Solving linear design problems using a linear-fractional value function

  • Authors:

  • J. Randall Brown;Aviad A. Israeli

  • Affiliations:

  • Department of Management and Information Systems, College of Business Administration, Kent State University, Kent, OH 44242, USA;Department of Management and Information Systems, College of Business Administration, Kent State University, Kent, OH 44242, USA and The Department of Hotel and Tourism Management, The Guilford Gl ...

  • Venue:
  • Decision Support Systems
  • Year:
  • 2013

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Abstract

Previous papers developed a method to easily elicit a decision maker's (DM) preferences and account for changes in the DM's preference structure. Those preferences are modeled by piecewise linear indifference curves with varying slopes producing a piecewise linear-fractional value function. Compared with traditional optimization problems which traditionally use cost minimization or revenue maximization, this model is DM-specific, it generates a knowledge set (KS) and allows the DM to find an optimal solution based on his/her expertise and preferences. When combined with real world constraints, maximizing the DM's preferences generates a decision support system (DSS) for solving specific organizational problems. This paper develops an efficient algorithm to solve a mathematical programming problem with a linear fractional objective function that models changing DM preferences and linear constraints. A DSS is developed and its algorithm is illustrated by constructing a specific example of the DSS for scheduling a police force when the objective is to maximize the police chief's expertise and preferences regarding law enforcement.