One machine multiple-product problem with production-inventory system under fuzzy inequality constraint

This paper presents a one machine multiple-product problem with bounded production rate to minimize the total linear cost of inventory under imprecise space constraint. The demand is dependent on time and known. Also the production is a control variable and unknown. The net discount rate of inflation is fuzzy in nature. At first defined the expected value of fuzzy number, then the system is transferred to the fuzzy expected value model. The model is formulated as an optimal control problem and then reduced to an equivalent deterministic model and solved for optimum production function using Pontryagin's Optimal Control policy, the Kuhn–Tucker conditions and generalized reduced gradient (GRG) technique. The model is illustrated numerically and values of demand, optimal production and stock level are presented in both tabular and pictorial forms.