Optimum quantities of make and buy in multi-item manufacturing firms with restriction in production capacity

Sometimes, some companies with consideration to their production capacity cannot respond to their demand. If demand increases and company doesn't have sufficient capacity to respond to such demand, it will encounter backlogging. Also, in a multi-item company, if the number of products increases, the company may not be able to produce some products, thus backlogging will be occurred. In this paper, we consider such companies that will encounter the mentioned conditions and will be enforced to buy some products from outside. The aim of this paper is determination of optimum quantities of make and buy for each product to minimize total inventory cost. We refer to the proposed model as make-with-buy model. In this paper we formulate the make-with-buy model and solve it by genetic algorithm through Matlab software.