Three Approaches to Find Optimal Production Run Time of an Imperfect Production System

Ai, The Jin and Astanti, Ririn Diar and Bintoro, Agustinus Gatot and Wibowo, Thomas Indarto (2013) Three Approaches to Find Optimal Production Run Time of an Imperfect Production System. In: Institute of Industrial Engineers Asian Conference 2013, 2013, Institute of Industrial Engineers.

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Abstract

This paper considers an Economic Production Quantity (EPQ) model where a product is to be manufactured in batches on an imperfect production system over infinite planning horizon. During a production run of the product, the production system is dictated by two unreliable key production subsystems (KPS) that may shift from an in-control to an out-of-control state due to three indepen- dent sources of shocks. A mathematical model describing this situation has been developed by Lin and Gong (2011) in order to determine production run time that minimizes the expected total cost per unit time including setup, inventory carrying, and defective costs. Since the optimal solution with exact closed form of the model cannot be obtained easily, this paper considered three approaches of finding a near-optimal solution. The first approach is using Maclaurin series to approximate any exponential function in the objective function and then ignoring cubic terms found in the equation. The second approach is similar with first approach but considering all terms found. The third approach is using Golden Section search directly on the objective function. These three approaches are then compared in term computa- tional efficiency and solution quality of through some numerical experiments.

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