Fair methods for resource allocation, production smoothing and demand management

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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.