Abstract
Typically, traditional inventory models operate under the assumption of perfect quality. In this paper we modify an inventory model with finite-range stochastic lead time to allow for a random number of defective units in a lot. However, there is an extra cost for holding the defective items in the lot for the period before it is returned to the supplier. This paper also considers the option of investment to improve quality. Closed-form relationships are obtained for a quality-adjusted model as well as a quality improvement model. Numerical examples confirm that the option of investment in quality improvement results in significant cost savings. Sensitivity analysis shows that the quality improvement model is robust.
Highlights
Lot size research owes its beginnings to the traditional square root EOQ formula
Javad Paknejad et al 179 where D = demand per unit time, K = setup cost per setup, h = holding cost per unit per unit time, p = backorder cost per unit per unit time, AC(q,t) = expected average cost per unit time, Q = lot size per order, q = Q/D = number of time units of demand satisfied by each order, t = time differential between placing an order and the start of q time units that will be satisfied by a given order, r = lead time in units of time, g(r) = lead-time probability density function, α = lower bound of lead-time distribution, β = upper bound of lead-time distribution, μ = mean of lead-time distribution
(b) The resulting approximately optimal number of time units of demand satisfied by each order, qi∗mp, and the approximately optimal time differential between placing an order and the start of qi∗mp time units that will be satisfied by a given order, ti∗mp, are given by qi∗mp =
Summary
Lot size research owes its beginnings to the traditional square root EOQ formula. This relationship is the result of classical optimization of inventory related costs under a series of highly restrictive assumptions. The optimal lot size is intuitively appealing since it indicates an inverse relationship between lot size and process capability While this previous work relaxes the perfect quality assumption, it considers demand to be deterministic. Paknejad et al [7] present a quality-adjusted lot-sizing model with stochastic demand and constant lead-time They investigate the case of continuous review (s,Q) models in which an order of size Q is placed each time the inventory position (based on nondefective items) reaches the order point s. Heard and Plossl [4] portray high lead-time variability as a major reason for a plant’s inability to achieve inventory goals, and to incur longer average throughput This suggests that it would be worthwhile to investigate the relationship between quality and lead-time variability, and their impact on lot size and inventory cost. The purpose of this paper is to begin the analytical investigation of these relationships
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