【正文】 ock 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 and the echelonstock R,s,S control system. Based on the results,there are a number of observations as follows. each case shown in ,the minimum total costs for both control systems are obtained at the fill rate approximately between 97%and99%.When the fill rates are higher or lower than this,the total costs are also ,the fill rate that gives the lowest total costs may change according to the supply chain cost structure(see also Section ). ,it is clear that the IDP control system provides better results for nonstationary average total costs of the IDP control system are always lower than those of the echelonstock R,s,S control system for all values of fill rate(see cases 2,4,6,and 8).The pvalue of zero also reveals that the difference is statistically ,incase of stationary demand,the difference between both systems is not significant at the significant level of (see cases 1,3,5,and 7). ordering cost is varied to evaluate the effect of lot sizes on the performance of bot on the experimental results in ,the IDP control system significantly outperforms the echelonstock R,s,S control system when demand is nonstationary for both levels of ordering costs(both small and large lots). onewarehouse/tworetailer supply chain represents a small supply chain while the onewarehouse/sixretailer supply chain represents a large supply can be seen from F the IDP control system still significantly outperforms the echelonstock R,s,S control system when demand is nonstationary for both supply chain sizes. on the experiments,the IDP control system always provides at least 90%of fill rate(see ),even though the safety stock policy[K1,K2]is set to the worst case[0,0].For theechelonstock R,s,S control system,the system fill rate can be lower than 90%,if the control parameters are set improperly(not shown here).Thus,the user must carefully set the control parameters of the echelonstock R,s,S control system,otherwise the system performance may be unacceptable. It is noted that the IDP control system alwaysoutperforms the echelonstock R,s,S control system when demand is ,one might argue that a method in which the echelonstock R,s,S control system uses to deal with the nonstationary demand situation(see Appendix A)might not be ,to the best of our knowledge,theoptimal method is notavailable in the existing ,the method to deal with nonstationary demand in this paper follows a logical sense— pensate the control parameters(s,S)by the associated lead time(seeAppendix A for details).Thus,the dominance of the IDPcontrol system toward the echelonstock R,s,S control system is proved under this experimental reserve the determination of the optimal method of the echelonstock R,s,S control system to deal with nonstationary demand as future ,in contrast to the above result,De Kok and Fransoo(2020)also pared the performance of a backlogging LPbased system with a stochastic inventory model under the SBS SBS operates under the concept of the base stock policy in which the inventory position willbe brought up to desired target level in every inventory Kok and Fransoo(2020)