Modelling and Analysis of Multi-period Distribution-Allocation Problem in a Two-Stage Supply Chain

A supply chain has a network structure and all the production-distribution decisions involve several variables and constraints which vary both quantitatively and qualitatively. Mostly, production and distribution functions are managed independently, with little or no coordination which results in huge inventory holding costs and backorder costs. Hence, supply chains are exploring strategies to reduce the inefficiencies and the redundancies along the manufacturing/distribution channel, which can eventually lead to a closer coordination between the various supply chain partners. One such strategy is to effectively allocate the downstream entities to the upstream entities. Hence, this paper considers a multi-period distribution-allocation problem(MPDAP) subjected to backorder and inventory constraints. It's mathematical formulation is difficult to solve due to the presence of fixed costs which causes nonlinearities in the objective function. The MPDAP is known to be Non-deterministic Polynomial-time hard problem. The complexity of the problem increases as and when more constraints are imposed into the model and problem size increases. In this work, an MPDAP is solved using an Ant colony optimization based heuristic to get a near-optimal solution. The proposed heuristic has been evaluated for the solution robustness by comparing it with that obtained using LINGO solver. A range of problem instances were considered in which suppliers, customers and time-periods were varied from 2-8. The percentage deviation of ACO cost from optimal solution obtained from LINGO was around 2%.