A Branch and Bound Algorithm Based on DC Programming and DCA for Strategic Capacity Planning in Supply Chain Design for a New Market Opportunity

This paper addresses the problem of supply chain design at the strategic level when production/distribution of a new market opportunity has to be launched in an existing supply chain. The new market opportunity is characterized by a deterministic forecast expected to occur per period. The product (or service) is assumed to be produced (or provided) in a three-stage capacitated supply chain where the first stage concerns suppliers, the second stage producers and the final stage customers. There could be multiple alternatives at each stage which are defined as nodes. Nodes in each stage are connected to the next stage through capacitated transportation systems. Production capacity at the second stage (i.e. producers) are also limited since they may already be involved in other existing activities. The objective is to perform strategic capacity planning in the supply chain in order to meet the demand of the new opportunity at minimal cost. A linear running cost is associated with each node. If the decision is to increase the capacity of a node, then a fixed cost applies, followed by a cost that is proportional to the additional capacity. The overall problem can be modelled as a large-scale mixed integer linear programming problem. A solution algorithm is developed to overcome difficulties associated with the size of the problem and is tested on empirical data sets. The overall contribution is an analytical tool that can be employed by managers responding to the new market opportunity at the strategic level for supply chain design.