A combined Inventory and Delivery Model for Repairable Items

Traditionally, logistics analysts have treated the delivery problem separate from the inventory and repair problems. In other words, each of these three problems-delivery, inventory, and repair-are treated individually. We combine the vehicle routing problems and inventory allocation problems in a single formulation. Furthermore, lateral re-supply is considered, in that supplies are not only available from the main depot, but also from other bases. After we get the lateral re-supply information, we set a delivery allocation plan out of the main depot. Such allocations are then delivered via vehicles stationed at the main depot. There is a repair capability for each base other than the main depot as well. There is a newsboy inventory-cost function associated with each base to the every other base. We set up a model for repairable items only. Each base has two Options: accept the repairable items, or deliver the repairable items, but not both. If the base chooses the accept Option, we make sure that base has used all its available resources, initial inventoried items and repair capabilities, before it receives re-supplies. In the transportation/delivery submodel, we place limitation on the crew duty hours available. The objective function is to satisfy the demands by minimizing traveling cost and inventory cost. We solve the same problem by using a generalized Benders decomposition technique. The decomposition allows us to attack larger problems and use general failure and repair functions familiar to logistics analysts. Computational experience suggests that efficiency is achieved by combining the delivery and inventory functions. Lateral re-supply and computational efficiency is particularly useful in emergency situations