On Some Aspects of Bounded Transportation Problem

Kavita Gupta

doi:10.31181/sor31202648

Authors

Kavita Gupta Department of Mathematics, Kirori Mal College, University of Delhi, Delhi-110007, India Author https://orcid.org/0000-0003-4642-3765

DOI:

https://doi.org/10.31181/sor31202648

Keywords:

Capacitated transportation problem, Time minimization, Fractional programming, Trade-off, paradox

Abstract

This paper presents various aspects of the capacitated transportation problem by incorporating into the classical transportation problem some realistic constraints such as limited capacities, restrictions on total flow, time-sensitive delivery of goods, and linear, quadratic, and fractional objectives. It delves into cost minimization, time minimization, and the trade-off between these two aspects. A special class of non-linear programming problems such as the fixed-charge bi-criterion transportation problem with an indefinite quadratic objective function with restriction on total flow is examined. The fractional problem, along with paradoxical scenarios where it is possible to ship more total goods for less total cost, is also presented. Each model is supported with mathematical formulations, some of which are illustrated through real-life applications such as the military transportation problem of the Indian Army.

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