Annals of Management Science


We develop a model for production-distribution and transportation planning in flexible multi echelon supply chains. When solved, the model produces the optimal quantity of each product to be produced at each plant in each period, transported from each plant to each distribution centre (DC) in each period, shipped from each DC to each retailer in each period, transported directly from some plants to some retailers in each period, kept in inventory at each plant and at each DC in each period, and subcontracted at each DC in each period. It also produces the optimal amount of extensions needed at each DC. The model provides two ways for shipping finished goods to retailers, namely: shipments from plants to retailers via the DCs, and direct shipment from plants to retailers. Three sets of numerical examples were given to test and illustrate the model. The first set of numerical examples show that the model works very well and that it produces good results. The second set show that using a single model to optimize all SC key components simultaneously can greatly enhance supply-chain efficiency. The third set of examples involve small-, medium-, and large-scale problems whose numbers of variables and constraints range from 2791 to 59591 and 1121 to 11306 respectively. The results of the solutions to the problems show that our model will produce good results if applied to any real world SC problem of any size – small, medium, or very large. The results also show that the CPLEX optimizer will be useful for solving the model if applied to solve real world large-scale SC problems.