Exact and Heuristic Algorithms for the Job Shop Scheduling Problem with Earliness and Tardiness Over a Common Due Date

Scheduling has turned out to be a fundamental activity for both production and service organizations. As competitive markets emerge, Just-In-Time (JIT) production has obtained more importance as a way of rapidly responding to continuously changing market forces. Due to their realistic assumptions, job shop production environments have gained much research effort among scheduling researchers. This research develops exact and heuristic methods and algorithms to solve the job shop scheduling problem when the objective is to minimize both earliness and tardiness costs over a common due date. The objective function of minimizing earliness and tardiness costs captures the essence of the JIT approach in job shops. A dynamic programming procedure is developed to solve smaller instances of the problem, and a Multi-Agent Systems approach is developed and implemented to solve the problem for larger instances since this problem is known to be NP-Hard in a strong sense. A combinational auction-based approach using a Mixed-Integer Linear Programming (MILP) model to construct and evaluate the bids is proposed. The results showed that the proposed combinational auction-based algorithm is able to find optimal solutions for problems that are balanced in processing times across machines. A price discrimination process is successfully implemented to deal with unbalanced problems. The exact and heuristic procedures developed in this research are the first steps to create a structured approach to handle this problem and as a result, a set of benchmark problems will be available to the scheduling research community

A Connectionist Method To Solve Job Shop Problems

We propose a novel framework to solve job shop scheduling problems based on connectionist ideas of distributed information processing. In our approach each operation of a given job shop problem is considered to be a simple agent looking for a position in time such that all its time and resource constraints are satisfied. Each agent considers the current time position of its constraint neighbors to gradually change its own position to reach this goal. All agents together form a recurrent dynamical system which either self-organizes after some iterations to a feasible schedule or fails to do so depending on the constrainedness of the problem. By gradually increasing the constrainedness through decreasing the allowable overall processing time for a valid schedule, better and better solutions are found up to the point where no further improvements can be made. INTRODUCTION In classical job shop scheduling we are given a set of jobs, each of which consists of a chain of operations, and a s..