Stochastic Manufacturing & Service Systems
Jim Dai and Hyunwoo Park School of Industrial and Systems Engineering Georgia Institute of Technology October 19, 2011

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Contents
1 Newsvendor Problem 1.1 Profit Maximization 1.2 Cost Minimization . 1.3 Initial Inventory . . 1.4 Simulation . . . . . . 1.5 Exercise . . . . . . . 5 5 12 15 17 19 25 25 27 29 29 31 32 33 34 39 39 40 40 42 44 46 47 48 49 51 51 51 52 54 55 57

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Suppose we are running a business retailing newspaper to Georgia Tech campus. We have to order a specific number of copies from the publisher every evening and sell those copies the next day. One day, if there is a big news, the number of GT people who want to buy and read a paper from you may be very high. Another day, people may just not be interested in reading a paper at all. Hence, you as a retailer, will encounter the demand variability and it is the primary uncertainty you need to handle to keep your business sustainable. To do that, you want to know what is the optimal number of copies you need to order every day. By intuition, you know that there will be a few other factors than demand you need to consider. • Selling price (p): How much will you charge per paper? • Buying price (cv ): How much will the publisher charge per paper? This is a variable cost, meaning that this cost is proportional to how many you order. That is why it is denoted by cv . • Fixed ordering price (cf ): How much should you pay just to place an order? Ordering cost is fixed regardless of how many you order. • Salvage value (s) or holding cost (h): There are two cases about the leftover items. They could carry some monetary value even if expired. Otherwise, you have to pay to get rid of them or to storing them. If they have some value, it is called salvage value. If you have to pay, it is called 5