Abstract
We develop a two-warehouse production model with imperfect items. Production rate is taken as the linear combination of on-hand inventory and demand, while demand rate is taken as function of time. Most of the researchers consider that the production rate is independent from the demand rate. In this paper we assume production rate as being dependent on the demand rate, and this assumption is more realistic. Shortages are allowed and partially backlogged with time-dependent backlogging rate. Due to different preservation facilities we consider that the deterioration rate is time dependent in own warehouse (OW) and Weibull distribution deterioration in rented warehouse (RW). Holding cost in RW is greater than in OW. We developed a fuzzy model with fuzzifying all the costs of the model as triangular fuzzy numbers. The present model is developed in both crisp and fuzzy senses. Finally, numerical example is shown, and sensitivity is also illustrated.
Highlights
One of the weaknesses of some production-inventory models is the unrealistic assumption that all items produced are of good quality
I Production rate is greater than the demand rate. ii Production rate is the linear combination of on-hand inventory and demand rate. iii Demand rate is exponentially an increasing function of time. iv Model is considered for imperfect items. v Deterioration is taken as time dependent for OW, while, Weibull distribution for RW. vi Inflation is taken in this model. vii Costs are considered as a triangular fuzzy numbers. viii Model is presented in both fuzzy and crisp senses
This paper presented a warehouse imperfect production-inventory models for deteriorating items having time varying demand patterns with Weibull distribution deterioration and partial backlogging under the effect of inflation and time value of money
Summary
One of the weaknesses of some production-inventory models is the unrealistic assumption that all items produced are of good quality. R. Singh 4 developed an imperfect production process with exponential demand rate, Weibull deterioration under inflation. Yao and Chiang 8 considered an inventory model with total demand and storing cost as triangular fuzzy numbers. They performed the defuzzification by centroid and signed distance methods. Halim et al developed a fuzzy inventory model for perishable items with stochastic demand, partial backlogging, and fuzzy deterioration rate. Lee and Yao developed an economic production quantity EPQ model in which the demand and the production quantity are assumed to be fuzzy. Halim et al addressed the lot sizing problem in an unreliable production system with stochastic machine breakdown and fuzzy repair time They defuzzified the cost-per-unit time using the signed distance method. I Production rate is greater than the demand rate. ii Production rate is the linear combination of on-hand inventory and demand rate. iii Demand rate is exponentially an increasing function of time. iv Model is considered for imperfect items. v Deterioration is taken as time dependent for OW, while, Weibull distribution for RW. vi Inflation is taken in this model. vii Costs are considered as a triangular fuzzy numbers. viii Model is presented in both fuzzy and crisp senses
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