 g. 3539.25/111000=0.032

Teddy Bower is an outdoor clothing and accessories chain that purchases a line of parkas at $9 each from its Asian supplier, TeddySports. Unfortunately, at the time of order placement, demand is still uncertain: Teddy Bower forecasts that its demand is normally distributed with mean 2200 and standard deviation 1500. Teddy Bower sells these parkas at $23 each. Unsold parkas have little salvage value; Teddy Bower simply gives them away to a charity (and also doesn't collect a tax benefit for the donation). What is the probability this parka turns out to be a "dog", defined as a product that sells less than half of the forecast? Use Excel. (Round your answer to 4 decimal places.) b. How many parkas should Teddy Bower buy from TeddySports to maximize expected profit? Use Table 13.4. c. If Teddy Bower orders 2750 parkas, what is the in-stock probability? Use Excel. (Round your answer to 4 decimal places.) d. If Teddy Bower orders 2750 parkas, what is expected leftover inventory? Use Excel. (Round your answer to 2 decimal places.) e. If Teddy Bower orders 2750 parkas, what is expected sales? Use Excel. (Round your answer to 2 decimal places.) f. If Teddy Bower orders 2750 parkas, what is expected profit? Use Excel. (Round your answer to 2 decimal places.) g. How many parkas should Teddy Bower order to ensure a 98.5% in-stock probability? how many parkas should Teddy Bower's order? Use Table 13.4.

a. 50% of the mean forecast is 1100 units. This corresponds to z = (1100 - 2200)/1500 = -0.7333. Using Excel, F(-0.7333) = 0.2317. b. We have Cu = 23 - 9 = 14 and Co = 9 - 0 = 9. This gives the critical ratio of 14/(14 + 9) = 0.6087. Using Table 13.4 and the round-up rule, this corresponds to z = 0.3. The optimal order quantity is 2200 + 0.3 × 1500 = 2650. c. An order quantity of 2750 corresponds to z = (2750 - 2200)/1500 = 0.37. Using Excel, the in-stock probability is F(0.37) = 0.6431. d. An order quantity of 2750 corresponds to z = (2750 - 2200)/1500 = 0.37. Using Table 13.4 and the round-up rule, we have that the expected left-over inventory = 0.6304*1500 = 945.60. e. If the order quantity is 2750, the expected inventory (from question 28) is 945.60. The expected sales are 2750 - 945.60 = 1804.40 f. Using the answers from the previous questions, the expected profit when the order quantity is 2750 is 14 × 1804.40 - 9 × 945.60 = 16751.20. g. According to Table 13.4, a 98.5% in-stock probability requires z = 2.2. This yields an order quantity of 2200 + 2.2 × 1500 = 5500.

Joe Birra needs to purchase malt for his micro-brew production. His supplier charges $35 per delivery (no matter how much is delivered) and $1.25 per gallon. Joe's annual holding cost is 30% of the price per gallon. Joe uses 225 gallons of malt per week. a. Suppose Joe orders 1000 gallons each time. What is his average inventory? b. Suppose Joe orders 1750 gallons each time. How many orders does he place with his supplier each year? c. How many gallons should Joe order from his supplier with each order to minimize the sum of ordering and holding costs? d. Suppose Joe orders 2500 gallons each time he places an order with the supplier. What is the sum of ordering and holding costs per gallon? e. Suppose Joe orders the quantity from part (c) that minimizes the sum of the ordering and holding costs each time he places an order with the supplier. What is the annual cost of the EOQ expressed as a percentage of the annual purchase cost? f. If Joe's supplier only accepts orders that are an integer multiple of 1,000 gallons, how much should Joe order to minimize ordering and holding costs per gallon? g. Joe's supplier offers a 3.00% discount if Joe is willing to purchase 8000 gallons or more. What would Joe's total annual cost (purchasing, ordering and holding) be if he were to take advantage of the discount?

a. 500.00. Average inventory = 1000 × .5 = 500.00 b. 6.69. Orders = (225 per week × 52 weeks) / 1750 = 6.69 c. 1477.84. Order size = Sqrt (2 × 35 × 225 × 52) / (1.25 × 0.3) = 1477.84 d. $0.054. (225 per week × 52 weeks) / 2500 = 4.68 orders. Annual order cost = 4.68 × $35 = $163.80. Annual holding cost = .5 (2500 × 1.25× 0.3 ) = $468.75. Annual order + holding costs = 163.80 + 468.75 = $632.55. (Annual order + holding costs) / annual demand = cost per gallon. $632.55/ 11700 = $0.054 e. 3.79%. (225 per week × 52 weeks) / 1477.84 = 7.92 orders. Annual order cost = 7.92 × $35 = $277.09. Annual holding cost = .5 (1477.84 × 1.25 × 0.3) = $277.09. Annual order + holding costs = 277.09 + 277.09 = $554.19. Annual purchase cost = $1.25 × 11700 = $14625.00. $554.19 Annual order + holding costs / $14625.00 = 3.79% f. 2000. From part c the EOQ = 1477.84. For 1000 order quantity, Annual order cost = 11.70 orders × $35 = $409.50. Annual holding cost = .5 (1000 × 1.25 × 0.3) = $187.50. Annual order + holding costs = 409.50 + 187.50 = $597.00. For 2000 order quantity, Annual order cost = 5.85 orders × $35 = $204.75. Annual holding cost = .5 (2000 × 1.25 × 0.3) = $375.00. Annual order + holding costs = 204.75 + 375.00 = $579.75. An order size of 2000 has the lowest annual order + holding costs. g. 15692.44. For 8000 order quantity, Annual order cost = (11700/8000) orders × $35 = $51.19. Annual holding cost = .5 (8000 × 1.21 × 0.3) = $1455.00. Annual order + holding costs + purchasing cost = 51.19 + 1455.00 + 14186.25 = $15692.44.

Sarah's Organic Soap Company makes organic liquid soap. One of the raw materials for her soaps is organic palm oil. She needs 1500 kgs of palm oil per day on average. The supplier charges a $53 delivery fee per order (which is independent of the order size) and $4.5 per kg. Sarah's annual holding cost is 20%. Assume she operates and sells 5 days per week, 52 weeks per year. a. If Sarah wants to minimize her annual ordering and inventory holding costs, how much palm oil should she purchase with each order (in kgs)? b. If Sarah orders 3500 kgs with each order, what would be the annual sum of ordering and holding costs? c. If Sarah orders 7800 kgs with each order, what would be sum of ordering and holding costs per kg sold? d. Sarah's supplier is willing to sell her palm oil at a 5% discount if she purchases 15,000 kgs at a time. If she were to purchase 15,000 kgs per order what would be her annual sum of ordering and holding costs?

a. 6777.41. Order size = Sqrt (2 × 53 × 390000) / (4.5 × 0.2) = 6777.41 b. $7480.71. Orders per year = 390000 annual kgs / 3500 = 111.43 orders. Annual order cost = 111.43 × $53 = $5905.71. Annual holding cost = .5 (3500 × 4.5 × 0.2) = $1575.00 Annual order + holding costs = 5905.71 + 1575.00 = $7480.71 c. $0.016. Orders per year = 390000 annual kgs / 7800 = 50.00 orders. Annual order cost = 50.00 × $53 = $2650.00. Annual holding cost = .5 (7800 × 4.5 × 0.2) = $3510.00 Annual order + holding costs = 2650.00 + 3510.00 = $6160.00. Annual order + holding costs per kgs = $6160.00 / 390000 kgs = $0.016 d. $7790.50. Orders per year = 390000 annual kgs / 15000 = 26.00 orders. Annual order cost = 26.00 × $53 = $1378.00. Annual holding cost = .5 (15000 × 4.28 × 0.2) = $6412.50. Annual order + holding costs = 1378.00 + 6412.50 = $7790.50.

CPG Bagels starts the day with a large production run of bagels. Throughout the morning additional bagels are produced as needed. The last bake is completed at 3 pm, and the store closes at 8 pm. It costs approximately $0.20 in materials and labor to make a bagel. The price of a fresh bagel is $0.55. Bagels not sold by the end of the previous day are sold the next day as "day-old" bagels in bags of six, for $0.99 a bag. About two-thirds of the day-old bagels are sold, the remainder are just thrown away. There are many bagel flavors, but for simplicity, concentrate just on the plain bagels. The store manager predicts that demand for plain bagels from 3 pm until closing is normally distributed with mean 54 and standard deviation 25. How many bagels should the store have at 3 pm to maximize the store's expected profit (from sales between 3 pm until closing)? (Hint: Assume day-old bagels are sold for $0.99/6 = $0.165 each, i.e., don't worry about the fact that day-old bagels are sold in bags of six.) Use Table 13.4 and round-up rule. b. Suppose the store manager has 100 bagels at 3 pm. How many bagels should the store manager expect to have at the end of the day? Use Table 13.4 and round-up rule. (Round your answer to a whole number.) c. Suppose the manager would like to have a 0.99 in-stock probability on demand that occurs after 3 pm. How many bagels should the store have at 3 p.m. to ensure that level of service? Use Table 13.4 and round-up rule.

a. The salvage value per bagel is 0.99/6 = 0.165, but only two-third of the bagels are sold. This yields an effective salvage value of 0.165 × 2/3 = 0.11. We have Cu = 0.55 - 0.20 = 0.35 and Co = 0.20 - 0.11 = 0.09. This gives the critical ratio of 0.35/(0.35 + 0.09) = 0.80. Using Table 13.4 and the round-up rule, this corresponds to z = 0.90. The optimal order quantity is 54 + 0.90 × 25 = 76.50. b. An order quantity of 100 corresponds to z = (100- 54)/ 25 = 1.84. Using Table 13.4 and the round-up rule, the expected inventory is 1.91 × 25 = 48. c. Using Table 13.4 and the round-up rule, we see that a 0.99 in-stock probability requires z = 2.4. The order quantity is 54 + 2.4 × 25 = 114.

The Kiosk sells spicy black bean burritos during the weekday lunch hour. The Kiosk charges $4.00 for each burrito and all burritos are made before the lunch crowd arrives. Virtually all burrito customers also buy a soda that is sold for 65¢. The burritos cost the Kiosk $1.75 while sodas cost the Kiosk 5¢. Kiosk management is very sensitive about the quality of food they serve. Thus, they maintain a strict "No Old Burrito" policy, so any burrito left at the end of the day is disposed of. Table 13.9 gives the distribution function of demand for the burrito. a. Suppose burrito customers buy their snack somewhere else if the Kiosk is out of stock. How many burritos should the Kiosk make for the lunch crowd? Use Table 13.9 and round-up rule. b. Suppose the Kiosk makes 24 burritos. How many burritos should they expect to discard at the end of the day? Use Table 13.9. (Round your answer to 2 decimal places.) c. Suppose the Kiosk makes 24 burritos. How many burritos should they expect to sell? Use Table 13.9. (Round your answer to 2 decimal places.) d. Suppose the Kiosk makes 24 burritos. What is the Kiosk's expected profit, including the profit from the sale of sodas? (Round your answer to 2 decimal places.) e. Suppose the Kiosk makes 32 burritos. What is the probability that some customer is unable to purchase a burrito? (Round your answer to 4 decimal places.) f. If the Kiosk wants to be sure that they have inventory for their customers with at least a 0.975 probability, how many burritos should they make? Use Table 13.9 and round-up rule. g. Suppose that any customer unable to purchase a burrito settles for a lunch of Pop-Tarts and a soda. Pop-Tarts sell for 80¢ and cost the Kiosk 25¢. (As Pop-Tarts and soda are easily stored, the Kiosk never runs out of these essentials.) Assuming that the Kiosk management is interested in maximizing profits, how many burritos should they make? Use Table 13.9 and round-up rule.

a. We have Cu = (4.00 + 0.65) - (1.75 + 0.05) = 2.85 and Co = (1.75 + 0.05) - 0.05 = 1.75. This assumes that the soda maintains its value if the burrito is not sold; otherwise. This gives the critical ratio of 2.85/(2.85 + 1.75) = 0.6196. Using Table 13.9 and the round-up rule, this corresponds to q=19. b. From Table 13.9, we have I(24) = 6.18. c. From Table 13.9, we have I(24) = 6.18. The expected sales is 24 - 6.18 = 17.82. d. From the previous two questions, the expected inventory is 6.18 and the expected sales are 17.82. The expected profit is 2.85 × 17.82 - 1.75 × 6.18 = 39.97. e. From Table 13.9, we have F(32) = -1.0000. The probability that a customer cannot purchase a burrito is 1 - F(32) = 2.0000. f. From Table 13.9 and the round-up rule, the order quantity that will achieve at least a 0.975 in-stock probability is 27. g. The kiosk makes a profit of $0.55 on each Pop Tart and $0.60 on each soda. This represents a profit of $1.15. We still have Co = (1.75 + 0.05) - 0.05 = 1.75, but now Cu = 2.85 - 1.15 = 1.70. The critical ratio is 1.70/(1.70 + 1.75) = 0.4928. From Table 13.9 and the round-up rule, this yields a quantity of 18.

To ensure a full line of outdoor clothing and accessories, the marketing department at Teddy Bower insists that they also sell waterproof hunting boots. Unfortunately, Teddy Bower does not have expertise in manufacturing those kinds of boots. Hence, Teddy Bower contacted several Taiwanese suppliers to request quotes. Due to competition, Teddy Bower knows that it cannot sell these boots for more than $52. However, $44 per boot was the best quote from the suppliers. In addition, Teddy Bower anticipates excess inventory will need to be sold off at a 40% discount at the end of the season. Given the $52 price, Teddy Bower's demand forecast is for 450 boots, with a standard deviation of 276. If Teddy Bower decides to include these boots in its assortment, how many boots should Teddy Bower order from the supplier? Use Table 13.4. b. Suppose Teddy Bower orders 360 boots. What is Teddy Bower's expected profit? Use Table 13.4. (Round your answer to 2 decimal places.) c. The marketing department insists that their in-stock probability be at least 98%. Given this mandate, how many boots do they need to order? Use Table 13.4. d. John Briggs, a buyer in the procurement department, overheard at lunch a discussion of the "boot problem". He suggested that Teddy Bower ask for a quantity discount from the supplier. After following up on his suggestion, the supplier responded that Teddy Bower could get a 12% discount if they were willing to order at least 775 boots. If the objective is to maximize expected profit, how many boots should Teddy Bower order given this new offer?

a. We have Cu = 52 - 44 = 8 and Co = 44 - 20.80 = 23.2. This gives the critical ratio of 8/(8+23.2) = 0.2564. Using Table 13.4 and the round-up rule, this corresponds to z = -0.60. The optimal order quantity is 450 + -0.60 × 276 = 284.40. b. An order quantity of 360 corresponds to z = (360 - 450)/276 = -0.33. Using Table 13.4 and the round-up rule, we have that the expected left-over inventory = 0.27 × 276 = 73.64. The expected sales are 360 - 73.64 = 286.36. The expected profit is 8 × 286.36 - 23.2 × 73.64 = 582.53. c. According to Table 13.4, a 98% in-stock probability requires z = 2.1. This yields an order quantity of 450 + 2.1 × 276 = 1029.6. d. In part a, we determined that the optimal order quantity was 284.40 from z = -0.60. Using Table 13.4, we have that the expected left-over inventory = 0.1687 × 276 = 46.56. The expected sales are 284.40 - 46.56 = 237.84. The expected profit is 237.84 × 8 - 46.56 × 23.2 = 822.49. If we order 775 units, the discounted price will be 40 ×(1 - 12%) = 38.72. The order quantity of 775 corresponds to z = (775 - 450)/276 = 1.18. Using Table 13.4 and the round-up rule, we have that the expected inventory = 1.26 × 276 = 346.68. The expected sales are then 775 - 346.68 = 428.32. The expected profit is then 428.32 × 8 - 346.68 × 8 = -524.53. Therefore, ordering 284.40 will maximize expected profit..

A seasonal index tells us how a season (period) differs on average from the overall average. A.True B.False

a. true

The basic idea behind the EOQ is that

as order size (batch size) increases - the number of orders per time period decreases, while - average on hand inventory increases.

Dan McClure owns a thriving independent bookstore in artsy New Hope, Pennsylvania. He must decide how many copies to order of a new book, Power and Self Destruction, an exposé on a famous politician's lurid affairs. Interest in the book will be intense at first and then fizzle quickly as attention turns to other celebrities. The book's retail price is $18, and the wholesale price is $13. The publisher will buy-back the retailer's leftover copies at a full refund, but McClure Books incurs $5 in shipping and handling costs for each book returned to the publisher. Dan believes his demand forecast can be represented by a Normal distribution with mean 150 and standard deviation 80. b. Dan will consider a book a "dog" if it sells less than 50% of his mean forecast. Using Excel, calculate the probability that this expose will be a dog. c. Use Table 13.4 to determine the probability that demand for this book will be within 20% of the mean forecast. h. Suppose Dan orders 300 copies of the book. What is Dan's expected profit? Do not round intermediate calculations.

b. The book is a "dog" if it sells less than 75 copies. We compute z = (75 -150)/80 = -.9375. Using Excel, F(-.9375) = 0.1743. c. If demand for the book is within 20% of the mean forecast, it would be between 120 and 180 copies. The z-score for 120 copies is -0.38 and for 180 is 0.38. Using Table 13.4 to calculate F(0.38) - F(-0.38) = 0.6554 - 0.3821 = 0.2733 h. Using the answers from questions f and g, the expected profit when the order quantity is 300 is 147.11 × 5 - 5 × 152.89= -28.88.

Actual profits depend upon

both the order level, Q, and the actual demand, D. Since we cannot choose D, we cannot maximize actual profits