An imperfect EPQ model for deteriorating items with promotional effort dependent demand

In this paper, a multi-item economic production quantity (EPQ) model for deteriorating seasonal products is developed with stock and promotional effort dependent demand in an imperfect production process. The promotional efforts are advertising, delivery facilities, better services, etc. The production process produces some imperfect quality units which are instantly reworked at a cost to bring back its quality to the perfect ones. Here, the rate of production is time dependent. Unit production cost is a function of production rate including the defective ones and the deterioration rate is considered as constant. The model is formulated as a profit maximization problem with space and budget constraints in the form of an optimal control problem. The total profit function with the effect of inflation and time-value of money is expressed as a finite integral over a finite planning horizon. The problem is solved using variational calculus to determine the minimum defective rates of the production process for which the total profit is maximum. Another three models are developed considering the constraints as uncertain (fuzzy, random and rough) in nature. For fuzzy model, three types of fuzzy numbers are considered. To deal with the fuzzy constraints, fuzzy possibility measure is used. Also, stochastic and rough constraints are reduced to the approximate crisp ones following chance constrained approach and rough expectation respectively. Numerical experiments are performed to illustrate the models. Also, some sensitivity analyses are performed and presented.

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