Teaching Use of Binary Variables in Integer Linear Programs: Formulating Logical Conditions

Abstract

Abstract. Binary variables are often needed in linear programming models to indicate whether particular alternatives should be implemented and to impose logical relations among decisions. However, it is usually not obvious to students how to use binary variables to transform conditional statements of logic into linear relations. We propose to address this difficulty with a simple two-step approach. It provides rules for decomposing a conditional requirement into a group of elementary implications and then translating each of these into linear constraints. Pre-and post-test results from a sample of undergraduate business students are presented to support the effectiveness of this pedagogical approach.

Correlated Equilibria and Fairness in Concurrent Stochastic Games

“…Future work includes exploring the use of further game-theoretic topics within this area, such as techniques for mechanism design or other concepts such as Stackelberg equilibria. We plan to implement SFCE computation in Gurobi using the big-M method [16] to encode implications and techniques from [38] to encode conjunctions, which should yield a significant speed-up in their computation.…”

Optimization model for production scheduling taking into account preventive maintenance in an uncertainty-based production system

“…This leads to nоn-convexity of the admissible region and so the problem posed is not linear. This drawback can be fixed by introducing additional unknown binary variables [ 26 , 27 ]: …”