ILOG CPLEX 11.0 User's Manual

The constraints in conflict with this new limitation are all of the skill requirements. Whenviewed in this light, the inconsistency is easy to spot: one employee is obviously needed forconstraint c4, two are needed for c3, and a simple calculation reveals that three are neededfor c2. Since there is no overlap in the skill sets, five employees are too few.Unless management or the formulator of the model is willing to compromise about theskills, (for example, to relax the righthand side of any of these constraints), constraint c11needs to be taken out again, since it is unrealistic to get by with only five employees:change delete constraint c11This change results in a model with an optimal cost of 335, using six employees.Changing Bounds on CostNo better cost is possible in this formulation. Still, you may wonder, "Why not?" To try yetanother scenario, instead of limiting the number of employees, try focusing on the cost bychanging the upper bound of the cost to 330, like this:change bound cost upper 330optimizeconflictdisplay conflict allThis series of commands again renders the model infeasible and shows a minimal conflict:Subject Toc1: - cost + 80 x1 + 60 x2 + 55 x3 + 30 x4 + 25 x5 + 80 x6 + 60 x7+ 35 x8 + 80 x9 + 55 x10 = 0c2: x1 + x2 + 0.8 x3 + 0.6 x4 + 0.4 x5 >= 2.1c3: x6 + 0.9 x7 + 0.5 x8 >= 1.2c5: 0.2 x2 + x3 + 0.5 x4 + 0.5 x5 + 0.2 x7 + 0.5 x8 + x10 - service= 0c9: x4 + x5 + x8