# Supply Chain Optimization in Contract Manufacturing

Contract manufacturing companies that produce, fill and package products according to customer recipes need optimal procurement strategies. A software tool based on mathematical models has been developed for supply chain optimization.

Production activities at contract manufacturing companies are typically based on a "make to order" policy. This means that the company procures raw and packaging materials and starts production only after receiving the customer orders. Usually, materials from suppliers are offered at graduated prices, i.e. the price gradually decreases as the order quantity increases. By cleverly combining customer orders and taking advantage of the graduated prices, the total cost of production can be reduced.

The dependency of the total costs on the order quantities (which in turn depend on the graduated prices) can be formulated by means of a linear mathematical model. If one wants to minimize these total costs, an integer linear optimization problem results. The optimal solution to this minimization problem provides the optimal purchase quantities for the material.

However, one is actually not interested in minimum total costs, but in minimum costs per unit of production. This makes the mathematical model more complex, in particular its linearity is lost. In order to still be able to apply efficient algorithms for integer linear optimization, one can transform the problem into a series of approximated linear problems. Among the optimal purchase quantities resulting from these problems, one can determine the one with the minimum cost per unit of production.