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## South African Journal of Industrial Engineering

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*On-line version* ISSN 1012-277X

### S. Afr. J. Ind. Eng. vol.21 n.1 Pretoria 2010

**GENERAL ARTICLES**

**Two-commodity perishable inventory system with bulk demand for one commodity**

**V.S.S. Yadavalli ^{I}; O. Adetunji^{II}; B. Sivakumar^{III}; G. Arivarignan^{IV}**

^{I}Department of Industrial & Systems Engineering, University of Pretoria, South Africa, sarma.yadavalli@up.ac.za

^{II}Department of Industrial & Systems Engineering, University of Pretoria, South Africa, olufemi.adetunji@up.ac.za

^{III}Department of Applied Mathematics and Statistics, Madurai Kamaraj University, India sivabkumar@yahoo.com

^{IV}Department of Applied Mathematics and Statistics, Madurai Kamaraj University, India, arivarignan@yahoo.com

**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.

**“Full text available only in PDF format”**

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