Question

Based on Lanzenauer et al. (1987). To process income tax forms, the IRS first sends each form through the data preparation (DP) department, where information is coded for computer entry. Then the form is sent to data entry (DE), where it is entered into the computer. During the next 3 weeks, the following quantities of forms will arrive: week 1, 40,000; week 2, 30,000; and week 3, 60,000. All employees work 40 hours per week and are paid $500 per week. Data preparation of a form requires 15 minutes, and data entry of a form requires 10 minutes. Each week, an employee is assigned to either data entry or data preparation. The IRS must complete processing all forms by the end of week 5 and wants to minimize the cost of accomplishing this goal. Assume that all workers are full-time employees and that the IRS will have the same number of employees each week. Assume that all employees are capable of performing data preparation and data entry. Determine how many workers should be working and how the workers should allocate their hours during the next five weeks.

Week 4 and Week 5 will be solved with the Solver add in with Excel.

Answer 1

We will solve this problem using linear programming.

Setup Solver with decision variables, objective function and constraints as shown below.

Click on Solve to get the optimal solution:

Total 271 workers are needed every week for 5 weeks as per below allocation of workers for each task per week.

	Week 1	Week 2	Week 3	Week 4	Week 5
Data preparation	270	261	2	188	92
Data Entry	1	10	269	83	179

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