This study was conducted to estimate the company's optimal profit by considering the product supply chain in a company that receives orders from several distributors. If all orders cannot be fulfilled by the available production capacity, the company will offer a solution in allocating capacity to distributors by considering scheduling costs and other constraints. The main work in estimating the company's profit is modeling the scheduling costs and constraints in the capacity allocation problem in the company. That is, the company makes order scheduling to minimize costs to achieve maximum profit by applying the Karush-Kuhn-Tucker (KKT) method. Karush-Khun-Tucker can be used to find the optimal solution of the function formed from the allocation and scheduling problems whether linear or nonlinear. In the process, the KKT method basically involves the same steps as the Lagrange method to be able to calculate the critical point and find the optimum solution. It is suggested for further research to involve more varied variables with more interesting cases.
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