Integrated scheduling of production and distribution with two competing agents

This paper studies a two-agent scheduling problem on a single batch machine. Each job j has a processing time pj and a size sj. Jobs should be delivered to the agent as soon as possible. The objective is to minimize the service span of the first agent subject to an upper bound on the makespan of the other agent. We propose two approximation algorithms when jobs have identical processing times and in the general case. Then we conduct theoretical analyses to provide the provable guarantees on the performances of the algorithms. Finally, we conduct simulation analyses based on randomly generated instances to evaluate the average performances of the algorithm in the general case.