CH. 13 Newsvendor Model (Inventory Management with Perishable Demand)

Make-to-order systems are most effective in environments with which type of characteristics?

1. customers are sufficiently patient. 2. customers have a strong preference for variety. 3. leftover inventory is expensive 4. production is reasonably quick

Cu = $100 Co = $25 What is the critical ratio?

= $100 / 125 = 0.80

Expected benefit of ordering one more unit (formula)

= (1 - F(Q)) x Cu

Expected Profit formula

= (Price x Expected Sales) + (salvage value x Expected Inventory) - (cost per unit x Q)

Expected cost of ordering one more unit (formula)

= F(Q) x Co

Define assemble-to-order.

A make-to-order system in which a product is assembled from a set of standardized modular components after an order is received.

Describe a make-to-order system.

A production system in which an items production begins after the customer for the item is known. In a make-to-order system, units are generally delivered to a customer immediately after production is complete, thereby not spending time in inventory.

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

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

Negative correlation in demand for individual is best for reducing ______.

COV

Determine Overage cost. Explain: Orders 3000 units Demand = 2999 units Salvage value = $70 Note: Purchase cost = $100

Co = $30 ($100-70) Because of the salvage value, you do not lose the complete $ amount of the purchase cost.

_________________________ 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.

Delayed customization

If the demand uncertainty is too high and/or the critical ratio is too low, then what option should you choose?

Don't sell the product.

Maximum profit =

Expected Demand x Profit per unit sold This is the highest possible expected profit.

How do you convert I(z) into the expected inventory for the actual demand?

Expected inventory = σ x I(z)

A make-to-order system cannot have high utilization. Why is this bad?

Idle equipment and labor costs still exist even if they are not producing.

What does it mean if two events are positively correlated?

If the outcome of one event is "high" then the outcome of the other event tends to be "high" as well. -the outcomes tend to have similar outcomes.

What is the Round-up Rule?

If your critical ratio falls between two entries in the table, choose the higher probability.

the probability a firm has stock available for every customer is known as what?

In-stock probability.

If our forecast is 3000 units, then why don't we just order that?

It can be more costly to run out of inventory than to have left over units in inventory at the end of the season.

What is the essential feature of demand forecast?

It must give probability for all of the possible outcomes of demand, and not just the most likely demand.

The newsvendor models objective is bet an amount that balances the opposing forces. What are the "opposing forces"?

Opposing forces = -betting too high (inventory that is salvaged for a loss of each unit) -betting too low (opportunity cost of lost sales.)

Expected Sales + Expected Inventory =

Q

Sales + Inventory = ?

Q

What would be the in-stock probability if a firm orders the quantity that maximizes expected profit?

The in-stock probability would equal the critical ratio.

Whats the problem with a make-to-order system? (the Achilles heel)

Time. -the customer has to be willing to wait for the product. -also, if the reputation of the delivery is slow then it may deter receiving orders.

The forecast for the demand across a set of products is more accurate than the forecast for each individual product. (T/F)

True this is why product pooling works.

Define mass customization.

a make-to-order system in which each customers order is unique, customized to his or her exact preferences.

Describe the term "Quick Response". Example?

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

The maximum profit is the average profit resulting from...

all possible demands.

For products with moderate to low critical ratio, an increase in _________________ lowers profits substantially.

coefficient of variation

One way to reduce the coefficient of variation is to.......?

combine or pool, the demand across products.

What is the problem with the make-to-stock system?

leads to mismatch costs. either too many units produced or not enough.

Given mismatch costs: Expected Profit =

maximum profit - mismatch costs

Reduce the coefficient of variation, and you reduce _____________________.

mismatch costs

The maximum profit does not suffer from the two types of _____________.

mismatch costs

The difference between the Max profit and expected profit is the sum of....?

mismatch costs.

Pooling products provides more benefit if the products are _________ correlated.

negatively still effective for positively correlated products, but not as effective.

Overage cost = cost of order ________ too many.

one unit

Underage cost = the cost of ordering ____________ too few.

one unit

The larger the critical ratio, the larger the...?

optimal order quantity.

The cost of ordering too many units is called..? Represented by what variable?

overage cost (Co).

_______________________ is an example of statistical economies of scale.

product pooling

The capacity used in the second order is sometimes called _____________.

relative capacity

The distribution function is __-shaped.

s

If the standard deviation is large relative to the mean, then the bell is.....?

short and wide.

Make-to-order systems help to reduce __________.

stockouts.

If the standard deviation is small relative to the mean, then the bell is....?

tall and thin.

Relative capacity is...?

the capacity that allows a firm to react to changes in demand forecast.

Which factor influences mismatch costs?

the coefficient of variation

Product pooling is most effective if.....?

the coefficient of variation (COV) of the Universal product is lower than the COV of the individual products.

the key measure of demand uncertainty is ____________________.

the coefficient of variation.

The gap between maximum profit and expected profit is due to.....?

the consequences of demand uncertainty.

A common measure of service to customers is...?

the in-stock probability.

Two events are independent when..

the outcome of one event has no relationship to the outcome of the other event.

What does it mean if two events are negatively correlated?

the outcomes tend to have dissimilar magnitudes. -one event is high, the other is low.

Define stockout probability.

the probability that some demand was not able to purchase a unit; that is, the demand experiences a stockout.

Define the coefficient of variation.

the ratio of the standard deviation to the mean. Ex: mean = 3000 SD = 1000 =1000/3000 = 0.33

Define Salvage Value.

the value that can be obtained per unit for the inventory left over at the end of the selling season.

In terms of expected gain/loss, to what point should we order additional units?

to the point where the expected gain from ordering more is less than the expected loss.

Actual sales can exceed expected demand. (T/F)?

true

You can use the standard normal distribution for all products with normally distributed demand. (T/F)?

true. The standard normal is like the master lock to the family of normal distributions.

The cost of ordering too few is called the ____________________. Represented by what Variable?

underage cost. (Cu)

Product pooling is also known as....?

universal design

What is the easiest way to determine the outcomes of the demand forecast?

using the statistical distribution function.

How do you convert the order quantity to the z value?

z = (Q - μ) / σ

What does each symbol mean in the respected equation? Q = μ + (z x σ)

z = the quantity in the standard normal distribution μ = the mean of the true demand distribution σ = the standard deviation of the true demand distribution Q = the order quantity for the true demand distribution

two events are found to be independent if their correlation is _____.

zero

Describe the process of finding the order quantity that maximizes expected profit.

1. Evaluate the critical ratio 2. Use a statistical table or Excel. 3. Convert z found in previous step to an order quantity with the equation.

Describe the process of finding optimal order quantity using Excel.

1. Find z using the critical ratio z = NORM.S.INV(critical ratio) 2. Now, plug the z provided by Excel into the conversion equation. Q = μ + (z x σ) 3. The answer is the optimal order quantity

Name Newsvendor applications.

1. Goods sold seasonally -Halloween costumes -Christmas trees -ski equipment 2. Goods/services that have short shelf lives - high fashion goods - certain electronics - books?

What are some limitations of product pooling/universal design?

1. a universal design may not provide key functionality to consumers with special needs. 2. a universal design may be more expensive to produce because additional functionality may require additional components. . a universal design may eliminate brand/price segmentation opportunities.

What 2 factors determine the following questions? -when is expected profit relatively close to maximum profit? -when are mismatch costs relatively small relative to maximum profit?

1. coefficient of variation 2. critical ratio

What are the 3 key inputs to the newsvendor model?

1. cost of ordering too little 2. a cost of ordering too much 3. a demand forecast

The coefficient of variation measures the amount of __________________ relative to ___________________.

1. demand uncertainty (SD) 2. expected demand (mean)

When selling a product that has high mismatch costs, what are your options to manage this situation?

1. don't sell the product 2. increase the profit margin (increase Cu), relative to the cost of leftover inventory (Co). Thus, increasing the critical ratio 3. reduce demand uncertainty 4. develop the capability to order or produce additional supply before the end of the season. 5. only make a customers product after the customer orders it.

What are the 5 Newsvendor Performance Measures?

1. expected inventory 2. expected sales 3. expected profit 4. in-stock probability 5. stockout probability

Describe the process of using standard normal to find an order quantity.

1. find the order quantity that maximizes expected profit. 2. look for the z on the table that represents the critical ratio we want. -apply the round-up rule if the CR falls between two probabilities. 3. Now, using the Z you will convert the SND quantity to a corresponding quantity in another normal distribution. Use this equation: Q = μ + (z x σ) 4. The answer to the equation is your optimal order quantity.

What are ways to reduce demand uncertainty?

1. improve the quality of the forecast. 2. change which products are available so each face less demand uncertainty -- via product pooling.

In many situations, the objective of the newsvendor model can be described as...? But in other situations, the objective is better described as...?

1. maximize expected profits 2. Minimize expected costs

What are the 2 types of mismatch costs?

1. the cost of inventory (too much supply) 2. the opportunity cost of stockouts (ordering too little)

The relative consequence to mismatch costs is small if.....

1. there is little demand uncertainty. 2. if the critical ratio is high

Name the 3 methods for determining the optimal order quantity that maximizes expected profit. Which is best and explain why.

1. using a graph 2. using a statistical table 3. using a computer program like excel. 1. graphical method provides the best intuition but is least convenient to use. 2. Statistical table is best method if no access to a computer. 3. Using a computer is the fastest method

Therefore, Expected Sales =

Q - Expected Invetory

In-stock probability =

F(Q) =1 if demand is less than or equal to order quantity.

Formula for maximizing expected profit (critical ratio).

F(Q*) = Cu / Co + Cu

How can you find the in-stock probability?

Use the distribution function. Otherwise, calculate for z and use the SND function table.

How to calculate for expected inventory. Ex: Ordered 4000 units

Use the z-table to determine expected inventory. I(4000) = 1083 units leftover

The plot of the density function for a normal distribution has....

a bell curve.

Define correlation.

a measure of the interaction between two uncertain events. Correlation ranges from -1 to 1

The probability that demand is less than or equal to Q* is known as the ____________. Q* = quantity that maximizes expected profit

critical ratio

As the standard deviation for demand increases, the expected profit in the newsvendor model __________.

decreases.

How can you choose an order quantity to satisfy customer service level?

-If distribution function table is available, scan the f(z) column till you reach the desired in-stock probability (Use round-up function). -Otherwise find the f(z) that satisfies the desired in-stock probability. Then, use the conversion equation: Q = μ + (z x σ). This will give you the quantity to order.

For the mean to be the optimal order quantity, the critical ratio must be _____.

0.50 -this only happens if the underage and overage costs are identical.

Stockout probability =

1 - in-stock probability

Describe the process to determine the expected inventory.

1. Convert order quantity Q into its corresponding z value. 2. look up the expected inventory for the standard normal. 3. convert that expected inventory into the expected inventory that would occur for the actual demand distribution.

What is Density Function?

A function that returns the probability a given outcome occurs for a particular statistical distribution.

What is Distribution Function?

A function that returns the probability the outcome of a random event is a certain level or lower. For example, if F(Q) is the distribution function of demand, then F(Q) is the probability that demand is Q or lower.

A standard normal distribution is..?

A normal distribution with a mean = 0 and a standard deviation = 1

Describe a Make-to-Stock system.

A production system in which an items production begins before the customer for the item is known. In a make-to-stock system, units are generally placed in inventory to await customer demand.

Determine underage cost. Explain: Orders 3000 units Demand = 3001 units Selling Cost = $190 Note: Purchase cost = $100

Cu = $90 ($190-100) Underage cost is based on incremental profit. Not revenue

Define expected inventory.

the expected number of units not sold at the end of the season that therefore must be salvaged.

Define expected sales.

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

Define expected profit.

the expected profit earned from the product, including the consequences of inventory that needs to be salvaged.

Define in-stock probability.

the probability that enough inventory is available to satisfy ALL demand.

Define product pooling.

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