1. Introduction and Objectives
Service departments (such as Maintenance, IT, and HR) support the factory but do not produce goods directly. Because final products do not pass through service departments, their accumulated overhead costs must be re-apportioned into the active production departments (such as Assembly and Machining). This process is known as Stage 2 Distribution.
 
2. Mathematical Re-Apportionment Methods
  • Direct Method: Allocates service department costs directly to production departments. It completely ignores any services that support departments provide to each other.
  • Step-Down (Sequential) Method: Allocates service department costs sequentially. The department that provides services to the greatest number of other support departments is cleared first. Once a service department’s costs are allocated out, no subsequent costs can be allocated back to it.
  • Reciprocal (Algebraic) Method: Fully accounts for mutual services provided between support departments. It builds a system of simultaneous linear equations to calculate the true total overhead for each department before final distribution.

3. Computational Ledger Simulation
A factory operates two production departments (Machining, Assembly) and two service departments (Maintenance, HR). The initial Stage 1 overheads are:
  • Maintenance: $10,000
  • HR: $6,000

The reciprocal service relationships are structured as follows:
  • Maintenance provides 20% of its services to HR and 80% to production.
  • HR provides 10% of its services to Maintenance and 90% to production.

python
import numpy as np

# Setting up simultaneous equations:
# M = 10000 + 0.10 * H  =>  M - 0.10*H = 10000
# H = 6000 + 0.20 * M   => -0.20*M + H = 6000

A = np.array([[1.0, -0.10], 
              [-0.20, 1.0]])

B = np.array([10000, 6000])

# Solving for [M, H]
solutions = np.linalg.solve(A, B)
M_total = solutions[0]
H_total = solutions[1]

print(f"True Reciprocal Overhead - Maintenance (M): ${M_total:.2f}")
print(f"True Reciprocal Overhead - Human Resources (H): ${H_total:.2f}")
 

 

Evaluating these equations confirms:
  • Maintenance True Budget (M) = $10,816.33
  • Human Resources True Budget (H) = $8,163.27
  • These true values are then distributed to the Machining and Assembly departments using their final production usage percentages.

 
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