Optimal (s,S) policies for inventory systems with a maximum issue quantity restriction
"OPTIMAL (s,S) POliCIES FOR INVENTORY SYSTEMS WITH A MAXIMUM ISSUE QUANTITY RESTRICTION"
submitted by LAI KAM-KEUNG, B.Sc. (mg.) (Hons.)
for the degree of Doctor of Philosophy
at The University of Hong Kong in November 1994.
The objective of this research is to analyse inventory systems for organizations which have the alternative of satisfying a customer order from inventory or by scheduling a special replenishment order and shipping the goods from the supplier directly to the customer, thus bypassing the inventory system. A maximum issue quantity restriction is incorporated such that customer orders with sizes not exceeding the maximum issue quantity will be satisfied routinely from the inventory. Otherwise, they will be filtered out of the :inventory system and will be met
by spedal orders so as to avoid disru.pting the inventery system.
In this research, mathematical models are developed for the synthesis of control policies with the incorporation of a maximum issue quantity, w. In the formulation of the basic model, the continuous review
(s,S) .tlver::::cry policy is adopted as the control disr';pline. The d~!!land
pattern is governed by a discrete compound Poisson distribution. It is assumed that the replenishment order takes a constant and known lead time to arrive, and demands during the stockout period are completely backordered. In the analysis, the characteristics of the total inventory cost function with respect to the control parameters, w, s and S, are studied in detail. Based on the theoretical results acquired, an algorithm is developed for the joint determination of the optimal control parameters. Theoretical tesults obtained are elucidated by using numerical examples. Sensitivity analysis is conducted to examine the effects of changes in cost and system parameters on the optimal solution. Particular attention is also paid to the
case that the demand pattern follows a stuttering Poisson distribution. A simple algorithm is developed to determine the optimal solution.
The basic models are then extended to consider the case that when a critical level, A, is also incorporated into the control policy to facilitate the replenishment of inventory. When a large customer order with a transaction size greater than the maximum issue quantity arrives and the current inventory position is equal to or lower than A, a joint replenishment order is placed such that the replenishment order will not only initiate a direct shipment to the customer, meeting the correct ~mount required, but will also raise the inventory position to the maximum inventory level, 5. The characteristics of the total inventory cost function vvith respect to the control parameters, w, A, s and 5, are studied. Algorithms are also developed for determining the optimal values of the control parameters. The theoretical results acquired are exemplified. In particular, when the demands are stuttering Poisson distributed, simple formulae are derived for determining the stationary probabilities of the inventory positions.
School:The University of Hong Kong
School Location:China - Hong Kong SAR
Source Type:Master's Thesis
Keywords:inventory control mathematical models
Date of Publication:01/01/1995