Optimal time-dependent production policy under random time horizon

Abstract

A production inventory model with linearly time dependent production rate to a certain period and then with constant production rate is developed in random time horizon under inflation and time value of money. It is assumed that time period i.e. business period is random and follows exponential distribution with known mean. Demand is linearly stock-dependent. With experience unit production cost decreases with cycles and a part of the set up cost decreases with time. Here also holding and set up costs are imprecise and the optimistic/pessimistic equivalent of fuzzy objective function is obtained by using possibility/necessity measure of fuzzy event. The model is formulated as a cost minimization problem for a production controlled inventory system and solved with the help of GRG (LINGO-14.0) technique(cf. Gabriel and Ragsdell in AMSE J Eng Ind 99:384–00, 1977). The results of the models are obtained for some numerical data and then presented in tabular forms. Some sensitivity analyses are presented for the expected total cost of a model with respect to demand, combined effect of inflation, the time value of money and mean value of time horizon distribution. In real-life the inventory parameters are uncertain. Here in general format, a production controlled inventory model is formulated with imprecise data and made crisp using fuzzy measures in both optimistic and pessimistic senses. It is shown numerically that cost in pessimistic sense is more than that in optimistic sense.