Production–inventory model for a deteriorating item with imprecise preparation time for production in a finite time horizon

In this paper, realistic production–inventory models with shortages for a deteriorating item with imprecise preparation time for production (hereafter called preparation time) has been formulated and an inventory policy is proposed for maximum profit in a finite time horizon. Here, the rate of production is constant, demand depends on selling price, marketing cost, and inventory level, and setup cost depends on preparation time. The imprecise preparation time is assumed to be represented by a fuzzy number and is first transformed to a corresponding interval number and then following interval mathematics, the objective function for total profit over the finite time horizon is changed to respective multi-objective functions. These functions are maximized and solved for a set of Pareto optimal solution with the help of the weighted sum method using the generalized reduced gradient technique. Different case studies have been made depending upon the occurrence of shortages. The models have been illustrated by numerical data. Pareto-optimal solutions for different weights are obtained and presented in tables and graphs.