Supply-chain coordination model with insufficient production capacity and option for outsourcing

In this paper, a mathematical model is developed to analyze the situation of lost sales from the supply-chain coordination perspective. In a two-stage supply chain, the supplier's production capacity is less than the annual demand of the retailer. The supplier may recover the deficit by procuring the same from an external source at a certain price and then supplying it back to the retailer. Here, the conditions have been derived when the practice of external procurement may be a viable solution to enhance the profits of both the supplier and retailer in a coordinated approach. A numerical example is carried out to illustrate the efficacy of the developed model and the procedure developed for solving the problem.