【正文】 helonstock inventory control difference between them is mainly based on information used to make an inventory replenishment echelonstock inventory control system allows the planner to utilize the work information, while the installationstock control system allows the planner to use only local of the two categories can be seen in Axsa168。 ter and Rosling(1994). Many research works try to determine control parameters of classical inventory control systems in supply aim to minimize the total costs including inventory costs(ordering,holding,and shortage costs)and transportation costs(transportation and intransit holding costs).Schneider and Rinks(1991) and Schneider et al.(1995)provided a good approximation for parameter setting for the echelonstock R,s,S control model is developed based on the backlogging model of a onewarehouse multiplestores supply han(1999)studied a nonlinear programming model which accounts for inventory and transportation the model by the Newton or the conjugate gradient method,the planner obtains nearoptimal control parameters of the installationstock s,Q et al.(2020)studied inventorycontrol systems of a onewarehouse/Nretailer work under centralized and decentralized authors obtained inventory control parameters(replenishment times and reorder quantities)by solving various types of mathematical models concerning holding and ordering determination of control parameters on a onewarehouse/Nretailer work belongs to Axsa168。 ter(2020).The author proposed a technique to approximate optimal reorder model considers holding costs at all locations and backorder costs at (2020)studied a multiDC/multiRetailer model controlled by the installationstock R,S target inventory and the transportation amountare determined so as to minimize the sum of transportation,holding,and shortage ras(1999)considered the installationstock R,S system in a onewarehouse/Nretailer work.Orderupto quantities are calculated by solving a mathematical model concerning holding,shortage,and transshipment costs,if the transshipment between retailers is stock levels in general divergent works under the echelonstock R,S system was studied by Heijden(2020).The objective is to achieve target fill rates and to minimize total holdingcosts of the entire ,control parameters of the traditional R,S system for serial supply chains were improved by Xie et al.(2020).The authors propose a twolevel supply chain coordination algorithm to adjust the values of R and S,which are regularly determined by the local numerical experiments have been conducted and it is found that the supply chain performance is increased due to the new values of R and and Rossetti (2020)proposed an efficient heuristic optimization algorithm to determine the control parameters of the s,Q model is a onewarehouse/multiretailer supply goal is to minimize the inventory investment that is affected by average annual ordering frequency and expected number of continuous review s,Q policy were also studied by Seifbarghy and Akbari Jokar(2020).The authors study a one centralwarehouse/multiidenticalretailer supply chain,which faces independent Poisson dema the batch size is given,the related reorder point at each facility is determined bya proposed approximate cost function. The remainder of this paper is organized as 2 describes a supply chain IDP control system and safety stock policies are presented in Sections 3 and 4, 5 contains the echelonstock R,s,S control system and an approach to determine its control experimental design is shown in Section 7 discusses the experimental ,the results are concluded in Section 8. supply chain model A supply chain under consideration prises of onewarehouse and multiple identical retailers as depicted in faces uncertain demand of a single the demand is not satisfied,it is considered as a lost retailers replenish their inventories from the central warehouse,which in turn replenishes its inventory from an incapacitated vendor outside the concerned supply is assumed that all storage and transportation capacities are occurs after orders have been placed from the destinati transshipments between retailers are not related costs are ordering,holding,intransit holding,transportation,and lostsale costs. If insufficient products are sent to fulfill customer demands,the system would have lowfill rate and high lostsale contrast,if excessive products are sent instead,the systemwould have high holding ,place and time of delivery also affect the system fill rate and total products to a wrong place in an inappropriate period may result in both low fill rate and high ,it is interesting to optimize the product flow through the concerned supply chain,such that the system can give the desired fill rate withthe lowest total ,the relevant decision in this model is the determination of shipping quantity sent from the warehouse to each retailer in each this paper,the concerned supply chain is controlled by the IDP which is obtained by solving the proposed mixedinteger linear programming model presented in the next section. IDP control system The IDP model is formulated as a mixedinteger linear programming aims to minimize the sum of ordering,holding,holding in transit,transportation,and lostsale constraints are safety stock policies and material balance are defined asfollows: Indices t period index(1,y,T) i node index(0,y,N), Note that the warehouse has index i?0,the retailer has index i40. Decision variables Tti shipping quantity sent from a source node to node i at the beginning of period t Bti binary variable representing whether an order is placed by node i in period t ki safety stock factor at node i LSti lostsale quantity at node i at the end of period t(note that lost sales may o