Question

(Economic Lot Sizing Model) A company must deliver d; units of its product at the end of the ith month. Material produced during a month can be delivered either at the end of the same month or can be stored as inventory and delivered at the end of a subsequent month; however, there is a storage cost of h dollars per month for each unit of product held in inventory. The year begins with zero inventory. In month i, the company decides its production quantity. If it decides to produce, there is a fixed cost K which is independent of the production quantity and an additional cost c per unit referred to as the variable cost. The objective is minimize the total cost of the production and inventory schedule over a period of twelve months. Assume that inventory left at the end of the year has no value and does not incur any storage costs. Let xi be the order quantity and Г the inventory carried over from period i to period i + 1. The relationship of the ordering quantities and inventory levels can be described by the following linear system: 12 12 where Show that the extreme points of the above linear system correspond to ordering and inventory decisions with Žero-Inventory-Ordering (ZIO) property, i.e., no order is placed when there is positive inventory.