This work proposes a new mathematical model based on a multi-objective solution for the optimization problem in supply chain. The analyzed supply chain includes the suppliers, manufacturers, distribution centers and wholesalers, considering that orders come from customers to wholesalers. A mathematical model that solves the optimization problem regarding durations and costs in the execution of customer orders is proposed. Many constraints are supported in this mathematical model such as suppliers and manufacturers capacities and balanced stocks. The aim of the proposed method is to find a near-optimal solution that minimizes criteria of cost and time along the whole supply chain process. The mathematical model was tested on WEMY Industries Limited supply chain, the results obtained by executing the heuristics approach and the mathematical model shows that it is more efficient than the heuristic. The GAP 15.02 % gotten from the proposed model improves the actual solution, this will assist in reducing costs of production and transportation of the goods and profit will be maximized as the customer of physical distribution and logistics emerged in the 1960s and 1970s. In the 1990s, a new name emerges: "Supply demands are meant genuinely respecting the delivery date of the customer.