ILOG CPLEX 11.0 User's Manual

Describing the ProblemThe problem is to schedule a number of jobs over a group of resources. In this context, a jobis a set of activities that must be carried out, one after another. Each resource can processonly one single activity at a time.For each job, there is a due date, that is, the ideal date to finish this job by finishing the lastactivity of this job. If the job is finished earlier than the due date, there will be a costproportional to the earliness. Symmetrically, if the job is finished later than the due date,there will be a cost proportional to the tardiness.As “just in time” inventory management becomes more and more important, problems likethis occur more frequently in industrial settings.Understanding the Data FileThe data for this problem are available online with your installation of the product in the fileyourCPLEXhome/examples/data/etsp.dat.The data of this example consists of arrays and arrays of arrays (that is, matrices).One array of arrays represents the resources required for each activity of a job. For example,job0 entails eight activities, and those eight activities require the following ordered list ofresources:1, 3, 4, 1, 2, 4, 2, 4A second array of arrays represents the duration required for each activity of a job. Forjob0, the following ordered list represents the duration of each activity:41, 32, 72, 65, 53, 35, 53, 2In other words, job0 requires resource1 for a duration of 41 time units; then job0requires resource3 for 32 time units, and so forth.There is also an array representing the due date of each job. That is, array[i] specifies thedue date of jobi.To represent the penalty for the early completion of each job, there is an array of penalties.Likewise, to represent the penalty for late completion of each job, there is an array ofpenalities for tardiness.368 ILOG CPLEX 11.0 — USER’ S MANUAL