Chapter 13: inventory management with perishable demand

Newsvendor performance measures

*Expected inventory* *Expected Sales* *expected profit* *in-stock probability* *stockout probability*

standard normal distribution

A normal distribution with a mean of 0 and a standard deviation of 1.

newsvendor model

A single-period inventory control model that aims to define optimal order quantities so as to minimize expected overstock costs. if the newsvendor buys too many newspapers, some will get thrown out if the newsvendor buys too few newspapers, then some sales are lost

strategies to manage mismatch cost

Don't sell product Increase profit margin (increase Cu) relative to the cost of left over inventory (Co) thus increasing the critical ratio -Raise price -Reduce purchase cost Reduce demand uncertainty through product pooling Develop the capability to order additional supply before the end of the planning period (order multiple times rather than just once) -Quick response to updated demand information Only make a customer's product after the customer orders -Make to order, mass customization, assemble to order

mismatch costs in the newsvendor may exist

Either the chosen order quantity is greater than demand (units need to be salvaged) or less than demand (lost sales and poor customer satisfaction) -Demand - supply mismatch cost exists High demand uncertainty and variability with low to medium critical ratio

Intro

Goal of operations management is to match supply and demand How much to order -want to minimize underage and overage costs

Quick Response

Increase order flexibility by having the ability to place subsequent orders rather than just 1 before selling to customer occurs -Updated order quantity based on more accurate demand information -order less with initial order and thus reduce mismatch cost of leftover inventory while second order reduces the risk of stock-outs -By one additional opportunity to place another inventory order, it can increase expected profits for reducing both types of mismatch costs by responding to updated more accurate demand information

Make-to-order

Most effective in environments with the characteristics associated with: Leftover inventory is expensive Customer are willing to wait for product after ordering Strong preference for product variety -Mass customization = individual product design -Lean Operations Fast production capabilities Assemble to order Lean Operations

Product Pooling to Reduce Demand Uncertainty and variability

Reducing the variety offered to customers so that each faces less demand uncertainty by combining, or pooling demand across similar products -Forecast for the total demand across a set of products is more accurate than the forecast for each individual product --For 2 different products, expected pooled demand is equal to 2 times the mean forecasted demand (assuming each product has the same mean forecasted demand) --Expected profit from the pooled demand between 2 different products depends on their correlation coefficient •Positive •Negative •Independent Can result in higher profits to sell just 1 common product rather than 2 different products that are relatively similar

Optimal order quantity

This order size minimizes total annual cost. Q = µ+ (z * σ)

distribution function

a function that returns the probability the outcome of a random even is a certain level or lower

Density function

a function that returns the probabilty a given outcome occurs for a particular statistical distribution, the plot of the density funciton for a normal distribution has a bell shape. if the standard deviation is small relative to the mean, the bell is tall and thin if standard deviation is large, it is wide and short

forecast for demand

crucial input for deciding how many units to order

Expected inventory

expected number of units not sold at the end of the season that therefore must be salvaged as order quantity increases, so does the expected inventory σ * I(z) z= Q - µ / σ

Expected profit

expected profit earned from the product, including the consequences of inventory that needs to be salvaged = (selling price x expected sales) + (salvage value x expected inventory) - (purchase cost per unit x Q)

salvage value

if o'neill has inventory at the end of the season, it is o'neill's experience that it is able to sell the inventory through various channels for $70 per wet suit. *salvage value* is the value that can be obtained per unit for inventory left over at the end of the selling season.

overage cost

opportunity cost of ordering one too many = unit purchase cost - unit salvage value

statistical table method

the critical ratio value may lie between 2 numbers. in that case, use the *round up rule*. if the probability you look up in a statistical table falls between two entries, choose the one with the larger probability.

demand forecast

the essential feature of the demand forecast is that it must give a probability for all of the possible outcomes of demand, and not just most likely demand easiest way to express the probability for all outcomes is to use a statistical distribution function

Expected Sales

the expected number of units sold during the season at the regular price. = Q - expected inventory

the objective of and inputs to the newsvendor model

the newsvendor model represents a situation in which a decision maker must make a single bet (order quantity) before some random even occurs (demand). Buying too much or too little has consequences. *3 key inputs* underage cost, overage cost, and a demand forecast

underage cost

the opportunity cost of ordering *one* unit too short, marginal = sales price - unit purchase cost

how to determine the optimal order quanity

the order quantity that maximizes expected profit and minimizes underage/overage costs *3 methods* using a graph, using a statistical table, using excel

In stock probability

the probability that enough inventory is available to satisfy all demand = F(Q) found by using z score and looking up on F(z) chart

stockout probability

the probability that some demand was not able to purchase a unit. = 1 - instock probability

the critical ratio

the ratio of the underage cost to the sum of the overage cost and underage cost Use the critical ratio to find Z F(z) = Cu/(Cu+Co)