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**A model for allocated versus actual costs in assignment and transportation problems.**
*(English)*
Zbl 0933.90009

Summary: 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.

### MSC:

90B06 | Transportation, logistics and supply chain management |

91B32 | Resource and cost allocation (including fair division, apportionment, etc.) |

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\textit{C. Pilot} and \textit{S. Pilot}, Eur. J. Oper. Res. 112, No. 3, 570--581 (1999; Zbl 0933.90009)

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### References:

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[4] | Locke, E. A., Relationship of goal level to performance level, Psychological Reports, 20, 1068 (1967) |

[5] | Locke, E. A.; Lee, C.; Bobko, P., Effect of self-efficacy, goals and task strategies on task performance, Journal of Applied Psychology, 69, 241-251 (1984) |

[6] | Latham, G. P.; Shell, T. P.; Saari, I. M., The effects of participation and goal difficulty on performance, Personnel Psychology, 35, 667-686 (1982) |

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