【正文】 gement 23 Swimsuit production Solution Find order quantity that maximizes weighted average profit. Question: Will this quantity be less than, equal to, or greater than average demand? Example – Swimsuit production Inventory Management 24 What to Make? Average demand is 13,000 Look at marginal cost Vs. marginal profit – if extra swimsuit sold, profit is 12580 = 45 – if not sold, cost is 8020 = 60 So we will make less than average (12022) Example – Swimsuit production Inventory Management 25 Expected profit of production quantity Q1 Di=the ith demand Pi=the profit of production quantity Q at demand Di ? ? ? ?? ?i i iii12 5 D 80 Q 10 00 00 20 Q D if Q DP12 5 Q 80 Q 10 00 00 if Q D ? ? ? ? ? ? ??? ? ? ? ??Inventory Management 26 Expected profit of production quantity Q2 f(Pi)=the probability of Di When production quantity=Q Expect Profit of Q: E(P) ? ? ? ?iiiE P P f P? ?Inventory Management 27 Swimsuit production Expected Profit E x p e c t e d P r o f it$0$ 1 0 0 , 0 0 0$ 2 0 0 , 0 0 0$ 3 0 0 , 0 0 0$ 4 0 0 , 0 0 08000 12022 16000 20220O r d e r Q u a n t i t yProfitExample – Swimsuit production Inventory Management 28 Swimsuit production : Important Observations Tradeoff between ordering enough to meet demand and ordering too much Several quantities have the same average profit Average profit does not tell the whole story Question: 9000 and 16000 units lead to about the same average profit, so which do we prefer? Example – Swimsuit production Inventory Management 29 Swimsuit production Expected Profit E x p e c t e d P r o f i t$0$ 1 0 0 , 0 0 0$ 2 0 0 , 0 0 0$ 3 0 0 , 0 0 0$ 4 0 0 , 0 0 08000 12022 16000 20220O r d e r Q u a n t i t yProfitExample – Swimsuit production Inventory Management 30 Probability of Outes 0%20%40%60%80%100%300000100000100000300000500000R e v e n u eProbabilityQ = 9 0 0 0Q = 1 6 0 0 0Example – Swimsuit production Inventory Management 31 Key Insights from this Model The optimal order quantity is not necessarily equal to average forecast demand The optimal quantity depends on the relationship between marginal profit and marginal cost As order quantity increases, average profit first increases and then decreases As production quantity increases, risk increases. In other words, the probability of large gains and of large losses increases Example – Swimsuit production Inventory Management 32 Initial Inventory Suppose that one of the swimsuit designs is a model produced last year. Some inventory is left from last year Assume the same demand pattern as before If only old inventory is sold, no setup cost Question: If there are 5000 units remaining, what should swimsuit production do? Example – Swimsuit production Inventory Management 33 Initial Inventory and Profit 01000002022003000004000005000005000 6000 7000 8000 900010000 11000 12022 13000 14000 15000 16000P r o d u c t i o n Q u a n t i t yProfitExample – Swimsuit production Inventory Management 34 Tradeoff between Produced and not Produced Example – Swimsuit production 3 7 5 0 0 0 X 8 0 1 2 5 X375000X 8 5 0 045? ? ? ???Let X is the tradeoff point ?If initial inventory is below 8500 units, we produce to raise the inventory level to 12022 units. On the other hand, if initial inventory is at least 8500 units, we should not produce anything. Inventory Management 35 (s, S) Policies For some starting inventory levels, it is better to not start production If we start, we always produce to the same level Thus, we use an (s,S) policy. If the inventory level is below s, we produce up to S. s is the reorder point, and S is the orderupto level The difference between the two levels is driven by the fixed costs associated with ordering, transportation, or manufacturing Inventory Management 36 Supply Contracts: Case Study1 Example: Demand for a movie newly released video cassette typically starts high and decreases rapidly – Peak demand last about 10 weeks Blockbuster purchases a copy from a studio for $65 and rent for $3 – Hence, retailer must rent the tape at least 22 times before earning profit Retailers cannot justify purchasing enough to cover the peak demand – In 1998, 20% of surveyed customers reported that they could not rent the movie they wanted Inventory Management 37 Supply Contracts: Case Study2 Starting in 1998 Blockbuster entered a revenue sharing agreement with the major studios – Studio charges $8 per copy – Blockbuster pays 3045% of its rental ine Even if Blockbuster keeps only half of the rental ine, the breakeven point is 6 rental per copy The impact of revenue sharing on Blockbuster was dramatic – Rentals increased by 75% in test markets – Market share increased from 25% to 31% (The 2nd largest retailer, Hollywood Entertainment Corp has 5% market share) Inventory Management 38 Supply contracts1 供應(yīng)合約中，買(mǎi)方和供應(yīng)商通常會(huì)規(guī)範(fàn)以 下條款： 價(jià)格和數(shù)量 折扣 最小與最大訂購(gòu)量 運(yùn)輸前置時(shí)間 (交期 ) 產(chǎn)品或原料 品質(zhì) 退貨政策 Inventory Management 39 Manufacturer Manufacturer DC Retail DC Stores Fixed Production Cost =$100,000 Variable Production Cost=$35 Selling Price=$125 Salvage Value=$20 Wholesale Price =$80 Supply Contracts2 Example – Swimsuit production Inventory Management 40 Distributor Expected Profit E x p e c t e d P r o f i t01000002022003000004000005000006000 8000 10000 12022 14000 16000 18000 20220O r de r Q ua nt i t yExample – Swimsuit production Inventory Management 41 Supply Contracts3 Distributor optimal order quantity is 12,000 units Distributor expected