A stochastic inventory model with stock dependent demand items

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.

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ON A STOCHASTIC INVENTORY MODEL WITH DETERIORATION AND STOCK-DEPENDENT DEMAND ITEMS

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964802162024 ◽

2002 ◽

Vol 16 (2) ◽

pp. 151-165 ◽

Cited By ~ 8

Author(s):

Lakdere Benkherouf ◽

Lakhdar Aggoun

Keyword(s):

Impulse Control ◽

Infinite Horizon ◽

Inventory Model ◽

Algebraic Equations ◽

Expected Return ◽

Stochastic Inventory ◽

Stochastic Inventory Model ◽

Stock Dependent Demand ◽

Optimal Impulse ◽

Dependent Demand

In this article, we propose a new continuous-time stochastic inventory model with deterioration and stock-dependent demand items. We then formulate the problem of finding the optimal impulse control schedule that minimizes the total expected return over an infinite horizon, as a quasivariational inequality (QVI) problem. The QVI is shown to lead to an (s, S) policy, where s and S are determined uniquely as a solution of some algebraic equations.

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A stochastic inventory model for an immediate liquidation and price-promotion decision under price-dependent demand

International Journal of Production Research ◽

10.1080/00207543.2014.990233 ◽

2014 ◽

Vol 53 (12) ◽

pp. 3789-3809 ◽

Cited By ~ 10

Author(s):

Xiaoyan Zhu ◽

Sila Cetinkaya

Keyword(s):

Inventory Model ◽

Price Promotion ◽

Stochastic Inventory ◽

Stochastic Inventory Model ◽

Dependent Demand

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Stochastic inventory model with income and price dependent demand

International Journal of Procurement Management ◽

10.1504/ijpm.2019.102156 ◽

2019 ◽

Vol 12 (5) ◽

pp. 606

Author(s):

R.H. Waliv ◽

H.P. Umap

Keyword(s):

Inventory Model ◽

Stochastic Inventory ◽

Stochastic Inventory Model ◽

Dependent Demand

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Stochastic Inventory Model with Income and Price Dependent Demand

International Journal of Procurement Management ◽

10.1504/ijpm.2019.10019242 ◽

2019 ◽

Vol 1 (1) ◽

pp. 1

Author(s):

Hemant Umap ◽

Rahul Waliv

Keyword(s):

Inventory Model ◽

Stochastic Inventory ◽

Stochastic Inventory Model ◽

Dependent Demand

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A Stochastic Inventory Model with Quality-Dependent Demand

Calcutta Statistical Association Bulletin ◽

10.1177/0008068319970307 ◽

1997 ◽

Vol 47 (3-4) ◽

pp. 215-222

Author(s):

G. Mohan Naidu ◽

K. V. S. Sarma

Keyword(s):

Inventory Model ◽

Optimal Order ◽

Stochastic Inventory ◽

Stochastic Inventory Model ◽

Demand Rate ◽

Optimum Cost ◽

Quality Material ◽

Theoretical Results ◽

Dependent Demand

This paper deals with an inventory model in which the demand rate is influenced by the quality of the material received . The case considered is a situation in which the consumption rate is adjusted whenever the incoming material does not have the desired quality but still usable. This leads to uncertainity in the inventory cycle and may create unplanned shortages. The model takes into account differential prices of the material based on quality. The behaviour of the optimal order level and the optimum cost has been studied as a function of the probability with which good quality material can be received. Numerical illustrations are given in support of the theoretical results.

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Optimal policies for a deterministic continuous-time inventory model with several suppliers

RAIRO - Operations Research ◽

10.1051/ro/2020037 ◽

2020 ◽

Author(s):

Lakdere Benkherouf ◽

Brian Gilding

Keyword(s):

Unique Solution ◽

Continuous Time ◽

Infinite Horizon ◽

Planning Horizon ◽

Inventory Model ◽

Inventory Level ◽

Discounted Cost ◽

Continuous State ◽

Quasi Variational Inequality ◽

Necessary And Sufficient

This paper is concerned with determining the optimal inventory policy for an infinite-horizon deterministic continuous-time continuous-state inventory model, where, in the absence of intervention, changes in inventory level are governed by a differential evolution equation. The decision maker has the option of ordering from several suppliers, each of which entails differing ordering and purchasing costs. The objective is to select the supplier and the size of the order that minimizes the discounted cost over an infinite planning horizon. The optimal policy is formulated as the solution of a quasi-variational inequality. It is shown that there are three possibilities regarding its solvability: it has a unique solution that corresponds to an $(s,S)$ policy; it does not admit a solution corresponding to an $(s,S)$ policy but does have a unique solution that corresponds to a generalized $(s,S)$ policy; or, it does not admit a solution corresponding to an $(s,S)$ policy or a generalized $(s,S)$ policy. A necessary and sufficient condition for each possibility is obtained. Examples illustrate their occurrence.

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