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In today’s competitive world, customers expect their demands to be met at the shortest possible time, while manufacturers aspire to deliver the orders within a convenient time and at a minimum cost. Thus, manufacturers are compelled to seek ways of lowering the costs of their services in order to satisfy customers and survive the competition in their respective industries. This research paper investigates a multi-product problem in a two-echelon supply chain consisting of a single manufacturer and several retailers. The main objective of this research is to develop and present a multi-product optimization model in which retailers receive their orders through discrete delivery and surplus manufactured goods are stored in the manufacturer’s warehouse. The objective function of the mathematical model in the economic dimension includes the minimization of the total supply chain costs and the maximization of profit. The retailers in this model place new orders when their inventory level drops to zero, and the manufacturer responds to the retailers’ orders at the same time as it begins processing each product. After delivering the last set of orders, the manufacturer stores surplus items in its warehouse in case the retailers place new orders. This optimization problem is modeled using mixed integer nonlinear programming, while numerical scenarios are coded using the MATLAB software which helps estimate the total cost within a short time. Finally, a sensitivity analysis is performed to determine the effects of a number of factors on the total cost, including problem parameters, demand and production rates, the production quantity, and the number of times the manufacturing machines are operated at each production cycle.
Tajik et al. (2024) studied this question.