Abstract
Demand for a seasonal product persists for a fixed period of time. Normally the “finite time horizon inventory control problems” are formulated for this type of demands. In reality, it is difficult to predict the end of a season precisely. It is thus represented as an uncertain variable and known as random planning horizon. In this paper, we present a production-inventory model for deteriorating items in an imprecise environment characterised by inflation and timed value of money and considering a constant demand. It is assumed that the time horizon of the business period is random in nature and follows exponential distribution with a known mean. Here, we considered the resultant effect of inflation and time value of money as both crisp and fuzzy. For crisp inflation effect, the total expected profit from the planning horizon is maximized using genetic algorithm (GA) to derive optimal decisions. This GA is developed using Roulette wheel selection, arithmetic crossover, and random mutation. On the other hand when the inflation effect is fuzzy, we can expect the profit to be fuzzy, too! As for the fuzzy objective, the optimistic or pessimistic return of the expected total profit is obtained using, respectively, a necessity or possibility measure of the fuzzy event. The GA we have developed uses fuzzy simulation to maximize the optimistic/pessimistic return in getting an optimal decision. We have provided some numerical examples and some sensitivity analyses to illustrate the model.
Highlights
Existing theories of inventory control implicitly assumed that lifetime of the product is infinite and models are developed under finite or infinite planning horizon such as that of Bartmann and Beckmann 1, Hadley and Whitin 2, Roy et al 3, and Roy et al 4
Padmanabhan and Vrat, Hariga and Ben-Daya, Chen, Dey et al, etc. have been done in this area, none has considered the imprecise inflationary effect on EPQ model, especially when the lifetime of the product is random. In dealing with these shortcomings above, this paper shows an EPQ model of a deteriorating item with a random planning horizon, that is, the lifetime of the product is assumed as random in nature and it follows an exponential distribution with a known mean
It is observed that in all cases genetic algorithm Genetic Algorithm (GA) gives the better results than simulated annealing SA
Summary
Existing theories of inventory control implicitly assumed that lifetime of the product is infinite and models are developed under finite or infinite planning horizon such as that of Bartmann and Beckmann 1 , Hadley and Whitin 2 , Roy et al 3 , and Roy et al 4. Moon and Yun 6 developed an Economic Ordered Quantity EOQ model in a random planning horizon. Roy et al 8 and Roy et al 9 , developed inventory models with stock-dependent demand over a random planning horizon under imprecise inflation and finite discounting. Have been done in this area, none has considered the imprecise inflationary effect on EPQ model, especially when the lifetime of the product is random. In dealing with these shortcomings above, this paper shows an EPQ model of a deteriorating item with a random planning horizon, that is, the lifetime of the product is assumed as random in nature and it follows an exponential distribution with a known mean. It is illustrated with some numerical data, and some sensitivity analyses on expected profit function are so presented
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