Recent Advances in Applications of Mathematical Programming to Business and Economic Problems

ABSTRACTIt is well known that Mathematical Programming techniques are well-developed and with widespread application. It would be useful for researchers and practitioners in the information systems field to have a categorization that would show the types of problems that have been solved using these techniques. This paper provides this categorizationJEL: A22, A23KEYWORDS: Mathematical Programming Applications, Linear Programming, Stochastic, Economic and Business Models(ProQuest: ... denotes formulae omitted.)INTRODUCTIONApplication of business, financial and economic problems to mathematical programming is of ongoing interest. Users include insurance companies, mutual funds, farmers and shipping companies. Many fields including the fields of micro-economics and finance have been impacted directly as both private business and governments have made use of Mathematical Programming, and in particular, Linear Programming. Its use in the production and allocation of resources cannot be underestimated. Linear Programming (LP) has been said to be one of the ten most important discoveries of the last century (Dongarra and Sullivan, 2000, and Fourcans and Hindelang, 1974).Mathematical programming is used when an optimization decision has constraints that limit decisions. For example, a business may use mathematical programming to allocate scarce resources in an optimal way, an insurance company may be required to keep a small percentage of its assets in treasuries and another percentage in fixed income securities and a farmer's crops may require a minimum amount of fertilizer.In the remainder of this paper we provide a literature review that shows the vast scope of business and economic applications of mathematical programs. We then develop the generic Linear Programming model and then apply the model to a specific application. Finally we conclude with and give a specific direction for future research that we believe would be useful for practitioners.LITERATURE REVIEWApplications of optimization problems extend over many fields. For example, in the fields of economics and finance, linear programming may be applied to production problems, shipping problems, asset allocation, crop growing, allocation of sewage, mortgage backed securities portfolios other similar problems.In the area of crops and resource management, Myers and Mcintosh et al (2008) apply optimization techniques to crop rotation for Idaho potatoes. Fritzsch and Wegener et al (2011) discuss linear programming applied to farm households in Europe. Lu and huang (2010) apply linear programming to water resource management, fan and huamg (2012) model Linear Programs in an environmental context. Hadani and Alwi (2010) apply integer linear programming to optimization of water networks and Zeng and Kang et al (2010) apply it to water management and additionally to agriculture and crop area planning. Similarly, Becker (1990) applies optimization to agriculture on a farm. April, Glover and Kelly (2002) discuss an application of optimization to portfolio optimization for capital investment products. Ho and presantat (2010) provide a literature review for supplier evaluation and selection.Optimization is also big for financially related problems. Cagan, Camero and Zenios (1993) apply optimization to pricing mortgage backed securities. We also discussed this topic in the context of the subprime mortgage problem (Yarmish, Fireworker and Nagel, 2008). Fourcans and Hindelang (1974) applied optimization to capital management for the multinational firm. Hiller and Schaack (1990) classified bond portfolio modeling techniques and Markowitz (1952, 1959) applies optimization to diversifying a portfolio. Schrage (1994) provides an overview of some financial optimization problems in the context of the LINDO optimization package and Cooper and Steinberg (1974) discuss general methods and applications.In many applications the coefficients of the modal are not known with certainty. …