Sequencing Games With Outsourced Operations

Consider the outsourcing process between the manufacturer and thethird party supplier in a production scheduling model. We study thecooperative game between a group of manufacturers and a single thirdparty supplier, looking for the existence of a global optimized solution.The objective function is the booking cost plus the work-in-processinventory cost. Of which, booking cost is non-linear, representing thedifferent booking price for normal working hours and overtime workinghours, hence a two-stage piecewise constant function. While the WIPinventory cost is the weighted flow time. Greedy algorithm combined withdynamic programming is applied to solve this problem. An equilibriumallocation rule for the related cooperative game is also provided. Finally anexample was provided to illustrate the optimization algorithm, with a25%decrease of production cost.