Constraint multiproduct joint-replenishment inventory control problem using uncertain programming

An uncertain economic order quantity (UEOQ) model with payment in advance is developed to purchase high-price raw materials. A joint policy of replenishments and pre-payments is employed to supply the materials. The rate of demand is considered LR-fuzzy variables, lead-time is taken to be constant, and it is assumed that shortage does not occur in the cycles. The cycle is divided into three parts; the first part is the time between the previous replenishment-time to the next order-time ( 0 t ), the second part is the period between 0 t to a payment-time ( k t ), and the third part is the period between k t to the next replenishment-time. At the start of the second part ( 0 t ), %  of the purchasing cost is paid. The (1 )%   remaining purchasing cost is paid at the start of the third part ( k t ). The cost of the model is purchasing under incremental discount for each order with rough cost per unit, clearance cost, fixed-order cost, transportation cost, holding, and capital cost. Holding cost is for on-hand inventory and capital cost is for the capital that is paid for the next order. The constraints of the problem are space, budget, and the number of orders per year. Further, lead-time is considered less than a cycle time. We show that the model of this problem is a fuzzy integer-nonlinear-programming type and in order to solve it, a hybrid method of harmony search, fuzzy simulation, and rough simulation is proposed. In order to validate the results and examine the performance of the proposed method, a genetic algorithm, as well as a particle swarm optimization method is also employed. The results of a numerical example show that the proposed procedure has the best performance in terms of the mean of the objective function in different simulation runs. At the end, a case study along with a sensitivity analysis is given to demonstrate the applicability of the proposed methodology in real world inventory control problems and to provide some managerial insights.