Inventory Models with Alternative Delivery Lead times, Demand Backlogging, and Priority Rules

A supplier has a periodic review inventory system that provides several lead-time options to its customers. The inventory replenishment lead time is a multiple of the inventory review cycle. Customers are classified into two groups: short lead-time customers requiring the product immediately and long lead-time customers who allow the supplier the flexibility to deliver immediately or in the next cycle. We consider an inventory-commitment problem, in which the supplier allocates its on-hand inventory to these two groups of customers. When inventory runs out, the supplier backlog orders to future cycles. Therefore, the supplier faces two problems: how the onhand inventories are allocated between two classes of customers and how the backlogged orders are cleared when replenishments arrive? We consider the former as an inventory-commitment problem, and resolve the latter with priority rules. We formulate the inventory commitment decision as a dynamic programming problem, and study three priority rules in clearing backlogs. We also explore the optimal inventory replenishment issue and evaluate the performance of the models.