Research On Method Of Cost Allocation And Profit Distribution For Joint Replenishment Based On Cooperative Game

Economic globalization makes the competition between enterprises more and more intense,how to reduce costs is an important goal of most enterprises.Many scholars pay attention to the study of inventory replenishment,and joint replenishment as an effective strategy to reduce the cost of replenishment has been paid attention to by scholars.A joint replenishment is the consolidation of orders for multiple products into one order or product orders of multiple purchasers into one order to purchase from the same vendor.Buyers can reduce their inventory replenishment costs by sharing fixed replenishment costs.Multiple buyers form cooperative alliances for joint procurement with the goal of minimizing the total cost of replenishment of cooperative alliances.Multi-buyer alliances for joint replenishment require the willingness of participating purchasers to cooperate,and the distribution of benefits after cooperation will be a key factor affecting the formation of cooperation.A fair and reasonable distribution plan is necessary to facilitate the alliance of cooperation.Therefore,based on the cooperative game theory,this paper designs the cost-sharing scheme for the multi-cycle joint replenishment problem.Considering that suppliers supply multiple products and offer flexible lead times and quantity discounts,retailers form cooperative alliances to jointly replenish inventory to reduce long-run average inventory replenishment costs.Under the condition that the retailer is fully information-sharing,the long-run average cost model of periodic joint replenishment with unlimited time range is constructed to decide on crush cost and replenishment cycle.An approximation algorithm to meet arbitrary accuracy requirements is given,and a cost allocation scheme located in the core of joint replenishment game is designed based on cooperative game theory.The numerical experimental results show that the approximate algorithm can quickly solve the joint replenishment problem with no more than 640 product categories and the error accuracy of 0.0001.Numerical experiments also show the higher fixed cost and quantity discount leads to save more cost after cooperation and the stronger willingness to cooperate.Consider retailers selecting products and making decision on replenishment cycles under inventory capacity and minimum order volume constraints.Once the retailer has identified the purchase product,it reduces the purchase cost by sharing requirements,cost information,and inventory capacity for joint replenishment.Under the condition that retailers sell their products at uniform retail prices,a long-run average profit model of the cooperative alliance is established.Applying the cooperative game theory,the profit allocation scheme when the cooperative alliance inventory capacity is sufficient and insufficient is given respectively,in which the cost allocation scheme located in the cooperative game core is sufficient when the alliance inventory capacity is sufficient,and the cost allocation scheme when the alliance inventory capacity is insufficient is to satisfy individual rationality and collective rationality,and can encourage retailers to share their inventory capacity.Considering the use of third-party overseas positions by cross-border retailers to sell products abroad,small and medium-sized retailers form a joint replenishment to reduce the cost of stock replenishment in overseas warehouses by sharing the fixed costs incurred in logistics transportation and inventory replenishment.The mixed 0-1planning model is established to balance logistics cost and inventory cost,the polynomial time algorithm is designed to solve the model,and the cost allocation scheme is designed by using cooperative game theory.Numerical trials have shown that retailers can reduce costs by up to 30%,and that the more retailers involved,the higher the cost.In response to the high logistics costs of cross-border e-commerce,suppliers selling products to overseas retailers may need to accumulate orders to reduce the logistics costs per unit of product,thus extending the lead time in order to obtain volume discounts from logistics companies.Consider suppliers forming cooperative alliances for joint shipments to reduce logistics costs;Retailers form cooperative alliances to jointly replenish,on the one hand,to share fixed costs,on the other hand,to reach or closer to the supplier’s dispatch quantity to reduce the supplier waiting time for delivery,thereby reducing inventory replenishment costs.For the supplier alliance and the retailer alliance,the decision-making model of joint shipment and joint replenishment is established,respectively,and the cost allocation schemes are designed by applying cooperative game theory.Among them,the cost allocation scheme of supplier joint shipment is located in the core of cooperative game,and the cost allocation scheme of retailer joint replenishment is also located in the core of cooperative game under the given condition.Numerical experiments show that the cost-sharing scheme of joint replenishment by retailers can reduce the cost of retailers.This paper enriches the basic theory in the field of cost allocation scheme design of joint replenishment,broadens its application scope,and provides reference suggestions for how to decide the replenishment cycle of the cooperative alliance and how to allocate the total cost or profit the cooperative alliance.