Cooperative Strategies for Manufacturing Planning with Negotiable Third - Party Capacity

We consider a model where a group of manufacturers outsource finishing operations to a single third-party. Depending on the demand for her capacity, the third-party announces daily booking costs that may take on one of two prices regular or peak price. Each manufacturer books chunks of production capacity (called manufacturing windows) so as to optimize his booking and tardiness costs subject to window availability at the third party. For days that capacity is booked the manufacturer has the option to purchase overtime at a higher hourly rate. Upon booking her capacity to the manufacturers, the third-party computes the monetary benefit that could be achieved if all manufacturers cooperated to obtain an overall optimal solution. Then, using cooperative game theory she devises a savings sharing scheme so that, in monetary terms, every manufacturer is better off with the coordinated schedule than what each could get for himself by cooperating with a subset of manufacturers. For her work, the third party withholds a portion ρ of the booking revenue paid by the manufacturers for days that were utilized in the original schedule but released after coordination. Subsequently, the third-party has the option to resell her capacity for those days. Through this model we come up with insights that indicate that cooperation amongst manufacturers reduces costs by about 20%. ∗This research was initiated while the second author visited The Chinese University of Hong Kong, and was supported in part by the Research Grants Council of HK under Earmarked Grants No. CUHK 4166/01E and CUHK 4170/03E. †Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, NT, Hong Kong, [email protected] ‡Weatherhead School of Management, Department of Operations, Case Western Reserve University , 10900 Euclid Avenue, Cleveland, OH 44106-7235, [email protected]