1、運籌學(xué)與供應(yīng)鏈管理Operations Research and Supply Chain Management,第講,供應(yīng)鏈簡介,戰(zhàn)略與設(shè)計,供應(yīng)鏈管理的基本概念和意義 供應(yīng)鏈管理的基本理論 供應(yīng)鏈管理與企業(yè)競爭力 供應(yīng)鏈戰(zhàn)略與設(shè)計,供應(yīng)鏈管理的基本概念和意義,什么是供應(yīng)鏈？ 供應(yīng)鏈?zhǔn)怯稍牧狭悴考?yīng)商、生產(chǎn)商、批發(fā)商、零售商等一系列企業(yè)所組成。原材料零部件依次通過“鏈”中的每個企業(yè)，逐步變成產(chǎn)品，產(chǎn)品再通過一系列流通配送環(huán)節(jié)，最后交到最終用戶手中，這一系列的活動就構(gòu)成一個完整供應(yīng)鏈的全部活動。,什么是供應(yīng)鏈(續(xù)）？ 任何一個企業(yè)，都是由多個企業(yè)形成的相互聯(lián)系、相互作用的“鏈”或“網(wǎng)”中的

2、一份子。在它們的全部行為中，至少有一部分是作為其它企業(yè)的用戶或供應(yīng)商。,供貨商,顧客,顧客的顧客,供貨商的供貨商,Make,Deliver,Source,Make,Deliver,Make,Source,Deliver,Source,內(nèi)部或外部,內(nèi)部或外部,你的公司,Source,-Supply-Chain Council,,供應(yīng)鏈管理的基本思想,把整條“鏈”看作一個集成組織，把“鏈”上的各個企業(yè)都看作合作伙伴，對整條“鏈”進行集成管理。 目的：通過“鏈”上各個企業(yè)之間的合作和分工，致力于整個“鏈”上物流、信息流和資金流的合理化和優(yōu)化，從而提高整條“鏈”

3、的競爭能力。,物流 如何使其在必要的時侯，流動到必要的地點 如何使流動成本更低 如何使流動過程中可能出現(xiàn)的偏差更小 信息流 對物料的控制有賴于及時、可靠的相關(guān)信息 “用信息取代很費錢的庫存” 資金流,供應(yīng)鏈管理的主要對象：三種流,為什么要提出供應(yīng)鏈管理？,1、降低成本的注目點從企業(yè)內(nèi)部擴展到了外部 2、縮短產(chǎn)品的開發(fā)周期、生產(chǎn)周期、上市周期對企業(yè)競爭力越來越重要 一有必要注目整個“鏈”上物流和信息流的快速流動,3、企業(yè)越來越專注于自己的核心能力 一導(dǎo)致整個供應(yīng)鏈變長； 一更加需要“鏈”上各個企業(yè)加強合作； 一更加突出了加強供應(yīng)鏈管理的必要性 4、企業(yè)越來越需要與多個企業(yè)結(jié)成“聯(lián)盟”，共同與其它

4、“聯(lián)盟”競爭 一“聯(lián)盟”的盟友，首先是與本企業(yè)事業(yè)內(nèi)容相關(guān)的上下游企業(yè)，即供應(yīng)鏈上的其它成員,為什么要提出供應(yīng)鏈管理（續(xù)）？,典型的供應(yīng)鏈,制造業(yè)中典型的供應(yīng)鏈,分銷,零售,顧客,分銷,零售,顧客,服務(wù)業(yè)中典型的供應(yīng)鏈,顧客是供應(yīng)商,與供應(yīng)商的基本關(guān)系：競爭還是合作？,供應(yīng)鏈管理的益處,供應(yīng)鏈管理的要素,物料移動,生產(chǎn)率提高 文案工作減少 提前期縮短、存貨減少 準(zhǔn)時系統(tǒng)的簡易 資金的電子傳輸 改善運作控制 減少書記勞動 精確性增加,電子數(shù)據(jù)交換,流通配送環(huán)節(jié)管理的重要性,流通配送環(huán)節(jié)的鏈條越長，該環(huán)節(jié)對于產(chǎn)品競爭能力的影響越大 由于成品的附加值遠遠高于零部件的附加值，該環(huán)節(jié)任何冗余的庫存、時間

5、上的延誤、制造商和經(jīng)銷商之間的不友好關(guān)系都會給鏈上的各個成員帶來高額成本 “配送、流通是工業(yè)的黑色地帶，是可以大量節(jié)省成本的地方?！?P.F.德魯克,如何進行流通配送環(huán)節(jié)的管理？,1、設(shè)定合理的流通環(huán)節(jié) 2、建立和保持合作伙伴關(guān)系 3、合理設(shè)定各個環(huán)節(jié)的庫存 主要考慮因素：顧客服務(wù)水平和庫存水平的平衡 4、注意點之一：“牛鞭效應(yīng)”（Bullwhip effect),1、設(shè)定合理的流通環(huán)節(jié),原材料,零件制造,顧客,部件制造,產(chǎn)品裝配,分銷配送,分銷配送,N？,1、設(shè)定合理的流通環(huán)節(jié)（續(xù)） 比較兩種不同的配送系統(tǒng),3、合理設(shè)定各個環(huán)節(jié)的庫存,主要考慮因素： 顧客服務(wù)水平和庫存水平的平衡 顧客服務(wù)水

6、平的衡量：缺貨率,？,4、注意點之一：“牛鞭效應(yīng)”,什么是“牛鞭效應(yīng)” (Bullwhip Effect)？ 需求信息沿供應(yīng)鏈的傳遞過程中其波動會被依次放大,牛鞭效應(yīng)（例）,電子商務(wù)與供應(yīng)鏈管理,電子商務(wù)的最重要意義不在于它創(chuàng)造了一個全新的行業(yè)，而在于它為眾多的行業(yè)提供了一種有力的運作手段 電子商務(wù)在供應(yīng)鏈管理中的應(yīng)用 改變傳統(tǒng)的B2B、B2C模式 改變供應(yīng)鏈的結(jié)構(gòu) 改變供應(yīng)鏈上三種流的流動模式 對供應(yīng)鏈上各個企業(yè)收入和成本的影響,電子商務(wù)與供應(yīng)鏈管理（續(xù)）,電子商務(wù)與供應(yīng)鏈管理（續(xù)）,電子商務(wù)對供應(yīng)鏈結(jié)構(gòu)的改變,電子商務(wù)對供應(yīng)鏈運作的影響,電子商務(wù)與供應(yīng)鏈上的物流： - 渠道的簡化 - 時間

7、加速 - 設(shè)施集中化 - 物流效率 電子商務(wù)與供應(yīng)鏈上的信息流： - 何時何地 - 無與倫比的大量 - 信息個性化 - 信息流對物流的拉動作用 電子商務(wù)與供應(yīng)鏈上的資金流： - 靈活的價格策略 - 價格差別化、個性化 - 支付方式與效率,電子商務(wù)對供應(yīng)鏈績效的影響,降低成本 交易成本，管理成本，庫存成本，產(chǎn)品成本 縮短整個供應(yīng)鏈的TTM（Time -To-Market) 增大收入來源 改進顧客服務(wù) 增值服務(wù),案例討論：,從庫存管理的角度分析降低“牛鞭效應(yīng)”的方法。,主要專題,、供應(yīng)鏈簡介 、需求預(yù)測 、確定性需求下的庫存管理 、不確定性需求下的庫存管理 、運輸及網(wǎng)絡(luò)問題,第講,需求預(yù)測,預(yù)測:

8、 是關(guān)于未來的描述 預(yù)測用于幫助管理人員 系統(tǒng)計劃：產(chǎn)品服務(wù)的類型、設(shè)施配置、 廠址選擇 實施計劃：庫存、勞動力、采購、生產(chǎn)進度,預(yù)測的用途,假定系統(tǒng)中存在因果關(guān)系過去 = 未來 由于不確定性因素的存在使得預(yù)測很少準(zhǔn)確無誤 對一組事物的預(yù)測比 對單個事物預(yù)測準(zhǔn)確 當(dāng)預(yù)測時間跨度增加時， 預(yù)測精度將下降,好的預(yù)測方法的基本要素,預(yù)測進行的步驟,預(yù)測的類型,主觀判斷 主觀意見 時間序列 使用歷史數(shù)據(jù)，認為將來和過去相似 聯(lián)合模型 基于自變量預(yù)測未來,主觀預(yù)測,經(jīng)理人員的意見 與顧客直接接觸人員的意見 消費者調(diào)查 其它預(yù)測方法 德爾非法Delphi method,時間序列預(yù)測,長期趨勢 數(shù)據(jù)的長期移

9、動 季節(jié)性變動 數(shù)據(jù)短期規(guī)則變化 不規(guī)則變動 異常情況引起的變動 隨機變動 各種可能性引起的變動,Ch 10 - 7, 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e,需求變動的形式,需求,時間,趨勢變動,隨機變動,需求,時間,季節(jié)變動,需求,時間,需求,時間,周期變動,帶季節(jié)性的趨勢變動,簡單易用 基本上不需要成本 不需要數(shù)據(jù)分析 容易理解 不能提供較高的精度 能夠作為衡量精度的標(biāo)準(zhǔn),簡單預(yù)測法,平穩(wěn)時間序列數(shù)據(jù) F(t) = A(t-1) 季節(jié)變動 F(t) = A(t-n) 長期趨勢數(shù)據(jù) F(t) = A(t-1) + (A(t

10、-1) A(t-2),簡單預(yù)測法應(yīng)用,簡單預(yù)測,平均方法,移動平均 加權(quán)移動平均 指數(shù)平滑法,簡單移動平均,Ch 10 - 14, 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e,加權(quán)移動平均,可調(diào)整和反映簡單移動平均法中不同時期數(shù)據(jù)的影響,WMAn =,i = 1,Wi Di,此處,Wi = 第 i 期的權(quán)重，其百分值在 0 100 之間 Wi = 1.00,Ch 10 - 15, 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e,加權(quán)移動平均之例,月份 權(quán)重數(shù)據(jù) 八月 17

11、%130 九月 33%110 十月 50%90 十一月的預(yù)測,指數(shù)平滑法,假設(shè)最近的觀測具有最高的預(yù)測價值. 因此在預(yù)測時，應(yīng)該給更近的數(shù)據(jù)賦予更高的權(quán)重.,Ft = Ft-1 + (At-1 - Ft-1),指數(shù)平滑法舉例,選擇平滑常數(shù),線性趨勢方程,b 直線斜率,線性趨勢方程舉例,線性趨勢計算,Ch 10 - 25, 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e,季節(jié)性調(diào)節(jié),需求重復(fù)性地增加減少 使用季節(jié)因子來調(diào)節(jié)預(yù)測,Ch 10 - 26, 2000 by Prentice-Hall Inc Russell/Taylor Op

12、er Mgt 3/e,季節(jié)性調(diào)節(jié)之例,需求 (1000件季度) 年 1 2 3 4 總計 1995 12.6 8.66.317.545.0 1996 14.1 10.37.518.250.1 1997 15.3 53.6 總計 42.0 29.521.955.3148.7 Si 0.28 0.20 0.15 0.37 趨勢直線 y = 40.97 + 4.30 x 1998 (第4年)的預(yù)測 = 40.97 + 4.30 (4) = 58.17 199816.28 11.63 8.73 21.53,SF1 = (S1) (F5) = (0.28)(58.17) = 16.

13、28 SF2 = (S2) (F5) = (0.20)(58.17) = 11.63 SF3 = (S3) (F5) = (0.15)(58.17) = 8.73 SF4 = (S4) (F5) = (0.37)(58.17) = 21.53,關(guān)聯(lián)預(yù)測,有關(guān)的變量 預(yù)示這些量的值 回歸分析 用一條線去擬合一組點集 最小二乘法 使線與點間的距離平方和最小,線性模型,Ch 10 - 37, 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e,回歸方法,研究兩個或更多變量之間的關(guān)系 因變量隨自變量而變,Ch 10 - 38, 2000 by P

14、rentice-Hall Inc Russell/Taylor Oper Mgt 3/e,線性回歸計算,y = a + bx 此處, a=截距 b=直線斜率 x=自變量 y=給定 x 時的預(yù)測值 b= a=y - b x 此處, n=期數(shù) x= x , x 的平均值 n y=y , y 的平均值 n,Ch 10 - 39, 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e,線性回歸之例,xyxyx2 436.3145.216 640.1240.636 641.2247.236 853.042464 644.026436 745.6319

15、.249 539.019525 747.5332.549 49346.72167.7311,Ch 10 - 40, 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e,線性回歸直線,預(yù)測精度,誤差 實際值與預(yù)測值之間的偏差 絕對平均偏差(MAD) 誤差的絕對值的平均值 均方差(MSE) 誤差的平方的平均值 跟蹤信號 累計誤差與 MAD 之間的比率,MAD 因為，所以為無效值。 最優(yōu)解可通過比較和的大小而獲得。,按量折扣模型,分段折扣模型： 小結(jié) 對于每個價格區(qū)間，確定其對應(yīng)的成本代數(shù)表達式 將 的表達式代入表達式中 從上一步中確定最小的有

16、效值（即落在正確的區(qū)間中）,按量折扣模型,其它折扣模式：,資源受限時多品種庫存系統(tǒng),例： 商店在進貨方面的總投入不超過30000元,資源受限時多品種庫存系統(tǒng),解：,資源受限時多品種庫存系統(tǒng),解： 所需的最大進貨投入為35835元。 可是總投入要求不超過30000元，所得的EOQ解違反了該約束。 因此必須減少這些批量。如何做？,資源受限時多品種庫存系統(tǒng),解： 我們只需將各EOQ值乘以比率 30000 / 35835 = 0.8372 即可。,資源受限時多品種庫存系統(tǒng),一般地，假定 n 類品目其單位成本為 c1, , cn, 總的可利用投入為。,資源受限時多品種庫存系統(tǒng),兩種可能性：）所得的EOQ

17、解有效；）所得的EOQ解違反約束條件。 如果所得的EOQ解有效，則 如果所得的EOQ解違反約束條件，則,資源受限時多品種庫存系統(tǒng),如果下列條件成立，即 則可容易地獲得最優(yōu)解,資源受限時多品種庫存系統(tǒng),假定約束條件為庫存空間約束 則該問題很復(fù)雜 可證明最優(yōu)解是如下形式,資源受限時多品種庫存系統(tǒng),式中：值的選擇應(yīng)使下式成立 其具體值可用試錯法來確定。,資源受限時多品種庫存系統(tǒng),例： 考慮例中的情形。 假定可利用的存貨空間為 2000 平方米。 三種貨品中，每單件物品所占用的空間分別為 9 平方米, 12平方米, 和 18 平方米。,資源受限時多品種庫存系統(tǒng),例： 首先，檢查對應(yīng)的 EOQ 是否可被

18、滿足 由此可知，可利用的空間不能滿足EOQ 的量。,資源受限時多品種庫存系統(tǒng),例： 第二步，對各品目計算比率 wi / hi ，它們分別是 0.72, 0.14, 和 0.85。 由于它們不相等，我們必須確定常數(shù)值 經(jīng)多次試找后，可發(fā)現(xiàn) = 1.75，此時 對應(yīng)的空間要求為 ，滿足約束條件。,第講庫存管理（II）,Multi-Echelon Inventory in Supply Chain,Two Stage Echelon Inventory,Sequential stocking points with level demand Two-stage process,Two Stage E

19、chelon Inventory,Two-stage process: A little reflection shows that at least for the case of deterministic demand it never would make sense to have be anything but an integer multiple of . Therefore, we can think of two alternative decision variables and where (4.1),Two Stage Echelon Inventory,Two-st

20、age process: The first stage cost The second stage cost The total cost,Two Stage Echelon Inventory,Two-stage process: The warehouse echelon inventory is valued at while the retailer echelon inventory is valued at only,Two Stage Echelon Inventory,Two-stage process: The total relevant (setup plus carr

21、ying) costs per unit time are given by = average value of the warehouse echelon inventory, in units = average value of the retailer echelon inventory, in units,Two Stage Echelon Inventory,Two-stage process: Substituting from equation (4.1) and noting that the echelon stocks follow sawtooth patterns,

22、Two Stage Echelon Inventory,Select (an integer) and in order to minimize Partial derivation of TRC,Two Stage Echelon Inventory,Substitute the result into the cost equation We recognize that the n that minimizes the simpler expression,Two Stage Echelon Inventory,A convenient way is to first set which

23、 gives This solves for,Two Stage Echelon Inventory,Ascertain and where and are the two integers surrounding the Whichever gives the lower value of F is the appropriate n to use (because the F function is convex in n).,Two Stage Echelon Inventory,Two-stage process: Step 1Compute Step 2Ascertain the t

24、wo integer values, and , that surround .,Two Stage Echelon Inventory,Two-stage process: Step 3,Two Stage Echelon Inventory,Two-stage process: Step 4 Step 5,Two Stage Echelon Inventory,Example 1: Let us consider a particular liquid product that a firm buys in bulk, then breaks down and repackages. So

25、 in this case, the warehouse corresponds to the inventory prior to the repackaging operation, and the retailer corresponds to the inventory after the repackaging operation. The demand for this item can be assumed to be essentially deterministic and level at a rate of 1000 liters per year.,Two Stage

26、Echelon Inventory,Example 1: The unit value of the bulk material or is $1/liter, while the value added by the transforming (break and package) operation is $4/liter. The fixed component of the purchase charge ( ) is $10, while the setup cost for the break and repackage operation ( ) is $15. Finally,

27、 the estimated carrying charge is 0.24$/$/yr.,Two Stage Echelon Inventory,Example 1: Step 1: Step 2:,Two Stage Echelon Inventory,Example 1: Step 3: that is, Thus, use n = 2.,Two Stage Echelon Inventory,Example: Step 4: Step 5:,Two Stage Echelon Inventory,Example 1: In other words, we purchase 334 li

28、ters at a time; one-half of these or 167 liters are immediately broken and repackaged. When these 167 (finished) liters are depleted, a second break and repackage run of 167 liters is made. When these are depleted, we start a new cycle by again purchasing 334 liters of raw material.,Inventory Contro

29、l with Uncertain Demand,The demand can be decomposed into two parts, where = Deterministic component of demand and = Random component of demand.,Inventory Control with Uncertain Demand,There are a number of circumstances under which it would be appropriate to treat as being deterministic even though

30、 is not zero. Some of these are: When the variance of the random component, is small relative to the magnitude of . When the predictable variation is more important than the random variation. When the problem structure is too complex to include an explicit representation of randomness in the model.,

31、Inventory Control with Uncertain Demand,However, for many items, the random component of the demand is too significant to ignore. As long as the expected demand per unit time is relatively constant and the problem structure not too complex, explicit treatment of demand uncertainty is desirable.,Inve

32、ntory Control with Uncertain Demand,Example 2: A newsstand purchases a number of copies of The Computer Journal. The observed demands during each of the last 52 weeks were:,Inventory Control with Uncertain Demand,Example 2:,Inventory Control with Uncertain Demand,Example 2: Estimate the probability

33、that the number of copies of the Journal sold in any week. The probability that demand is 10 is estimated to be 2/52 = 0.0385, and the probability that the demand is 15 is 5/52 = 0.0962. Cumulative probabilities can also be estimated in a similar way. The probability that there are nine or fewer cop

34、ies of the Journal sold in any week is (1 + 0 + 0 + 0 + 3 + 1 + 2 + 2 + 4 + 6) / 52 = 19 / 52 = 0.3654.,Inventory Control with Uncertain Demand,We generally approximate the demand history using a continuous distribution. By far, the most popular distribution for inventory applications is the normal.

35、 A normal distribution is determined by two parameters: the mean and the variance,Inventory Control with Uncertain Demand,These can be estimated from a history of demand by the sample mean and the sample variance .,Inventory Control with Uncertain Demand,The normal density function is given by the f

36、ormula We substitute as the estimator for and as the estimator for .,Inventory Control with Uncertain Demand,Optimization Criterion,In general, optimization in production problems means finding a control rule that achieves minimum cost. However, when demand is random, the cost incurred is itself ran

37、dom, and it is no longer obvious what the optimization criterion should be. Virtually all of the stochastic optimization techniques applied to inventory control assume that the goal is to minimize expected costs.,The Newsboy Model (Continuous Demands),The demand is approximately normally distributed

38、 with mean 11.731 and standard deviation 4.74. Each copy is purchased for 25 cents and sold for 75 cents, and he is paid 10 cents for each unsold copy by his supplier. One obvious solution is approximately 12 copies. Suppose Mac purchases a copy that he doesnt sell. His out-of-pocket expense is 25 c

39、ents 10 cents = 15 cents. Suppose on the other hand, he is unable to meet the demand of a customer. In that case, he loses 75 cents 25 cents = 50 cents profit.,The Newsboy Model (Continuous Demands),Notation: = Cost per unit of positive inventory remaining at the end of the period (known as the over

40、age cost). = Cost per unit of unsatisfied demand. This can be thought of as a cost per unit of negative ending inventory (known as the underage cost). The demand is a continuous nonnegative random variable with density function and cumulative distribution function . The decision variable is the numb

41、er of units to be purchased at the beginning of the period.,The Newsboy Model (Continuous Demands),Determining the optimal policy: The cost function The optimal solution equation,The Newsboy Model (Continuous Demands),Determining the optimal policy:,The Newsboy Model (Continuous Demands),Example 2 (

42、continued): Normally distributed with mean = 11.73 and standard deviation = 4.74. Since Mac purchases the magazines for 25 cents and can salvage unsold copies for 10 cents, his overage cost is = 25 10 = 15 cents. His underage cost is the profit on each sale, so that = 75 25 = 50 cents.,The Newsboy M

43、odel (Continuous Demands),Example 2 (continued): The critical ratio is = 0.50/0.65 = 0.77. Purchase enough copies to satisfy all of the weekly demand with probability 0.77. The optimal is the 77th percentile of the demand distribution.,The Newsboy Model (Continuous Demands),Example 2 (continued):,Th

44、e Newsboy Model (Continuous Demands),Example 2 (continued): Using the data of the normal distribution we obtain a standardized value of = 0.74. The optimal is Hence, he should purchase 15 copies every week.,The Newsboy Model (Discrete Demands),Optimal policy for discrete demand: The procedure for fi

45、nding the optimal solution to the newsboy problem when the demand is assumed to be discrete is a natural generalization of the continuous case. The optimal solution procedure is to locate the critical ratio between two values of and choose the corresponding to the higher value. That is,The Newsboy M

46、odel (Discrete Demands),Example 2:,The Newsboy Model (Discrete Demands),Example 2: The critical ratio for this problem was 0.77, which corresponds to a value of between = 14 and = 15. Since we round up, the optimal solution is = 15. Notice that this is exactly the same order quantity obtained using

47、the normal approximation.,The Newsboy Model (Discrete Demands),Extension to Include Starting Inventory: The optimal policy when there is a starting inventory of is: Order if . Dont order if . Note that should be interpreted as the order-up-to point rather than the order quantity when . It is also kn

48、own as a target or base stock level.,Multiproduct Systems,ABC analysis: The trade-offs between the cost of controlling the system and the potential benefits that accrue from that control. In multiproduct inventory systems not all products are equally profitable. A large portion of the total dollar v

49、olume of sales is often accounted for by a small number of inventory items.,Multiproduct Systems,ABC analysis:,Multiproduct Systems,ABC analysis: Since A items account for the lions share of the yearly revenue, these items should be watched most closely. Inventory levels for A items should be monito

50、red continuously. More sophisticated forecasting procedures might be used and more care would be taken in the estimation of the various cost parameters required in calculating operating policies.,Multiproduct Systems,ABC analysis: For B items inventories could be reviewed periodically, items could b

51、e ordered in groups rather than individually, and somewhat less sophisticated forecasting methods could be used.,Multiproduct Systems,ABC analysis: The minimum degree of control would be applied to C items. For very inexpensive C items with moderate levels of demand, large lot sizes are recommended

52、to minimize the frequency that these items are ordered. For expensive C items with very low demand, the best policy is generally not to hold any inventory. One would simply order these items as they are demanded.,Lot Size-Reorder Point Systems,In what follows, we assume that the operating policy is

53、of the form. However, when generalizing the EOQ analysis to allow for random demand, we treat and as independent decision variables.,Lot Size-Reorder Point Systems,Assumptions The system is continuous-review Demand is random and stationary There is a fixed positive lead time for placing an order The

54、 following costs are assumed Setup cost at $ per order. Holding cost at $ per unit held per year. Proportional order cost of $ per item. Stock-out cost of $ per unit of unsatisfied demand,Lot Size-Reorder Point Systems,Describing demand: The demand during the lead time is a continuous random variabl

55、e with probability density function (or pdf) , and accumulative distribution function (or cdf) . Let and be the mean and standard deviation of demand during lead time.,Lot Size-Reorder Point Systems,Decision variables: There are two decision variables for this problem, and , where = the lot size or

56、order quantity and = the reorder level in units of inventory.,Lot Size-Reorder Point Systems,Decision variables:,Additional Discussion of Periodic-Review Systems,Define two numbers, and , to be used as follows: When the level of on hand inventory is less than or equal to , an order for the differenc

57、e between the inventory and is placed. If is the starting inventory in any period, then the policy is: If , order . If , dont order.,Additional Discussion of Periodic-Review Systems,Determining optimal values of,第五講 Transportation and Network Models,Introduction,Several specific models (which can be

58、 used as templates for real-life problems) will be introduced.,TRANSPORTATION MODEL,ASSIGNMENT MODEL,NETWORK MODELS,Introduction,TRANSPORTATION MODEL,ASSIGNMENT MODEL,Determine how to send products from various sources to various destinations in order to satisfy requirements at the lowest possible c

59、ost.,Allocating fixed-sized resources to determine the optimal assignment of salespeople to districts, jobs to machines, tasks to computers ,NETWORK MODELS,Involve the movement or assignment of physical entities (e.g., money).,Transportation Model,An example, the AutoPower Company makes a variety of battery and motorized unint