Multi-objective fuzzy inventory model for deteriorating items with shortages over a finite time horizon

We consider here the inventory problems with infinite rate of replenishment in crisp and fuzzy environments over a finite time horizon for deteriorating multi-items taking time dependent demand and allowing shortages and equal replenishment cycles. Here, the objectives of maximizing the profit and minimizing the replenishment cost are imprecise in nature. Total shortage cost is assumed to be limited but vague and imprecise in non-stochastic sense. The impreciseness in the above objectives and constraint goals have been expressed by fuzzy linear Membership Functions. Under these assumptions, a Decision Maker is confronted with four possibilities depending upon the nature of the first and last cycles and he/she has to choose the best one for maximum profit-ratio (i.e. the ratio of total profit to total cost). Hence, both crisp and fuzzy models with different shortage criteria are developed and solved by the weighted fuzzy non-linear programming and goal attainment methods. Fuzzy models have also been solved by an integrated goal attainment and fuzzy non-linear programming technique. Models are illustrated with numerical examples and the results are compared.