Scheduling Jobs with Precedence Constraints on Jobshops and Shops' Coordination

Abstract

Scheduling is one of the most important issues in the planing and operation of manufacturing systems. In practice, scheduling is often complemented by some simple heuristics or simulation methods. They are either time consuming or lack of validity. The interactions of jobs as they compete for limited resources(machines, pallet, etc.) is not visible. The dynamic changes in the systems are not easily accommodated. In the job-shops, operations are not only interacted by limited resources, but also processing pieces them self. This paper presents a method for scheduling jobs with different operations on jobshops and coordinations of jobshops with weak correlation. Each job consists of a number of operations with partial precedence constraints with application of Lagrangian relaxation technique. The methods also considers “timeout“for other usage. The objective function is the total weighted quadratic ”tardiness” of the schedule combining weighted job's makespan. A two layer hierarchical structure for shops' coordination and jobshop scheduling is proposed. As the problem discussed is NP-hard, we will present an efficient, near-optimal algorithm rather than the optimal solution. The major contribution of the paper has been three folds: (1)P.B. Luh's work is extended to the job-shop's scheduling and simpler algorithm has been devised; (2) The problem is considered in continuous time domain; (3) Coordination of jobshops is also considered.