Logistic Planning with Nonlinear Goal Programming Models in Spreadsheets

Logistic Planning with Nonlinear Goal Programming Models in Spreadsheets

Kenneth David Strang (Department of Business and Supply Chain Management, State University of New York, Plattsburgh, NY, USA, & APPC Research, Sydney, NSW, Australia)
Copyright: © 2012 |Pages: 14
DOI: 10.4018/jal.2012100101
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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.
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Literature Review

There are numerous techniques in operations research to analyze coal supply logistical problems. A recent operations research-management science handbook documented 152 topics, including: Age Replacement, Ant Colony, Branch and Bound, Clustering, Consensus Building, Fuzzy Search, Genetic Algorithms, JIT, Linear Programming, Markov, MRP, Risk Analysis, Scenario Analysis, Percolation Theory, Simplex, Spanning Tree, Stakeholder Participation, Queuing, Wardrop Equilibria, Warrant Models, and many other techniques (Cochran et al., 2011). Some of these are procedures for qualitative data more so than techniques (e.g., consensus building), while the field of quantitative data approaches ranges from stochastic forecasting (using probability theory), deterministic linear programming (when constraints are known), to nonlinear goal or search heuristics where infinite or no solutions may be possible. The implications are that one or several of the available techniques may be necessary to solve a complex logistical dilemma.

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