Abstract
This article considers a two-commodity continuous review inventory system in which the arriving customers belong to any one of three types, such that type 1 customers demand a single item of the first commodity, type 2 customers demand bulk items of the second commodity, and type 3 customers demand one item of the first commodity and bulk items of the second commodity. The arrivals of all three types of customers are assumed to be a Markovian arrival process (MAP). It is also assumed that the number of items demanded for the second commodity is a random variable. The ordering policy is to place orders for both commodities when the inventory levels are below prefixed levels for both commodities. The lead time is assumed to have a phase type distribution, and the demands that occur during stock out period are assumed to be lost. The joint probability distribution for both commodities is obtained in the steady state case. Various measures of system performance and the total expected cost rate in the steady state are derived. The results are illustrated with numerical examples. OPSOMMING ’n Tweeprodukstelsel se voorraad vir klante word kontinu hersien. Die vraag na die produktipes word gekenmerk deur klantvoorkeure. Die versoektempo van klante vir voorraad word aanvaar as ’n Markovproses. Aannames word gemaak oor vraaghoeveelhede en aanlooptyd. Die resultate van die ondersoek word voorgehou via syfervoorbeelde.
Highlights
One of the factors that contribute to the complexity of present day inventory systems is the multitude of items stocked, necessitating multi-commodity inventory systems
In continuous review inventory systems, Balintfy [6] and Silver [31] have considered a coordinated re-ordering policy, represented by the triplet (S, c, s), where three parameters, Si,ci and si are specified for each item i with si ci Si, for a unit sized Poisson demand and constant lead time
A further article of interest is that of Federgruen et al [9], which deals with the general case of compound Poisson demands and non-zero lead times
Summary
One of the factors that contribute to the complexity of present day inventory systems is the multitude of items stocked, necessitating multi-commodity inventory systems. In continuous review inventory systems, Balintfy [6] and Silver [31] have considered a coordinated re-ordering policy, represented by the triplet (S, c, s) , where three parameters, Si,ci and si are specified for each item i with si ci Si , for a unit sized Poisson demand and constant lead time. A seller may not be willing to place orders frequently, and may prefer to have one order to replenish stock in a given cycle These situations are modelled in this work by assuming demand processes that require a single item for one commodity, multiple items for the other commodities, or both commodities, and by assuming a joint re-order for both commodities.
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