Fair methods for resource allocation, production smoothing and demand management

公平资源分配和排序的分配方法。分配问题在于根据各州的人口比例在各州之间分配席位。由于代表的不可分割性，理想很难实现。分配理论的主要见解来自确保没有悖论的解决方案所必需的公理。为了补充运筹学的研究方法，提出了混合模式供应链中的工作量平衡、公平排队、硬实时和比例调度等运筹学方法。研究了它们的特性与人造系统(供应链、操作系统)所需的特性的一致性，例如周期性和对称性。我们预计这种公理方法将演变成一种更通用的方法，可以补充资源分配问题的优化方法。我们还期待分配方法为资源共享和调度问题提供新的解决方案，并提供对它们的有趣见解。生产和供应链的畅通。所有形式的变异性的减少使得混合模式的即时供应链变得顺畅。研究了同步装配线的生产与配送平滑问题。然而，许多加工和设置时间在不同型号之间变化的制造系统并不是同步装配线。我们提出了一种解决方案，即对同一型号的单元进行批量处理，并使用准时排序方法来顺利地进行此类系统的生产和交付。基于Pareto优化和分配方法的分批与调度。研究了改善运营管理的各种解决方案的可取特点。这是唯一的选择。大学课程表的特点是上课分组授课。这个问题是NP难的。我们提出了一种LP松弛和舍入过程来获得该排课问题的具有恒定绝对误差的近似解。我们研究了在多项式时间内可以找到最优舍入的情况。这些结果适用于抢先开放商店和超图着色。

APPORTIONMENT METHODS FOR FAIR RESOURCE ALLOCATION AND SEQUENCING. The apportionment problem consists in apportioning seats among states in proportion to their populations. The ideal can hardly be met due to indivisible nature of representatives. The theory of apportionment's main insights come from axioms necessary to ensure paradox-free solutions. The apportionment methods are proposed to complement operations research methods for: balancing workloads in mixed-model supply chains, fair queueing, hard-real time and proportional scheduling. Their characteristics are studied for consistency with properties, e.g. periodicity and symmetry, desirable for man-made systems (supply chains, operating systems). We anticipate this axiomatic method to evolve into a more general approach that could supplement optimization approach to resource allocation problems. We also anticipate the apportionment methods to provide novel solutions to resource sharing and scheduling problems and interesting insights into them. PRODUCTION AND SUPPLY CHAIN SMOOTHING. The reduction of variability in all forms makes just-in-time supply chains for mixed-models tick. The production and delivery smoothing problem has been studied for synchronized assembly lines. However, many manufacturing systems with processing and setup times varying among models are not synchronized assembly lines.  We propose a solution that batches units of the same model and uses just-in-time sequencing methods to smooth production and delivery for such systems. The batching and scheduling is based on Pareto optimization and apportionment methods. Desirable characteristics of  solutions to improve management of operations are studied. UNIVERSITYTIMETABLING. The university timetabling distinctive feature is that classes are grouped for lectures. The problem is NP-hard. We propose an LP relaxation and a rounding procedure to obtain approximate solutions with a constant absolute error for this timetabling problem. We study the cases for which optimal rounding can be found in polynomial time. These results apply to preemptive open shops and hyper-graph coloring.