Structure the model that the firm should solve to minimize

Question

Assigning snow removal personnel In Indiana in summer, highway personnel are as-signed to intensive construction and inspection duties throughout the state. However, as winter approaches, the personnel must be reassigned to snow removal and ice control duties on the state and Federal interstate highways.

Workers must travel, in swift fashion. to new jobsites during snow emergencies, and these sites may be distant from their homes. About 30,000 lane miles may be required in the entire state to he cleared on an emergency basis, reflecting the magnitude of the problem faced by the highwas department. A fleet of snow removal vehicles must he mobilized. in addition to a force of trained drivers. This problem concerns the assignment of drivers from their homes to jobsites from which snowplows fan out to their routes. The problem is conceived of as being solved for one of the highway districts in the state.

Assigning drivers to sites near their homes is a goal of the assignment process. Assignment to nearby jobsites means that the time to initiate snow removal is short. In addition, such assignments increase the likelihood that workers will actually he able to report to their job site. Furthermore, the rule of the highway department is that a worker assigned to a job site more than 15 miles from his home station will he assigned a state-owned vehicle for the winter season-with the proviso that the assigned jobsite is not his closest jobsite.

There is a limit, L. on the total number of vehicles that the state has available to assign to its snow removal workers. This factor forces nearby assignment as well. The firm of Wright On! has received a contract to assist the state in developing a plan for worker reassignment. The firm described the following parameters. decision variables, and constraints for the model it proposed to build for the highway department.

The parameter di is the distance from a worker is home to jobsite j. The variable x_ij is to be I if worker i is assigned to jobsite j and 0 otherwise. No worker can be assigned more than once.

At site j, exactly T_i workers are needed. Finally, the maximum number of state owned vehicles that can be assigned is L. To ascertain if a particular assignment requires a vehicle, the model uses the coefficient a_ij. which is I if the assignment of worker i to site j requires a vehicle. An upper limit on the distance a worker can be assigned is D. Hence variables x_ij for distances d_ij greater than D are simply excluded from the problem.

Structure the model that the firm should solve to minimize the average worker distance, given the other elements of the problem.