A stochastic inventory model with stock dependent demand items

Lakdere Benkherouf,Amin Boumenir,Lakhdar Aggoun

doi:10.1155/s1048953301000284

Lakdere Benkherouf, Amin Boumenir + Show 1 more

Open Access

https://doi.org/10.1155/s1048953301000284

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Abstract

In this paper, we propose a new continuous time stochastic inventory model for stock dependent demand items. We then formulate the problem of finding the optimal replenishment schedule that minimizes the total expected discounted costs over an infinite horizon as a Quasi-Variational Inequality (QVI) problem. The QVI is shown to have a unique solution under some conditions.

Highlights

This paper discusses a single item continuous time stochastic inventory model for stock dependent demand terms
There are some simple EOQ deterministic models such as Datta and Pal [3], Coswami and Chaudhuri [4] but no attempt has been made to incorporate this principle in continuous time stochastic inventory model due to the technical complication that arises from the inclusion of the stock dependent demand items
The solution to the Quasi-Variational Inequality (QVI) given by problem (6) is continuous differentiable and continuity at the boundary point s gives from (8) that y’(s) -c

Summary

Sultan Qaboos University

We propose a new continuous time stochastic inventory model for stock dependent demand items. We formulate the problem of finding the optimal replenishment schedule that minimizes the total expected discounted costs over an infinite horizon as a Quasi-Variational Inequality (QVI) problem. The QVI is shown to have a unique solution under some conditions.

Introduction

Let A and M be two operators defined by

The above implies

The first iteration gives

Consider the differential equation