Assigning snow removal personnel. In Indiana in summer, highway personnel are assigned 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 be cleared on an emergency basis. reflecting the magnitude of the problem faced by the highway department. A fleet of snow removal vehicles must be mobilized, in addition to a force of trained drivers. This problem concerns the assignment of drivers from their homes to job sites 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. ln addition, such assignments increase the likelihood that workers will actually be 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 be assigned a state-owned vehicle for the winter season- with the proviso that the assigned jobsite is no this 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 mode it proposed to build for the highway department.
The parameters dij is the distance from a workers i’s home to jobsite j. The variable xij is to be 1 if worker i is assigned to jobsite j and 0 otherwise. No worker can be assigned more than once, At site j exactly Tj 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. An upper limit on the distance a worker can be assigned is D. Hence variables xij for distance dij 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
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