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【正文】 H = (Q/2)hC Total annual cost = TC = CD + (D/Q)S + (Q/2)hC Figure shows variation in different costs for different lot sizes 11 169。 2023 Pearson Education 利用固定成本獲取規(guī)模經(jīng)濟(jì) ? 單一產(chǎn)品批量規(guī)模 Q（經(jīng)濟(jì)訂購批量） ? R＝產(chǎn)品年需求量 ? S＝每次訂購固定成本 ? C＝單位產(chǎn)品購買價(jià)格成本 ? H＝每年存儲(chǔ)成本 ? 年原料價(jià)格成本＝ CR ? 年訂購次數(shù)＝ R/Q ? 年訂購成本＝（ R/Q） *S ? 年存儲(chǔ)成本＝（ Q/2） H=(Q/2)hc ? 年總成本 TC＝ CR+ （ R/Q） *S+ （ Q/2） hc 13 169。 2023 Pearson Education 批量規(guī)模 成本 總成本 儲(chǔ)存成本 訂購成本 原材料成本 Q* 15 169。 2023 Pearson Education Example (continued) Annual ordering and holding cost = = (12023/980)(4000) + (980/2)()(500) = $97,980 Suppose lot size is reduced to Q=200, which would reduce flow time: Annual ordering and holding cost = = (12023/200)(4000) + (200/2)()(500) = $250,000 To make it economically feasible to reduce lot size, the fixed cost associated with each lot would have to be reduced 17 169。 2023 Pearson Education 例： best buy公司采購電腦，月需求 1000臺(tái)，固定成本每次 4000，進(jìn)價(jià)每臺(tái) 500，零售商庫存成本占 20％，求 Q* ? 解：年需求量 R=1000*12=12023 ? 每批訂購成本 S=4000 ? 單位采購成本 C=500 ? 年存儲(chǔ)成本 h＝ ? Q*=（（ 2*12023*4000） /（ *500） ） 1/2＝ 980 ? 循環(huán)庫存＝ Q*/2=490 ? 年訂購次數(shù)＝ R/Q*=120230/980= ? 訂購和存儲(chǔ)成本＝（ R/Q*） S+（ Q*/2） hC=97980 ? 平均周轉(zhuǎn)時(shí)間＝ Q*/2R=490/1200=＝ 19 169。 20 169。 ? Q*= ?年訂購次數(shù)＝ R/Q* ?平均周轉(zhuǎn)時(shí)間＝ Q*/2R ?結(jié)論：如果批量規(guī)模最佳，需求量增加，循環(huán)庫存周轉(zhuǎn)時(shí)間會(huì)減少。 2023 Pearson Education ? C、如果批量規(guī)模為 200，則： ? 年庫存成本 ? ＝（ R/Q） *S+(Q/2)hC ? ＝ （ 12*1000/200 ） *4000+（ 200/2） *500 ? =250000 97980 ? 為了減少批量規(guī)模，只能減少固定成本。 2023 Pearson Education Key Points from EOQ Model ? In deciding the optimal lot size, the tradeoff is between setup (order) cost and holding cost. ? If demand increases by a factor of 4, it is optimal to increase batch size by a factor of 2 and produce (order) twice as often. Cycle inventory (in days of demand) should decrease as demand increases. ? If lot size is to be reduced, one has to reduce fixed order cost. To reduce lot size by a factor of 2, order cost has to be reduced by a factor of 4. 23 169。 2023 Pearson Education Quantity Discounts ? Lot size based – All units – Marginal unit ? Volume based ? How should buyer react? ? What are appropriate discounting schemes? 25 169。 2023 Pearson Education AllUnit Quantity Discount Procedure (different from what is in the textbook) Step 1: Calculate the EOQ for the lowest price. If it is feasible (., this order quantity is in the range for that price), then stop. This is the optimal lot size. Calculate TC for this lot size. Step 2: If the EOQ is not feasible, calculate the TC for this price and the smallest quantity for that price. Step 3: Calculate the EOQ for the next lowest price. If it is feasible, stop and calculate the TC for that quantity and price. Step 4: Compare the TC for Steps 2 and 3. Choose the quantity corresponding to the lowest TC. Step 5: If the EOQ in Step 3 is not feasible, repeat Steps 2, 3, and 4 until a feasible EOQ is found. 27 169。 2023 Pearson Education AllUnit Quantity Discount: Example Order quantity Unit Price 05000 $ 500110000 $ Over 10000 $ q0 = 0, q1 = 5000, q2 = 10000 C0 = $, C1 = $, C2 = $ D = 120230 units/year, S = $100/lot, h = 29 169。 2023 Pearson Education AllUnit Quantity Discounts ? Suppose fixed order cost were reduced to $4 – Without discount, Q* would be reduced to 1265 units – With discount, optimal lot size would still be 10001 units ? What is the effect of such a discount schedule? – Retailers are encouraged to increase the size of their orders – Average inventory (cycle inventory) in the supply chain is increased – Average flow time is increased – Is an allunit quantity discount an advantage in the supply chain? 31 169。 2023 Pearson Education 月需求量 1000 訂購成本 100 儲(chǔ)存成本 20% 訂購數(shù)量 單價(jià) 05000 3 5
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