An approach to optimize the utility function of a logistic company using Lagrange multipliers
An approach to optimize the utility function of a logistic company using Lagrange multipliers

Summary/Abstract: This article deals with a particular application of Lagrange multipliers in the field of financial mathematics and their use to optimize the utility function of a logis tics company – the case of Interlogistica Ltd. After a careful analysis three main factors are identified in Interlogistica’s operations that contribute to the maximization of the company’s utility function and these are: Labour investment (wages, bonuses, training of employees, team-building, etc.); Direct Material Investment (acquisition/repair/lease of company/agent vehicles, lease of assets, IT, etc.), and Overhead Investment (electricity, maintenance of assets, etc.). These factors were given weights of importance. Moreover, a budget constraint for a monthly period was introduced that included money given to charity equalling Direct Material Investments. At the end the article shows the values of the three variables that maximize the utility function of Interlogistica in the case of the particular budget constraint. The paper can be used as a teaching tool in the field of financial mathematics and application of Lagrange multipliers.

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