Optimal Control Strategy Of Service-Inventory System

The service-inventory system refers to the need for both inventory and active service time to meet customer needs.Unlike the classic inventory system,the service-inventory system represents a service system with additional inventory,and an inventory system with a positive service time.Classic inventory systems assume negligible time to process inventory,while in a service-inventory system,time to process inventory is considered an integral part of the demand fulfillment process.This paper studies the optimal control strategy of the service-inventory system under different replenishment strategies.The service-inventory system with(r,Q)replenishment strategy is modeled with the M/M/1 queuing system,where the customer arrival rate is related to price.Under the(r,Q)strategy,the system continuously checks the inventory.Considering the system loss sales,we studied the long-term average profit function based on the joint queue length and the steady distribution of inventory when the inventory lead time is Erlang distribution.With the goal of maximizing system profit,construct an optimal control model of system satisfaction rate and service reliability level constraints,and seek an optimal control strategy for service-inventory systems.The structural properties of the objective function are discussed.By proving the convexity of the profit function,the constrained optimization model is solved by genetic algorithm,and the unique maximum value of the profit function and the optimal values of the decision variables r and Q are obtained.The effects of average replenishment lead time,service rate,fill rate and service reliability level on the optimal solution and overall system performance of the service-inventory system described in this paper are discussed.Numerical experiments analyze the sensitivity of the system performance,indicating that the optimal control strategy with Erlang distributed supply lead time can increase the profit of the system.Consider a service-inventory system with a booking strategy.The system is modeled with an M/M/1 queue with lost sales,where the inventory system has Erlang distributed supply lead times.According to the stable distribution of the M/M/1 queue,the steady-state performance index as the system cost control is obtained.A weighted purchase inventory strategy(BTWOS,buy-to-weighted-order-stock)is proposed for optimal booking and inventory control of service-inventory systems.By constructing a service-inventory system model under service level constraints,and with the goal of minimizing system cost,a constrained average cost function optimization model is established and solved.The service-inventory system under BTWOS control strategy is studied.Experiments show that,compared with BTS(buy-to-stock)and BTO(buy-to-order)strategies,BTWOS strategy can effectively coordinate the overall inventory control of the system,reduce the total cost of the system,and improve the actual service level of the system.