A New Approach to an Inventory with Constant Demand

Abstract

An inventory with constant demand is studied. We adopt a renewal argument to obtain the transient and stationary distribution of the level of the inventory. We show that the stationary distribution can be also derived by making use of either the level crossing technique or the renewal reward theorem. After assigning several managing costs to the inventory, we calculate the long-run average cost per unit time. A numerical example is illustrated to show how we optimize the inventory.

Keywords

• Inventory with constant demand;
• Level crossing technique;
• Long-run average cost;
• Poisson process;
• Renewal argument