Logistic Planning with Nonlinear Goal Programming Models in Spreadsheets

Abstract

This is a case study of a coal mining company to demonstrate how algebra principles and nonlinear goal programming can be applied for logistics planning using spreadsheet software. The paper asserts that mathematical programming techniques are not well-accepted by managers because the models are difficult to understand due to abstract notational conventions yet alternative commercial software is inflexible (and sometimes inaccurate). The relevant operations research literature was reviewed, highlighting techniques applicable for analyzing quantitative and qualitative logistics data. A practical supply-demand transportation logistics model was built which included determinist constraints and stochastic costing theories, while applying both linear and nonlinear calculus slope principles. The formulae were explained in algebraic standard form (citing corresponding spreadsheet functions). The logistics problem was optimized, illustrating how 6 mining sites could supply 4 countries with sufficient coal to meet different electricity demand levels, surpassing the break-even goal and projecting annual revenue of over $34 billion.