Multi-period optimal defective production problem with variable preparation time

In this paper, a multi-period optimal production control problem with variable preparation time is 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 linearly stock dependent. Defective rate is taken in four forms namely constant, fuzzy, random and fuzzy-random. The presented preparation time is assumed to be deterministic and treated as a variable. Production cost and set-up cost depend on preparation time. Here, preparation time influences the production cost negatively and set-up cost positively. The model is formulated as an optimal control problem and solved with the help of Calculus method and Generalised Reduced Gradient (GRG) technique. The optimum results are obtained and presented in tabular forms and graphically.