An operational policy for a three-stage distributive supply chain system with retailers’ backorders

This research deals with a production-inventory problem consisting of three-stage tree-type single-producer multi-distributor and multi-retailer supply chain network where a model has been developed for achieving the lowest total cost for operating a supply chain system with allowable shortage. In this research, the shortage is assumed to occur in a form of backorder. The refrigerator manufacturing can suitably be used to illustrate the scenario which makes the situation more rational and realistic. By assumptions, the customers will not go somewhere else, the cost of lost sale is not included in this case. The total cost of this tree-type distributive supply chain system is comprised of setup costs and holding costs at all echelons, and the backorder cost at retailer level only. A replenishment policy is sought to operate the system at a minimum cost. The problem is formulated as an unconstrained mixed-integer programming problem and a newly developed doubly hybrid meta-heuristic algorithm is adopted as the solution procedure. The solutions which determine the desired replenishment policy for the producer, distributors, and retailers are obtained to minimize the total system cost. A sensitivity analysis is performed to evaluate the outcome of the proposed solution procedure presented in this research. Numerical results are generated to demonstrate the solution procedure, and future research is indicated for further study.