MGT 302 Mod 7

Managing the stock of groceries at home and replenishing it on-demand is analogous to the inventory models we have learned. Assuming the fixed-order quantity model is adopted. Under which of the following instance, will you decrease the order size? (Note: Comparing before and after each instance described below, your annual demand for the grocery items does not change.) -You purchase a new refrigerator to stock your groceries. This new and powerful refrigerator allows you to keep the groceries fresh for a longer period. -Compared to your shopping habit in the past, recently you are more inclined to choose groceries of best deals over those of premium quality. (Note: No matter what type of groceries you purchase, for instance, grapes of high quality vs grapes of best deals, your overall annual demand will not change.) -You purchase the online membership which waives your shipping fee for the orders you place. -Thanks to the neighborhood watch program, burglaries in your neighborhood decrease. The reports on a variety of stolen household stuff including groceries are significantly reduced.

You purchase the online membership which waives your shipping fee for the orders you place. (this scenario suggests a decrease in ordering cost per order; this question focuses on the factors that will affect the EOQ value)

Single-Period Inventory Model

a model used for a one-time purchasing decision where the order quantity (Q) is designed to cover demand over a fixed period of time and the item will not be re-ordered; demand is random and characterized using a probability distribution (ex: vendor purchasing today's newspaper to sell)

Inventory

a stock of material used to facilitate production or to satisfy customer demands

Fixed-Order Quantity Models (Q-Model)

continually review the stock position (on-hand + on-order - backordered quantities); when the stock position drops to the reorder point R, a fixed quantity Q is ordered; order quantity is fixed and event triggered ordering; aka continuous review system

Shortage Costs

cost of running out of inventory; includes stockout costs and backorder costs

Holding (Carrying Costs)

cost of storage facility, handling, insurance, obsolescence, depreciation, pilferage, etc..; the opportunity cost of capital

Independent demand

demand for various items are unrelated to each other, set by market conditions, requires forecasting to estimate the demand (ex: the demand of finished goods inventory)

Stockout Costs

demand is not met and the order is cancelled

Multi-Period Inventory Models

demand is ongoing, multiple purchases, and inventory is kept in stock; designed to ensure that an item will be available on an ongoing basis throughout the year and the items will be ordered multiple times throughout the year (ex: grocery shopping)

Critical Ratio

indicates when the optimal stocking Q is adopted; likelihood of not running out of inventory (i.e. service level); probability that the demand is less than Q

Safety stock size affects the order _________ not the order __________.

interval, quantity

Ordering Costs

managerial and clerical costs to prepare the purchase or production order

Backorder Costs

order is filled at a later date

Inventory Models for Independent Demand

policies that determine (1) when and (2) how much inventory should be replenished

In a Fixed-Order Quantity Model, order _______ is fixed and in a Fixed-Time Period Model, order _______ is fixed.

quantity, interval

Manufacturing inventory

raw material, component parts, supplies, work-in-process, finished products

What is theta 0 in the safety stock (ss) formula?

represents standard deviation of daily demand

Fixed-Time Period Model (P-Model)

review the stock position (on-hand + on-order - backordered quantity) only at fixed periodic review intervals T. An amount equal to target inventory minus the stock position is ordered at each review; order interval is fixed and time triggered ordering; aka periodic review system.

What is theta L in the safety stock (ss) formula?

standard deviation of demand during the lead time

Safety Stock

the amount of inventory carried in addition to the expected demand during the lead time/vulnerable period (i.e. mean lead time demand)

Economic Order Quantity (EOQ)

the ideal/optimal order quantity Q a company should purchase to minimize inventory costs (total cost equation) such as holding costs, shortage costs, and ordering costs; occurs where total costs are at their minimum

Dependent Demand

the need for any one item is a direct result of the need for some other items, not independently determined by the market, calculate demand instead of forecasting it (ex: the demand of WIP and raw material inventory)

Distribution inventory

warehouse, retail store, in-transit

What is z in the safety stock (ss) formula?

z is the # of standard deviations for a specified desired service level

Which of the following is NOT a good reason to hold inventory? -To build a bank of finished goods to protect customers from a potential strike at your plant. -As needed to improve company cash flow. -As needed to shift from one raw material supplier to another. -To buy ahead in anticipation of significant raw material price increases.

As needed to improve company cash flow.

Which of the following statement(s) is correct? I: In the previous example, the vulnerable period (the period during which stock out may occur) is going to be 25 days. II: In the previous example, if a fixed-order quantity model is adopted, the vulnerable period will become shorter.

Both I and II are correct.

True or False: In a single-period inventory model, the critical ratio value indicates the probability of stockout when the order size is set to be the optimal order quantity.

False

True or False: In inventory models, high holding costs tend to favor high inventory levels.

False

True or False: The fixed-time period inventory system has a smaller average inventory than the fixed-order quantity system.

False

Which multi-period inventory system is used for high-priced, critical or important items? Optimal-cost Fixed-time period Fixed-order quantity Single-period

Fixed-order quantity

Name the two types of Multi-Period Inventory Models:

Fixed-order quantity model (Q model) Fixed-time period model (P model)

What are the two types of demand?

Independent demand and dependent demand

What is safety stock level determined by?

Lead time demand uncertainties (reflected in theta L) and the desired service level (affecting z)

What is L in the safety stock (ss) formula?

Lead time in days

What are the two types of inventories?

Manufacturing inventory Distribution inventory

What do you use to determine the optimal order quantity under a Single-Period Inventory Model?

Marginal Analysis (increase the order quantity Q one at a time, as long as the expected marginal benefits are more than the expected marginal costs; the optimal stocking level Q occurs at the point where expected benefits derived from carrying the next unit are less than the expected costs for that)

The daily demand is 78 units and constant. The order lead time is 3 days. The optimal order quantity (EOQ) is 100. Which of the following statement is correct when a fixed-order quantity model is used? I: The reorder point is 234 units. II: The average inventory level is 100.

Only I is correct (Reorder point = 78*3= 234. Since the demand is constant, the calculation of the reorder point does not involve safety stock. The average inventor level is Q/2)

List and describe the features of the Fixed-Order Quantity Model (Q-Model):

Order quantity: Q-constant (the same amount ordered each time) When to place order: R-when inventory position drops to the reorder level Recordkeeping: each time a withdrawal or addition is made Size of inventory: less than fixed-time period model Time to maintain: higher due to perpetual recordkeeping Types of items: higher-priced, critical, or important items

List and describe the features of the Fixed-Time Quantity Model (P-Model):

Order quantity: q-variable (varies each time order is placed) When to place order: T-when the review period arrives Recordkeeping: counted only at review period Size of inventory: larger than Q-model

The managerial and clerical costs to prepare purchase or production orders are called: Shortage costs Ordering costs Logistics costs Holding costs

Ordering costs

Fixed-Order Quantity Model with Safety Stock

Place an order of Q when inventory drops to the reorder (R) point. After the replenishment order is placed, when demand during lead time is more than inventory (demand during lead time > R), stockout will happen. The higher R level, the lower risk of running out of inventory. The order arrives L time later. Random demand; stockout is possible during lead time; safety stock is needed; average inventory = Q/2 + safety stock. R (Reorder Point) is the trigger, Q (Order Quantity) is fixed, L (Lead Time) is constant.

What is the purpose of carrying safety stock in a P-model?

Protect against demand (inventory usage) uncertainties throughout the entire review period, T, and order lead time, L.

What are the four stages involved in the Best Model for Managing Inventory?

Raw Materials > Manufacturing Plant Inventory > Warehouse Inventory > Retail Store Inventory

Southern Printing Corp. produces high-end booklets for university graduations listing all the participating students at a given university. What inventory model would Southern use to optimize the amount of booklet inventory produced for each graduation?

Single-period

Using the ABC classification system for inventory, which of the following is a true statement? -You should allocate about 50% of the dollar volume to "B" items. -Generally there are more "A" items than "C" items. -The "A" items are of high dollar volume. -The "C" items are moderate dollar volume.

The "A" items are of high dollar volume.

The Miami bookstore adopts the fixed-order quantity model with safety stock to manage its inventory of MacBook Air. If the supplier agrees to reduce the order lead time, which of the following statement is correct? (Assuming the bookstore maintains the same desired service level before and after the lead time change.) -The average inventory of MacBook Air in the bookstore will be reduced. -The bookstore will place orders earlier. -The probability of stock out decreases. -The order quantity will be reduced. -Order intervals will be shorter.

The average inventory of MacBook Air in the bookstore will be reduced. (In the fixed-order quantity model with safety stock, the average inventory level is Q/2+safety stock. A lead time reduction will reduce the level of safety stock required for the same service level.)

What affects the probability of running out of stock?

The size of safety stock and determined directly by the service level.

What is the purpose of safety stock in the Q model?

To protect against demand (inventory consumption) uncertainties during the lead time because stockout may occur between the time when the order is placed and when the order is received. When the order is received, we expect a 50% chance we still carry safety stock on hand, because R=avg. lead time demand + ss. So, the inventory drops from R to safety stock level.

What is the tradeoff involved in the Single-Period Inventory Model?

Tradeoff: Overstock (order quantity > demand) vs. Understock (order quantity < demand)

True or False: Both P and Q models can be used when demand is random. They can ensure the same stockout probability but with different safety stock levels.

True

True or False: Costs determine the critical ratio, which determines the desired service level, and in turn the desired service level affects Q.

True

True or False: In a fixed-time period inventory model, the interval of time between orders is fixed and order quantity varies.

True

True or False: Safety stock inventory levels are affected by the desired service level.

True

True or False: T+L is the vulnerable period during which stockout could occur.

True

True or False: The fixed-order quantity inventory model requires more time to maintain because every addition or withdrawal is logged.

True

True or False: The marginal analysis indicates that the optimal stocking level (in a newsvendor problem) occurs at the point where the expected benefits derived from carrying the next unit are less than the expected costs for that.

True

True or False: The reorder point in the basic fixed-order quantity model (when demand is constant) is lower than the reorder point in the fixed-order quantity model with safety stock (when demand is uncertain).

True

True or False: To achieve the same desired service level, fixed-time period models tend to have more safety stock than fixed-order quantity models because the inventory is not tracked as closely.

True

A company uses a continuous review system to manage its inventory. The average daily demand is 12, the lead time is 5 days, the desired "z" value is 1.96, and the standard deviation of demand during lead time is 3. Which of the following statement describes the company's policy regarding when to order? -Whenever the inventory drops to 73 units, place an order. -Whenever the inventory drops to 60 units, place an order. -Whenever the inventory drops to 66 units, place an order. -Place an order every five days.

Whenever the inventory drops to 66 units, place an order. (R=12*5 + 1.96*3 Note: if 3 units were the standard deviation of daily demand, R would be 12*5+1.96*sqrt(5)*3)

When a basic fixed-order quantity model is used, which of the following is the total annual ordering cost of inventory given an annual demand of 36,000 units, the cost of placing one order of $80 and a holding cost per unit per year of $4? $1,889 $2,267 $2,400 $1,200 $849

$2,400 (First find out the EOQ value, which is 1200. This means you will order 36000/1200 = 30 times a year. Hence ordering cost per year = 30*80=2400.)

What are the assumptions of a Basic Fixed-Order Quantity Model?

-Demand for the product is constant and uniform throughout the period. -Lead time (time from ordering to receipt) is constant. -Price per unit of product is constant. -Inventory holding cost is based on average inventory. -Ordering or setup costs are constant. -All demands for the product will be satisfied (no backorders or stock out are allowed).

Name the Costs of Inventory:

-Holding (or carrying) costs -Setup (or production change) costs -Ordering costs -Shortage costs

Name the actions involved in a Fixed-Time Period Model:

-Order every T time period. -Order arrives L lead time later. -Reorder quantity varies, depending upon the inventory level at the time when the order is placed. The goal is to order up to the same target inventory level.

What are the factors to consider when choosing between Q or P models?

-Timing of replenishment -Record-keeping system -The cost of the item

What are the purposes of inventory?

-To maintain independence of operations. -To meet variation in product demand. -To allow flexibility in production scheduling. -To provide a safeguard for variation in raw material delivery time. -To take advantage of economic purchase order size.

If a vendor has correctly used marginal analysis to select their stock levels for the day (as in the newsvendor problem), and the cost of demand underestimated is $0.90 and the cost of demand overestimated is $0.50, which of the following is the probability of stock out? 0.400 0.357 0.556 0.678

0.357 (The probability of stockout = 1-critical ratio=1-0.9/1.4=0.357.)

In a P-Model, how often would we run out of stock (use up all the inventory)?

1 minus the service level. This means demand during T+L is higher than the target inventory level.

What are the steps involved in a Basic Fixed-Order Quantity Model?

1. Inventory is consumed at a constant rate. 2. Always place a new order with a fixed order quantity Q units, when inventory reaches reorder point (R). 3. Order arrives after lead time (L). Inventory is raised to maximum level (Q). The receipt is scheduled when the inventory drops to zero.

If monthly demand is 1,000 units, the ordering cost is $6 per order, the unit cost is $100, and the annual carrying "interest" rate is 2.5%, which of the following is the optimal order quantity using the fixed-order quantity model? 61 120 576 240 56

240 (Since carrying interest rate (i.e. i) is per year and demand is monthly, you need to convert the monthly demand to annual demand.)

The Best Western hotel at Oxford always fills up in the evening before hockey games. History has shown that last-minute cancellations of reservation exist and when the hotel is fully booked, the number of cancellations follows a normal distribution with a mean of 5 and a standard deviation of 2. The average room rate is $80. When the hotel is overbooked, the policy is to find a room in a nearby hotel and to pay for the room for the customer. This usually costs the hotel approximately a net value of $220. How many rooms should the hotel overbook? Please use the normal distribution table to answer the question.

3

You would like to use the fixed-time period inventory model to compute the desired order quantity for a company. You know that vendor lead time is 10 days and the number of days between reviews is 15. Which of the following is the standard deviation of demand during the review and lead time period if the standard deviation of daily demand is 10? 25 73 40 100 50

50

How often would we need to use the safety stock during L period?

50% because 50% of the time inventory consumption (demand) will equal or be greater than the avg. lead time demand, reducing inventory level from R (avg. lead time demand + ss) to safety stock.

In a P-model, how often would we need to use the safety stock during the T+L period?

50% because this is the probability that the inventory usage during T+L equals the average demand during this vulnerable period.

In a P-model, during which time period would stockout occur?

?

Setup (Production Change) Costs

? arrange equipment, etc..

April manages the office supplies for the management department. She counts the inventory every 3 days and places an order whenever she reviews the stock. According to her observation, on average the department consumes 15 units of office supplies a day, and the standard deviation of daily demand is 3 units. When she places an order, it takes one day for the order to arrive. On a particular review day, she noticed 30 units of inventory on hand. To provide a 98% service level to her department, how many units of supplies should she order?

About 42.3 (First using the normal distribution table, you will find z=2.05 Standard deviation during lead time and review time = sqrt(3+1)*3=6 Target inventory level =4*15+2.05*6=72.3 Order size = 72.3-30=42.3)

Which of the following is not a component of total costs in a fixed-quantity inventory system? Annual production labor costs Annual holding costs Annual purchase costs Annual ordering costs

Annual production labor costs