a hybrid meta-heuristic method to optimize bi-objective single period newsboy problem with fuzzy cost and incremental discount

in this paper the real-world occurrence of the multiple-product multiple-constraint single period newsboy problem with two objectives, in which there is incremental discounts on the purchasing prices, is investigated. the constraints are the warehouse capacity and the batch forms of the order placements. the first objective of this problem is to find the order quantities such that the expected profit is maximized and the second objective is maximizing the service rate. it is assumed that holding and shortage costs, modeled by a quadratic function, occur at the end of the period, and that the decision variables are integer. a formulation to the problem is presented and shown to be an integer nonlinear programming model. finally, an efficient hybrid algorithm of harmony search, goal programming, and fuzzy simulation is provided to solve the model. the results are illustrated by a numerical example.