Fuzzy production inventory model for deteriorating items with shortages under the effect of time dependent learning and
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zzy production inventory model for deteriorating items with shortages under the effect of time dependent learning and forgetting: a possibility / necessity approach Savita Pathak & Samarjit Kar & Seema Sarkar (Mondal)
Accepted: 16 August 2012 / Published online: 20 September 2012 # Operational Research Society of India 2012
Abstract This study investigates the effects of learning and forgetting on the production lot size problems allowing shortages for the infinite planning horizon. Items deteriorate while they are in storage, and both demand and deterioration rates are arbitrary function of time. This paper extends the work of Alamri and Balkhi (Int. J. Prod. Econ. 107:125–138, 2007) by assuming the shortages in production lot size model subject to the effects of learning and forgetting in fuzzy environment. The system is subject to learning in the production stage and to forgetting while production ceased so that the optimal manufactured quantity for any given cycle is dependent on the instantaneous production rate. All cost are taken constants or fuzzy in nature. Hence two models are introduced separately with constant and fuzzy cost. A closed form for the total relevant costs is derived, that minimizes total cost of the underlying inventory system. Model with fuzzy costs is formulated as to optimize the possibility/ necessity measure of the fuzzy goal of the objective function. When costs are imprecise, optimistic and pessimistic equivalent of fuzzy objective function is obtained by using credibility measure of fuzzy event by taking fuzzy expectation. The models are illustrated with three examples as well as their numerical verifications are also given. Keywords Production-inventory model . Learning and forgetting . Variant time to total forgetting . Time-varying demand . Deterioration . Fuzzy cost . Credibility
1 Introduction Usually the performance of a system engaged in repetitive manufacturing operations improves with time. This is due to the learning phenomena, which is a decrease in the cost and / or the time required to produce each successive unit. Inherent factors to this S. Pathak (*) : S. Kar : S. Sarkar (Mondal) Department of Mathematics, National Institute of Technology, Durgapur, W.B. 713209, India e-mail: [email protected]
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OPSEARCH (Apr–Jun 2013) 50(2):149–181
improvement may include the more effective use of tools and machines, increased familiarity with operational tasks and work environment, and enhanced management efficiency [29]. It is reasonable to assume that if a large amount of time has elapsed between consecutive production runs then we would not follow the same learning curve at the point where production resumes. The production rate at the recommencement of production might not be as high as when the production ceased. Hence, the cost and / or the time needed to produce the first unit in the next production run will increase as the length of the break increases this loss of performance over the production break is due to the forgetting phenomena. In the literature of i
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