# A Scenario-Based Heuristic for a Capacitated Transportation-Inventory Problem with Stochastic Demands

## Abstract

A single-period multi-warehouse multi-retailer system with uncertain demands at the retailers and finite capacities at the warehouses is considered. The problem is to determine shipment sizes from each warehouse to each retailer at minimium costs. The cost components are the expected overage and underage costs at the end of the period, as well as the transportation costs corresponding to the shipments. The transportation costs have a fixed-charge structure. A scenario-based approach is proposed, and the corresponding approximating problem is solved by a generalization of the Dynamic Slope Scaling Procedure, which has been developed as a heuristic for fixed-charge network flow problems. The performance of the heuristic is tested by comparing to the optimal solution to the scenario-problem, as well as to a lowerbound on the true optimal costs.

## Keywords

Capacitated transportation/inventory problem fixed charge costs global optimization heuristics supply chain optimization## Preview

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