Scheduling Optimization of Manufacturing and Service Environments with Time-Lag Constraints

本提案的目的是进一步推进我在无等待和时滞调度优化领域的研究计划。无等待约束表示作业的连续操作之间不应该有等待时间，这是某些环境中的基本假设。具有时滞约束的调度问题是其无等待版本的一般化。时滞约束强制作业或作业的操作在前一个作业或操作完成后的一定时间窗口内开始或结束。无等待和时滞约束模型，在这种情况下，不鼓励在操作的开始时间和前一个操作的完成时间之间有很长的延迟，因为这可能会损坏或恶化产品。例如，在食品工业中，许多生产过程涉及易腐产品，即，一旦食品准备和烹饪，它必须在一定时间内经过冷却过程，否则必须丢弃。在必须降低产品污染风险的行业中也存在类似的限制。我们可以列举生物技术行业，例如输血。自动化医学实验室通常使用最小和最大时间滞后的组合来正确地安排化学反应。Hall和Sriskandarajah bbb和Deppner bbb对该问题的应用进行了全面的回顾。适当的目标函数包括最小化工厂的生产成本或合同的总处理时间；减少患者在医疗机构或客户在政府办公室的等待时间。另一种可能性是最大限度地利用现有资源。上述问题是np困难的。我在过去几年在这一领域的研究表明，要使用数学规划模型解决无等待或时滞调度问题的最优性，问题实例应该少于20个作业。本申请中提出的解决方法通过应用新颖的方法来解决我过去八年一直在研究的调度问题，从而进步了现有的文献。这些方法包括利用半定规划或拉格朗日松弛法求最优解的紧上界或下界；使用分解技术，如本德方法；并对不确定情况进行随机优化技术。上述问题和解决方法既复杂又基本，填补了目前文献中存在的空白。此外，所定义的问题和解决方法的实用性将导致加拿大和国际业务的效率提高和优化。

The objective of this proposal is to further advance my research program in the realm of the no-wait and time-lag scheduling optimization. No-wait constraints denote that there should be no waiting time between consecutive operations of a job, which is a fundamental assumption in certain environments. Scheduling problems with time-lag constraints are a generalization of their no-wait version. Time-lag constraints force the jobs or the operations of the jobs to start or finish within a certain time window after the previous jobs or operations are completed. No-wait and time-lag constraints model situations in which a long delay between the starting time of an operation and the finish time of the previous operations is discouraged because it may damage or deteriorate the product. For example, in the food industry, many of the production procedures involve perishable products, i.e., once the food is prepared and cooked, it must undergo the chilling process before a certain amount of time is elapsed or it must be discarded. Similar constraints are in place in industries in which the risk of product contamination must be reduced. One can list biotechnology industries, for example, blood transfusion as such fields. Automated medical laboratories usually use a combination of minimal and maximal time-lags to schedule the chemical reactions correctly. Hall and Sriskandarajah [16] and Deppner [17] provide a comprehensive review of the applications of the problem.The proper objective functions to consider include minimizing the cost of production or the total processing time of the contracts in a factory; reducing the waiting time of the patients in a healthcare setting or clients in a government office. Another possibility is maximizing the utilization of the available resources. The mentioned problems are NP-hard. My research in this area during the past few years reveals that to solve the no-wait or time-lag scheduling problems to optimality using mathematical programming models, the problem instance should have less than 20 jobs. The proposed solution methods in this application progress the available literature by applying novel approaches to the scheduling problems that I have been studying for the past eight years. These methods include finding tight upper- or lower bounds for the optimal solution using semidefinite programming or Lagrangian relaxation; using decomposition techniques such as Bender's method; and conducting stochastic optimization techniques to the non-deterministic cases. The mentioned problems and solution methods are sophisticated yet fundamental and fill the gaps that currently exist in the literature. Moreover, the practicality of the defined problems and the solution methods will lead to the efficiency improvement and optimization of the Canadian and international businesses.