Optimization model for multi-products multi-periods multi-suppliers raw-material selection and composition, and order quantity problem with one-year minimum order quantity contract

This paper concerns the optimization model for a multi-product multi-period raw-material selection and composition, and order quantity problem faced by a beverage company. • There are some criteria in raw material selection, which we accommodate all the criteria in the objective function. There are several suppliers, and one of the decision criteria is a one-year minimum order quantity contract between the company and the suppliers. The actual one-year demand for raw materials may deviate significantly from the one-year minimum order quantities. • We derive a function that can be regarded as a penalty function to maintain the total order quantities in one year to fulfill the minimum one-year order quantity contracts. This penalty function is a part of the objective function and can be relaxed once the one-year minimum order quantity contracts are fulfilled. • We performed several numerical experiments to check the optimal solutions for various demands and for various objective functions. These experiments show our MILP (Mixed Integer Linear Programming) gives the desired optimal solutions and show the influence of decision criteria on the optimal solution.