Optimal control of a production inventory system with deteriorating items

Tadj, Lotfi; Bounkhel, Messaoud; Benhadid, Yacine

doi:10.1080/00207720601014123

Cited by 32 publications

(19 citation statements)

References 16 publications

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“…In such study, the optimal inventory levels and rate of continuous supply were derived. The problem for controlling a production inventory model for both ameliorating and deteriorating items was studied by Tadj, Sarhan, and El-Gohary (2008). The necessary optimality conditions were derived using the Pontryagin maximum principle.…”

Section: Introductionmentioning

confidence: 99%

Optimal control of production-maintenance system with deteriorating items, emission tax and pollution R&D investment

2013

International Journal of Production Research

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It is widely acknowledged today that the control and maintenance of production inventories of deteriorating items have attracted much attention in inventory analysis because most physical goods deteriorate over time. In 2012, Bukhari and El-Gohary modelled an optimal control model of production-maintenance system with deteriorating items, and derived the optimal scheduled production rate and preventive maintenance rate. In this paper, we propose an alternative emission tax policy design, and extend the model of Bukhari and El-Goharys to an even more general model in which the emission tax and pollution R&D investment are taken into account. Our aim is to apply optimal control theory to solve the production-maintenance problem with deteriorating items, emission tax and pollution R&D investment; and derive the optimal schedule production rate, preventive maintenance rate and pollution R&D investment rate that minimise the total cost. The results are discussed with some illustrative examples for different demand rate and obsolescence rate of process performance in the absence of maintenance, and sensitivity analysis is conducted to study the effect of changing the parameters and coefficients on the objective function value.

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Section: Introductionmentioning

confidence: 99%

Optimal control of production-maintenance system with deteriorating items, emission tax and pollution R&D investment

2013

International Journal of Production Research

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“…Mandal et al [8] have formulated and solved a deterministic inventory model for ameliorating items considering partial selling and linear price dependent demand. Tadj et al [9] have considered a production inventory model for both ameliorating and deteriorating items. However, the above inventory models for both ameliorating and deteriorating items assume that during stockout either all demand is backlogged or all is lost.…”

Section: Introductionmentioning

confidence: 99%

The Influences of Inflation and Time-Value of Money on an EOQ Model for Both Ameliorating and Deteriorating Items with Partial Backlogging

2008

2008 4th International Conference on Wireless Communications, Networking and Mobile Computing

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Both amelioration and deterioration effects are seen simultaneously for the inventory system with the items such as broiler, duck, pig, etc. in the poultry farm, highbred fishes in pond. When these items are kept in the farm or in the sales counter, they will increase in value due to their growth, and decrease in value due to feeding expenses and/or diseases. This paper presents an inventory model for both ameliorating and deteriorating items, with constant demand, taking into account inflation and time-value of money. The economic order quantity is determined for minimizing the average total cost per unit time.In the present inventory model, six costs are considered: holding cost, deterioration cost, purchasing cost, amelioration cost, shortage cost, opportunity cost due to lost sales. An optimal production policy is analytically derived. The problem in the present inventory model cannot be directly solved in a closed form. Therefore, the Mathematica software, which can perform symbolic as well as numerical analysis, has been used to minimize the average total cost per unit time and to find the optimal order quantities. The influences of inflation and time-value of money on the inventory system are investigated with the help of some numerical examples.

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“…The optimal expected inventory level was derived from the condition of the stochastic optimal control principle. The problem for controlling a production inventory model for both ameliorating and deteriorating items was studied by Tadj et al (2008). The necessary optimality conditions were derived using the pontryagin maximum principle.…”

Section: Introductionmentioning

confidence: 99%

Optimal control of a production-maintenance system with deteriorating items

Bukhari

El-Gohary

2012

Journal of King Saud University - Science

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A production process whose performance deteriorates over time is studied in this paper. It is assumed that the process performance can be measured in terms of the proportion of good units of end items produced. Using the pontryagin principle, the optimal scheduled production rate and preventive maintenance rate will be derived as a function of both production rate and proportion of good units. The controlled system can be modeled by a system of non-linear differential equations and its solution will be discussed numerically. The sensitivity analysis for varying system parameters will be discussed for different cases of demand rate.

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Optimal control of a production inventory system with deteriorating items

Cited by 32 publications

References 16 publications

Optimal control of production-maintenance system with deteriorating items, emission tax and pollution R&D investment

Optimal control of production-maintenance system with deteriorating items, emission tax and pollution R&D investment

The Influences of Inflation and Time-Value of Money on an EOQ Model for Both Ameliorating and Deteriorating Items with Partial Backlogging

Optimal control of a production-maintenance system with deteriorating items

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