Design of cost allocation rule for joint replenishment with controllable lead time

To encourage retailers to form cooperative alliances to jointly replenish inventory,considering that the supplier provides a flexible lead time and quantity discount to retailers,a model of average total cost per unit time of periodic joint replenishment is constructed,and an approximate algorithm,which can satisfy the requirement of any given precision,is given.The cost allocation rule in the core of the joint replenishment game is designed based on the cooperative game theory.The numerical experiment results show that the proposed algorithm can quickly solve the joint replenishment problem when the item number is not greater than 640.The retailer's cost saving rate is always greater than 0,and it increases with the increase in quantity discount and fixed cost after adopting the given cost allocation rule.With the increase in the safety stock level,the retailer's cost saving rate increases first and then decreases;and the retailer's cost saving rate increases with the increase in the size of the alliance,but it decreases as the number of product category increases.The proposed cost allocation rule can reduce the retailer's cost up to 20%,which is conducive to forming a cooperative coalition.

Stochastic Joint Replenishment Optimization under Joint Inbound Operational Cost

With e-commerce concentrating retailers and customers onto one platform,logistics companies(e.g.,JD Logistics)have launched integrated supply chain solutions for corporate customers(e.g.,online retailers)with warehousing,transportation,last-mile delivery,and other value-added services.The platform’s concentration of business flows leads to the consolidation of logistics resources,which allows us to coordinate supply chain operations across different corporate customers.This paper studies the stochastic joint replenishment problem of coordinating multiple suppliers and multiple products to gain the economies of scale of the replenishment setup cost and the warehouse inbound operational cost.To this end,we develop stochastic joint replenishment models based on the general-integer policy(SJRM-GIP)for the multi-supplier and multi-product problems and further reformulate the resulted nonlinear optimization models into equivalent mixed integer second-order conic programs(MISOCPs)when the inbound operational cost takes the square-root form.Then,we propose generalized Benders decomposition(GBD)algorithms to solve the MISOCPs by exploiting the Lagrangian duality,convexity,and submodularity of the sub-problems.To reduce the computational burden of the SJRM-GIP,we further propose an SJRM based on the power-of-two policy and extend the proposed GBD algorithms.Extensive numerical experiments based on practical datasets show that the stochastic joint replenishment across multiple suppliers and multiple products would deliver 13∼20%cost savings compared to the independent replenishment benchmark,and on average the proposed GBD algorithm based on the enhanced gradient cut can achieve more than 90%computational time reduction for large-size problem instances compared to the Gurobi solver.The power-of-two policy is capable of providing high-quality solutions with high computational efficiency.

Developing a multi-objective,multi-item inventory model and three algorithms for its solution

We develop a multi-objective model in a multi-product inventory system.The proposed model is a joint replenishment problem(JRP) that has two objective functions.The first one is minimization of total ordering and inventory holding costs,which is the same objective function as the classic JRP.To increase the applicability of the proposed model,we suppose that transportation cost is independent of time,is not a part of holding cost,and is calculated based on the maximum of stored inventory,as is the case in many real inventory problems.Thus,the second objective function is minimization of total transportation cost.To solve this problem three efficient algorithms are proposed.First,the RAND algorithm,called the best heuristic algorithm for solving the JRP,is modified to be applicable for the proposed problem.A multi-objective genetic algorithm(MOGA) is developed as the second algorithm to solve the problem.Finally,the model is solved by a new algorithm that is a combination of the RAND algorithm and MOGA.The performances of these algorithms are then compared with those of the previous approaches and with each other,and the findings imply their ability in finding Pareto optimal solutions to 3200 randomly produced problems.