Inventory models with a mixture of backorders and lost sales

Abstract

This article presents several single-echelon, single-item, static demand inventory models for situations in which, during the stockout period, a fraction b of the demand is backordered and the remaining fraction 1 -b is lost forever. Both deterministic and stochastic demand are considered. although the caae of stochaatic demand is treated heuristically. In each situation, a mathematical model representing the average annual cost of operating the inventory system is developed. and an optimum operating policy derived. At the extremes b=l and b=O the models presented reduce to the usual backorders and lost sales cases, respectively.

Greenhouse gas penalty and incentive policies for a joint economic lot size model with industrial and transport emissions

“…Therefore, the buyer's expected holding cost per unit time is 2 ⁄ . Using the same approach as in Montgomery et al (1973), the expected net inventory level just before receipt of a delivery is 1 . The expected shortage quantity at the end of the cycle is given by √ , where, 1 , and Ø, Φ denote the standard normal density function (p.d.f) and c.d.f., respectively.…”

A Partial Backlogging Inventory Model with Time-Varying Demand During Shortage Period

“…A common characteristic of this model is the assumption that the percentage of orders arriving during the stockout period that will be backordered is exogenously determined. Montgomery et al [4],Rosenberg [5],Park [6],San Joséet al [7,8]and Pentico and Drake [9]all developed EOQ models with a constant backordering percentage. Montgomery et al and San Joséet al also developed models in which the backordering percentage depends on the time to replenishment.…”

A good approximation of the inventory level in a (Q, r) perishable inventory system

“…Now, the total expected average cost per unit time for the full backorder case is given by (16) where is one of the above four approximations. It is noted that , as given in equation (10), is also a function of the current order size, , and the reorder point,…”

“…Later, Das [5] introduced a inventory model with time-weighted (time-proportional) backorders. Several inventory models with a mixture of backorders and lost sales were proposed by Posner and Yansouni [16], Montgomery et al [10], Matthews [9], Rosenberg [19], Park [15] and Kin and Park [7]. Almost all the previous research works used , a fraction of the unsatisfied demand backordered (the remaining fraction 1-completely lost), to model partial backorders.…”