An Analysis of Inventory and Transportation Costs in a Constrained Network

The need to minimize inventory, production and transport costs has long been recognized by operations researchers. Traditionally, stages in materials handling have been optimized separately. This paper analyzes the complete materials handling process from production at supply points to consumption at demand points. Reasonable assumptions are made concerning production, inventory and transport costs along with production constraints and demand requirements. A local optimum is found using a generalized reduced gradient algorithm. Initial upper and lower bounds to the solution are also derived and a heuristic is introduced which finds a solution using linear network algorithms. The reduced gradient algorithm and the heuristic are applied to a hypothetical corporate sourcing problem. The problem is a small subset of the problem of acquiring and distributing new items. Results of this analysis show that for certain cases, the value of the reduced gradient algorithm solution is very close to the value of the lower bound and that there is a substantial improvement (as high as 21%) over the separate optimization solution. It is further found that the heuristic provides similar solutions to the reduced gradient algorithm but at much greater computational efficiency. It is concluded that simultaneous optimization should be considered when inventory and transport strategies are developed and that the overall advantage of simultaneous optimization depends on the magnitude of the parameters.