A model for allocated versus actual costs in assignment and transportation problems |
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| Affiliation: | 1. Department of Mathematics, University of Salerno, Via Giovanni Paolo II, 132, Fisciano 84084, SA, Italy;2. J.B. Speed School of Engineering, Industrial Engineering Department, University of Louisville, 132 Eastern Parkway, Louisville, Kentucky 40292, USA;1. LBE, Montpellier SupAgro, INRA, Univ Montpellier, Montpellier, France;2. Elsa, Research group for Environmental Lifecycle and Sustainability Assessment, Montpellier, France;3. Sustainable Engineering, Technische Universität Berlin, Berlin, Germany;4. Institute of Environmental Sciences (CML), Department of Industrial Ecology, Leiden University, Einsteinweg 2, 2333 CC Leiden, the Netherlands;5. Department of Econometrics and Operations Research, Vrije Universiteit Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, the Netherlands |
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| Abstract: | We present a simple mathematical model which will relate the actual cost spent in accomplishing a task to the dollars budgeted for that task. In the specific instances of assignment and transportation problems we show how to minimize total dollars spent given total dollars allocated. We show furthermore how to quantitatively measure the work done along each arc in such problems. The total work, which will measure how fixed costs are realized across various arcs for a given prescribed effort, can then be minimized. It is shown that this, in general, leads to a third type of optimal solution which is different from those optimal solutions obtained by minimizing either total cost or total dollars allocated. |
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