Job Delivery Research Articles

Industrial job-shop scheduling with random operations and different priorities

A classical job-shop scheduling problem with n jobs (orders) and m machines is considered. Each job-operation O il (the l − th operation of job i, l = 1,…, m, i = 1, 2,…, n) has a random time duration t il with the average value t ̄ il and the variance V il . Each job J i has its due date D i and its priority index ϱ i . Given p i ∗ , the desired probability for job J i to be accomplished on time, and p i ∗ ∗ , the least permissible probability for the job to meet its due date on time, the problem is to determine starting time values S il for each job-operation O il . Those values are not calculated beforehand and are values conditioned on our decisions. Decision-making, i.e., determining values S il is carried out at the moments when at least one of the machines is free for service and at least one job is ready to be processed on that machine. If at a certain moment t more than one job is ready to be processed, these jobs are compared pairwise. The winner of the first pair will be compared with the third job, etc., until only one job will be left. The latter has to be chosen for the machine. The competition is carried out by calculating the job's delivery performance, i.e., the probability for a certain job to meet its due date on time. Such a calculation is carried out by determining the probability to meet the deadline for the chain of random operations. Two different heuristics for choosing a job from the line will be imbedded in the problem. The first one is based on examining delivery performance values together with priority indices ϱ i . The second one deals with examining confidence possibilities p i ∗ and p i ∗ ∗ and does not take into account priority indices. A numerical example is presented. Both heuristics are examined via extensive simulation in order to evaluate their comparative efficiency for practical industrial problems.

An Integrated Optimization and Knowledge - Based Job Shop Scheduling System

The complexity of the job shop scheduling problem has led some researchers away from the difficulties associated with optimization approaches. Instead, they have chosen to pursue knowledge-based techniques more capable of handling dynamic changes such as machine breakdowns and new jobs. This paper presents a synergetic combination of optimization and knowledge-based methods in a system of distributed architecture. The high level knowledge-based component schedules the operations of a job through a contract negotiation process with relevant work centers. A scheduling algorithm based on Lagrangian relaxation is adapted to schedule individual work centers. Work centers “bid” on operations and the knowledge-based components “ward” contracts for their completion. Methods to prevent distributed components from violating the decisions of others are considered. The tradeoff between obtaining a good schedule and meeting originally promised job delivery dates is also examined. The net result is an effective, informative, and flexible job shop scheduling system.