Solution to IRS Data Processing[1]
To process income tax forms, the Internal Revenue Service (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 numbers of forms will arrive: week 1, 40,000; week 2, 30,000; 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 all employees are capable of performing data preparation or data entry, but must be assigned to one task for an entire week at a time.
Determine how many workers should be working and how the workers should allocate their hours during the next 5 weeks.
Managerial Problem Formulation
Decision Variables
Numbers of workers for two tasks over five weeks (10 decisions) and numbers of forms completed on each task in each week (10 decisions).
Objective
Minimize total cost.
Constraints
Forms arrive at a fixed schedule.
All work must be completed in five weeks.
Data prep task cannot begin until the forms arrive.
Data entry task cannot begin until data prep task is finished.
The plan can’t call for more labor than is available for either task in any week.
Mathematical Formulation
Decision Variables
Define Xij = Number of workers on task i during week j.
Define Pij = Production (forms processed on task i during week j).
i = tasks 1-2, j = weeks 1-5
Objective
Minimize Z =
Where Ci is the cost of hiring a worker for task i for one week.
C1 = C2 = $500
Constraints
A new kind of constraint: Balance Equations for each task in each week.
Define Iij = Inventory (work ready to be processed on task i at the end of week j).
Ending “inventory” = beginning inventory + new forms arriving – current period processing
Note that
Spreadsheet Model
Note that the balance equations are not constraints in the usual sense (i.e. specified in Solver). We build them into the model, linking the tasks and weeks together.
Conclusions
Minimum total cost is $677,073.
All work could be done in four weeks.
B60.23501Prof. Juran
[1] Based on 4-89 (p. 177) in Practical Management Science (2nd ed., Winston and Albright, 2001 Duxbury Press). Based on Lanzenauer et al. (1987). Solution by David Juran, 2001.