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Jurnal: Production Inventory Models for Deteriorating Items with Stochastic Machine Unavailability Time, Lost Sales and Price-Dependent Demand


Abstract: The economic production quantity (EPQ) model is widely employed in reality and is also being intensively developed in the research area. This research tries to develop more realistic EPQ models for deteriorating items by considering stochastic machine unavailability time (uniformly and exponentially distributed) and price-dependent demand. Lost sales will occur when machine unavailability time is longer than the non production time. Since the closed form solution cannot be derived, we use Genetic Algorithm (GA) to solve the models. A numerical example and sensitivity analysis is shown to illustrate the models. The sensitivity analyses show that a management can use price policy to minimize the profit loss due to machine unavailability time under a price- dependent demand situation.


Keywords: EPQ, deteriorating items, machine unavailability time, price-dependent demand.


Introduction
Production inventory models have been intensively investigated and most of the researches try to fit the models to real-world inventory problems. In recent years, many researchers had been trying to develop EPQ models for unreliable production facility since it is difficult to set a reliable facility in reality. Some production facilities face problems on producing the products on the right time and sometimes even defective products are produced. Unreliable production facility might be caused by material unavailability, machine repair or maintenance, and machine breakdown.

Abboud et al. developed EPQ models for unreliable machine where machine is not available when needed due to some problems such as seconddary jobs being processed, materials were unavailable, or the machine is maintained. They assumed the machine unavailability time is uniformly and exponentially distributed. Giri and Dohi developed EPQ models where machine capacity can be determined before the production run and the corrective and preventive maintenance times follow a general distribution. An EPQ model with stochastic machine breakdown, scrap products, and rework process was considered by Chiu et al. El- Ferik developed an EPQ model under preventive maintenance schedule where the production facility is subject to random failure and the maintenance process is imperfect.

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