Optimal production inventory problem in imprecise time period

In this paper, for defective items, realistic optimal production‐inventory models with fuzzy time period have been formulated and solved. Here, the rate of production is assumed to be a function of time and considered as a control variable. Also, the demand is time dependent and known. The values of an integral over a fuzzy interval are obtained with the help of Zimmerman's technique and fuzzy Riemann integral theory. Also, the surprise function is introduced to convert the fuzzy budget constraint to a crisp one. Then the problem is solved using calculus method and a nonlinear mathematical programming technique ‐ generalised reduced gradient (GRG) technique. The models have been illustrated by numerical data. The optimum results including profit, production and stock levels at different times over the fuzzy time period for different models are obtained and presented in tabular and graphical forms. A real‐life illustration is also presented.