【正文】 otherwise,nothing is done until the next r retailer inventory position is defined as onhand inventory plus inventory intransit from the warehouse to the warehouse inventory position is the sum of onhand inventory and inventory intransit from a vendor plus all downstream inventories including pipeline all retailer orders cannot be fulfilled by the onhand inventory at warehouse at any period,the available inventory at the warehouse will be rationed so asto maximize the minimum inventory position among all retailers(see Whybark andYang,1996).Unfortunately,an exact method to determine the optimal control parameters of the echelonstock R,s,S control policy for a lostsale model is not known in the good approximate method can be found in Schneider and Rinks(1991)and Schneider et al.(1995).Even though Schneider and Rinks(1991)and Schneideret al.(1995)provide a good approximation for parameter setting for the echelonstock R,s,S control policy,their model is developedbased on the backlogging model and the authors have not guaranteed the adaptation of their model to the lostsale model as studied in this ,in this paper,the method of Schneider and Rinks(1991) and Schneider et al.(1995)is used to determine the initial valuesof the control parameters s and S. Then,simulation experiments are conducted to manipulate the values of s and S until the best ones are obtained— the R value is fixed to one,s and S are manipulated until the required fill rate is obtained while other parameters are kept though there are many sets of s and S which can give the same value of desired fill rate,the one which can give minimum total cost is selected. design This section explains simulation experiments to investigate the effectiveness of the IDPcontrol experiments are divided into three parts as follows: on effects of safety stock factor ki of IDP control system:As discussed in Section4,the safety stock factor ki influences the effectiveness of the IDP control subsection is devoted to investigate the role of ki in terms of safety stock policy[K1,K2].Thevalues of K1 and K2 will be varied and the effects on fill rates and total costs will be analyzed. between the IDP and R,s,S control systems:The effectiveness of the IDP control system is evaluated against the echelonstock R,s,S control best results obtained from both control systems are statistically is noted that when the echelonstock R,s,S control system is used and the supply chain faces nonstationary demand,amethod presented in Appendix A is used to determine the control initial inventory at each node is set equal to the associated orderupto level S. on effects of cost structures of the supply chain:It is possible that the relative magnitude of cost structures of the supply chain may affect the abovementioned erefore,the cost structure is changed by increasing the unit lostsale cost by 20– 100%while other cost parameters(ordering,holding,and transportation costs)are kept constant. and discussions This section contains results of the simulation experiments. of the study on the effects of the safety stock factors The mean values of total costs and fill rates are recorded for all eight cases of the twolevel factorial experiment of three parameters:number of retailer, demand pattern,and ordering example of the simulation results for the onewarehouse/tworetailer supply chain operating under high rate of ordering cost and stationary demand is shown in shows effects of the safety stock factors on the mean values of total costs and fill rates. Based on the results,some interesting points are safety stock factors at the retailers (K2)affect the system fill shows that the system fill rate is significantly increased when the safety stock parameter at retailers(K2)is indicates that safety stocks carried at the retailers always contribute to customer service contrast, also shows that the safety stock parameter at the warehouse(K1) insignificantly affects the system fill rate,but it significantly affects the total cost(see ).The increaseof K1 increases the total costs without improving the system fill rates. It is also observed that there are many safety stock policies[K1,K2]that give the same system fill rate,for example,the policies[0,3],[1,3],[2,3],and[3,3]can give the same system fillrate of approximately 99%(see ).However,the best safety stock policy which can givethe system fill rate of99%is[0,3]because it provides the lowest total cost(see ). Note that the results for other seven cases(not shown here)are similar to the one in Fig.3,all caseslead to a conclusion that the safety stock parameter at the warehouse(K1)shouldbe zero(assuming that negative safety stock which leads to negative ending inventory is not allowed)and that at the retailers(K2)affect both system fill rates and total conclusion is also confirmed by the oneway ANOVA remark coincides with plenty of existing literature in the field,for example,the paper of De Kok and Fransoo(2020),Whybark and Yang(1996),Schwarz et al.(1985),and Badinelli and Schwarz(1988). results between the IDP and R,s,S control systems The average total costs of both control systems are plotted against the average fill rates in that the results in tabular form with appropriate control parameters are provided in Appendix each case in ,there are five points of fill rate in which the average total cost of the IDP control system is pared to that of the echelonstock R,s,Scontrol that the five points of the IDP control system are obtained by using the safety stock policies[0,0],[0,],[0,],[0,],and [0,], safety stock parameters at the warehouse are zero since they result in low total bold numbers on each chart are pvalue (observed significance level)obtained from the paired ttest between average total costs of the IDP control system