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Deterministic Throughput Capacity Planning Model

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Consider the following pattern of tax return arrivals at an IRS Regional Processing Center (from Exhibit D, Section J):

Week Returns

1 373,000

2 246,000

3 461,000

4 1,019,000

5 2,309,000

6 2,519,000

7 2,594,000

8 2,408,000

9 1,611,000

10 1,344,000

11 1,362,000

12 1,287,000

13 1,208,000

14 1,028,000

15 1,362,000

16 3,704,000

17 578,000

18 888,000

19 920,000

20 635,000

21 512,000

22 375,000

23 89,000

24 216,000

25 442,000

26 210,000

PROBLEM

Find minimum daily processing capacity needed to make sure that every return is processed within 17 days of arriving at the Center.

SOLUTION

The assumptions and the mathematical model for solving this problem are given below:

Assumptions

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This derivation has the following limitations:

1. The weekly input volume (arrival pattern) provided in Exhibit D, Section J is used as is, with no consideration of the fact that the weekly input volumes are random variables in reality, rather than constants as depicted in that section; further, weekly input volumes are assumed to be equally spread during the number of working days in each week.

2. First-come-first-served processing
sequence is used; in reality, other proven operations management techniques
could be used to optimize throughputs.

Aside: IRS may be required to use first-come-first-served sequencing by external
forces.

3. Service rate is assumed to be constant per return; in reality, this would be a random variable dependent upon the type of return, the performance levels of data perfectionists, etc.

Definitions

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Window = Constraint depicting the number of days within which every return must be processed.

Window capacity = The number of returns that can be processed within a window at a given level of daily service rate (processing capacity).

Problem Formulation

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Objective: Find the minimum daily processing capacity necessary to meet window requirements.

Let b[t] = beginning inventory of leftover returns on day t

A[t] = arrivals on day t

S = service rate (control variable) in terms of returns per day

W = number of days (window) within which a return should be processed

Then C = WS = window capacity

b[t] = max { b[t-1] + A[t-1] - S , 0 }

r[t] = max { C - b[t] , 0 } = remaining window capacity for handling A[t]

V[t] = number of returns out of A[t] that will blow the window constraint

= max { A[t] - r[t] , 0 }

Solution

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Find minimum value of S that will ensure the following:

V[t] = 0 for all t = 1,2,3,...,26*n (26 weeks times n working days per week)