A multi-agent resource bidding algorithm for order acceptance and assembly job shop scheduling

This study uses an agent-based approach with a combinatorial auction mechanism to solve the joint order acceptance and assembly job shop scheduling problem. A set of jobs is offered. Each job has a revenue, ready time, due date, deadline, and consists of a set of operations with precedence relationships. Jobs that deviate from their due dates incur earliness/tardiness penalties. An operation may require several units of capacity per time unit and a resource could have multiple units of capacity. The manufacturer can reject any job to satisfy the capacity constraints and maximise the overall profit. We develop a mathematical model for the problem, then use an agent-based approach to solve it. First, the relaxed problem is decomposed into a set of job-level subproblems. Each job is optimised individually without considering the capacity constraints. Profitable jobs at the individual level submit their optimal schedules as combinatorial bids to an auctioneer to acquire combinations of resource capacity-time units. Then, the auctioneer records the profit upper bound, resolves capacity conflicts to reach a feasible solution, records the profit lower bound, and updates the dual variables. Experimental results show that the proposed methodology can solve large-sized problems in reasonable CPU times.