A production inventory model for deteriorating item with ramp type demand allowing inflation and shortages under fuzziness

a r t i c l e i n f o Economic production quantity (EPQ) is the quantity of a product that should be manufactured in a single batch so as to minimize the total cost. In classical model EPQ only applies where the demand for a product and production rate is constant over the year. But in reality these parameters vary with time in different scenarios. In this paper we have considered a production inventory model for deteriorating items with ramp type demand rate under the effect of inflation and shortages under fuzziness. The deterioration rate is represented by a two-parameter Weibull distribution. As inflation erodes the value of money so we have also considered the effect of inflation when there is shortage in the stock under finite time horizon. Some parameters are vaguely or unclearly defined or whose values are imprecise or determined based on subjective beliefs of individuals. Therefore the inventory model is solved under fuzzy environment to evaluate the optimum solution of the model in different cases. We have optimized our solution by considering production time and production rate as decision variables in two separate cases. While incorporating symmetric triangular fuzzy number we use total λ-integral value to defuzzify the solution. Finally, utility of the model is presented by using some numerical examples and sensitivity analysis and the results are analyzed. Now a days, the facts like variation in the demand rate of an item, deterioration , shortages and inflation in the market, are in growing interest. Demand rates are of various types, sometimes it is linear or quadratic time dependent function, or it is a price and stock dependent type of function etc. Recently, many researchers have given considerable attention where the demand rate is a ramp type function of time. This type of demand rate is seen for a new brand item launching in the market. The demand pattern assumed here occurs not only for seasonal product, but also for fashion apparel, computer chips of advanced computer, spare parts, etc. The nature of demand for seasonal and fashionable products is increasing then steady then decreasing and finally becoming asymptotic. The demand of the item increases with time and then stabilizes after some time and ultimately becomes constant. Thus the demand rate is deterministic when any new brand product is launched in the markets, the demand rate linearly depends on time, and later it gets …