The Police Department in Fargo, North Dakota, begins the morning shift by informing all first-shift patrol persons of the previous evening’s activities and giving assignments to the various team members. On a particular day, the following three activities must be accomplished: (1) delivery of a DARE (Drug Abuse Resistance Education) lecture at a local elementary school; (2) instruction of the rookie police class in using the baton; and (3) preparation of a report for the evening’s City Council meeting on drug activities over the past three months.
To help fulfill the mayor’s promise of “keeping more police on the street,” only three officers will be assigned to these activities. The goal is to minimize the total time these officers will be absent from street patrol. Given the expertise of each officer, the table for problem 19 gives each officer’s time estimates for each activity, including any preparation time that may be needed. Because the assignments will be occurring simultaneously, each officer will be assigned to only one of the activities.
a. Determine the minimal time assignment by direct enumeration of all possible combinations.
b. Draw the network representation of this problem.
c. Give the linear programming formulation for this problem and solve using a linear programming module.
d. Interpret this problem as a special case of the transportation problem and solve using the transportation approach.
e. Use the assignment approach to solve the problem.