ILOG CPLEX 11.0 User's Manual

This simple model, for example, might represent a project-staffing problem. In that case, theten binary variables could represent employees who could be assigned to duty.The first constraint defines the cost function. In this example, the objective is to minimizethe cost of salaries. The next three constraints (c2, c3, c4) represent three nonoverlappingskills that the employees must cover to varying degrees of ability. The fifth constraintrepresents some additional quality metric (perhaps hard to measure) that most or all of theemployees can contribute to. It is called customer service in this example. That variable hasa lower bound to make sure of a certain predefined minimum level of 3.2.The remaining constraints represent various work rules that reflect either policy that must befollowed or practical guidance based on experience with this work force. Constraint c6, forexample, dictates that at least one person with managerial authority be present. Constraint c7requires at least two senior personnel be present. Constraint c8 indicates that several peopleare scheduled for off-site training during this period. Constraint c9 recognizes that threeindividuals are not productive together. Constraint c10 prevents two employees who aremarried to each other from working in this group in the same period, since one is a manager.Optimizing the ExampleIf you apply the optimize command to this example, you will see these results:Row 'c8' infeasible, all entries at implied bounds.Presolve time = 0.00 sec.MIP - Integer infeasible.Current MIP best bound is infinite.Solution time = 0.00 sec. Iterations = 0 Nodes = 0Interpreting the Results and Detecting ConflictThe declaration of infeasibility comes from presolve. In fact, presolve has already performedvarious reductions by the time it detects the unresolvable infeasibility in constraint c8. Thisinformation by itself is unlikely to provide any useful insights about the source of theinfeasibility, so try the conflict refiner, by entering this command:conflictILOG CPLEX 11.0 — USER’ S MANUAL 395