【正文】 ock 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)concluded that the SBS outperforms the LPbased system considerably because it uses a sophisticated ordering SBS allows the target level S to be changed in every review according to the This paper proposes a new control system called IDP control system for a onewarehouse/multiretailer supply IDP model,which is a MILP model,is developed to determine optimal inventory and distribution plan that minimizes total related costs including ordering,holding,holding in transit,transportation,and lostsale IDP is updated every period following oneperiod rolling horizon planning that the IDP control system can be easily extended to plan and control the supply chain with multiple warehousesand retailers by modifying the MILP model presented in Section 3. The IDP control system is evaluated against the echelonstock R,s,S control ed on the experimental results,the IDP control system has significantly lower total costs than the echelonstock R,s,S control system for any range of fill rates for nonstationary demand ,the IDP control system significantly outperforms the echelonstockR,s,S control system for different sizes and inventory cost structures of the supply owever,both systems are indifferent in case of the stationary demand situation. It can be concluded that the IDP control system is effective for both demand patterns.The IDP control system is effective since the decision for basic actions( time and amount)is more sophisticated than that of the echelonstock R,s,S control ishment orders are placed according to the optimal fact,the inventory and transportatio