# O i 1 4 caseweek for i r w d 21 psr 1 4 caseweek 22

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Oi, 1= 4 [case/week] fori=R,W,D(21)PSR1= 4 [case/week](22)IOi, 1= 4 [case/week] fori=W,D,F(23)Oistands forordersthat are placed by echeloni(retailer, wholesaler, and distributor).PSRstands for theproduction start rate, which is the production order given by the factory itself.IOistands for theincomingorders(the box right to the box of orders placed in Figure 1) that are received by echeloni. The purchase orders (O) placed by the retailer, wholesaler, and distributor and the production orders (PSR) given byfactory at weektare placed for week (t +1).Ordersplaced at week (t +1) by the retailer, wholesaler, and distributor become theincoming orders(IO), respectively, for the wholesaler, distributor, and factory atweek (t +2). Therefore, theend-customer demand(ENDCD), which is given by Equation 7,orders(O), andproduction start rate(PSR) have no value at week zero, but they are assigned a value for the first time atweek 1.219/10/2015
TCi, 0= 0 [$] fori=R,W,D,F(24)uihc= 0.5 [$/(week·case)](25)ubc= 1 [\$/(week·case)](26)TC,uihc, andubcstand for thetotal costgenerated by an echelon, theunit inventory holding cost, and theunit backlog cost, respectively.2.4The remaining model equations are given in an order based on the steps of the game presented in Sterman (1989). This sequence should strictly be followed while performing calculations to ensure an accuraterepresentation of the board version of The Beer Game (Figure 1).2.5After initializing the board, the game facilitator declares the time as week 1, and the game starts from Step 1. After the completion of all steps (at the end of Step 5), the facilitator adds one week to the current time,declares it, and the game continues repeating the same process.Step 1. Receive inventory and advance shipping delays2.6In The Beer Game, cases of beer flow from right to left (i.e., from the upper echelon to the lower) and orders flow from left to right (i.e., from lower echelon to the upper). In the first step of the game, the in-transitinventory (work-in-process inventory for the factory) that is immediately to the right of an inventory is added to the inventory by the participants. After that, the contents of the rightmost in-transit inventory boxes areshifted to the near-right in-transit inventory boxes, and the contents of the rightmost work-in-process inventory box are shifted to the near-right work-in-process inventory box. As a result, the rightmost in-transitinventory boxes andWIPI1become empty.Ii,t=Ii,t-1+ITI2i,t-1[case] fori=R,W,D(27)IF,t=IF,t-1+WIPI2t-1[case](28)ITI2i,t=ITI1i,t-1[case] fori=R,W,D(29)WIPI2t=WIPI1t-1[case](30)ITI1i,t= 0 [case] fori=R,W,D(31)WIPI1t= 0 [case](32)2.7Equations 31 and 32 are redundant in the sense that the exclusion of these equations will not prevent the correct simulation of the mathematical model, but we present them in order to follow the same exactprocess as in the board version of the game.

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Term
Winter
Professor
John