Abstract
This paper describes how to control the inventory production system with Weibull distributed deterioration items. The model is solved by two methods and a comparison between them is conducted. In the first method the model is solved using the control theory approach. In the second method the model is discretized then the Dynamic Programming (DP) technique is applied. The advantage of second method is easier than the first method in computational and its accuracy can be improved by increasing the number of discretization intervals (sampling).
Highlights
This paper describes how to control the inventory production system with Weibull distributed deterioration items
In this paper we compare between linear quadratic control (LQC) and dynamic programming(DP)
Due to using discretization to convert continuous time system to discrete time system LQC is more exact than Dynamic Programming (DP) but more complex in computational than DP. (Emamverdi 2011) presented optimal control of production inventory system with deteriorating items in which the deteriorating rate follows the Weibull distribution
Summary
(Zaher 2013) Optimal Control theory becomes very useful tool to solve dynamic inventory and production problems .The production system consists of manufacturing plant and finished goods in warehouse to store those products which are fabricated but not at once sold. The paper considered the case of three control variables, the manufacturing, and remanufacturing and disposal rates He used The Pontryagin's minimum principle to find the optimum control of the Holt, Modigiliani, Muth and Simon (HMMS) reverse logistics model of production inventory system with deteriorating items. (Adida, 2007) Investigated a continuous time optimal control model for a dynamic pricing and inventory system problem with no backorders They presented a continuous time solution approach using Pontryagin’s Principle for state-constrained problems. They illustrated the role of capacity and of the dynamic nature of demand in the model.( Yang 2006) Defined the deterioration as obsolescence decay, damage, spoilage, evaporation, , pilferage and loss of marginal value or looses of entity of a product that affect on decreasing usefulness from original one.
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