INDEPENDENT DEMAND SYSTEMS: DETERMINISTIC MODELS

Transcription

1 INDEPENDENT DEMAND SYSTEMS: DETEMINISTIC MODELS A major reason for aving inventory is to enable an organization to buy or produe items in eonomi lot sizes Eonomi lot sizing often applied wen organization want to maintain a regular inventory of items wi ave a fairly uniform, independent demand To determine an optimum inventory poliy, information on te following parameters is required Demands, Appropriate inventory osts and Lead times Inventory poliy find answers for - ow many and wen to order FIED ODE SIZE SYSTEMS Te stok level is reviewed wit ea transation Wenever te inventory position reaes a predetermined point, an order for a fixed number of units is plaed Te two parameters of te system are eorder point and Size of te order Tis system also is termed a -system Stok available Stok reeipt Demand ours (units witdrawn Determine stok position (on and + on order-bak order No Is stok position eorder point? Yes Issue replenisment order Fig. 1 Fixed Order uantity System National Institute of Tenology Caliut 37 Department of Meanial Engineering

2 Eonomi Order uantity (EO Single Item EO - Te order quantity tat minimizes te total inventory ost Notations Used annual demand in units P purase ost of an item C ordering ost per order H PF olding ost per unit per year lot size or order quantity in units F annual olding osts as a fration of unit ost TC total annual ost 6 5 Inventory Time.5 x 14 Fig. Inventory Variation grap Cost Total Costdata1 Annual order Cost Annual Carrying Cost Purase Cost National Institute of Tenology Caliut Order uantity Fig. 3 Annual Inventory Cost 38 Department of Meanial Engineering

3 Total annual ost purase ost + order ost + olding ost C H C PF Number of order per year Order interval eorder level m 1 T m B L 1 C H H C eplenisment order arrives just as te last item leaves te inventory wi restores te inventory level to te amount ordered B < -never more tan one order outstanding B > at least one order outstanding always Assumptions Demand rate known, onstant and ontinuous Lead time known and onstant Entire lot size is added to inventory at te same time No stokouts are permitted Cost struture is fixed Tere is suffiient spae and apital to proure te desired quantity Te item is a single produt; it does not interat wit any oter inventory item EO SENSITIVITY Determines ow te output of a model will be influened by anges or errors in te input data Insensitive input an assume a wide range of values witout appreiably affeting te output Analyses te errors in determining te parameters, H, C effet in te output Usefulness How errors in estimation ould affet deisions and resulting ost Input parameters may ange over time, so sensitivity analysis an elp in deiding at wat point it will be neessary to revise inventory deisions National Institute of Tenology Caliut 39 Department of Meanial Engineering

4 Te effet of adjusting te order quantity to above or below EO to take aount of Analysis Notations fators su as apaity limitations, transportation effiienies or pakaging restritions TVC total annual variable ost or total relevant ost - order quantity wit parameter errors eonomi order quantity Input Error Fator Estimation estimated demand demand error fator atual demand estimated order ost order ost error fator atual order ost estimated olding ost olding ost error fator atual olding ost C H TVC ( + (General total variable ost equation C H TVC ( H + (Total variable ost at optimum order quantity Error in EO due to error in input fator C H 1 order quantity error fration Sensitivity of te total variable ost per year to errors in input parameters C TVC ( + H Wen te inputs are measured erroneously, te above equation beomes National Institute of Tenology Caliut 4 Department of Meanial Engineering

5 C TVC ( + H 1 TVC error fration Tis sows tat for single parameter variations, te effet on total ost is te same irrespetive of te parameter (C,, or H Errors in parameters are dampened wen translated into teir impat on total inremental ost For example, if te ordering ost is in error by 4% on te ig side ( 1.4 it results in only an 18.3% inrease over te teoretially possible minimum total variable ost (efer Fig. 4 for errors in input fator estimation and te orresponding effet in TVC. Also refer Table 1 Sensitivity of te total variable ost per year to rounding in EO C H TVC + ( H C TVC ( + H estimated EO EO error fator atual EO + 1 C H + ( 1 H H TVC error fator Fairly sizable lot size errors result in omparatively small inreases in total variable osts (efer Fig. 4 for rounding errors in te EO and te orresponding effet in TVC. Also refer National Institute of Tenology Caliut 41 Department of Meanial Engineering

6 Table 1 Absolute TVC error EO Error.7 C,, or H Error Error Fator..8 Fig. 4 Effet of errors in C,, H, or Table 1 Error fator and Error in TVC Error Fator ( i or Error in Error in due to i due to i (estimated i/(atual i, were i is any of te tree parameters and tere are no errors in te oter two. Tus, if i were C, ten and H would ave no errors. As sown in fig. 4, te ost penalty is greater for errors of underestimation tan errors of overestimation Tis indiates te general desirability for estimates to be on te ig side to avoid te larger ost penalty for low estimates EO Sensitivity and Inventory Turnover EO formula indiates tat inventory sould inrease only wit te square root of demand Tus, a onstant inventory turnover is not justified as demand (sales inreases As demand inreases, a iger turnover rate sould be expeted Inventory turnover is te ratio of te annual ost of goods sold to te average or urrent inventory investment National Institute of Tenology Caliut 4 Department of Meanial Engineering