Optimal Multi-Period Manpower Planning with Substitable and Non-Substitutable Employee Types under Contract Period Constraint

Ling Xiangmin

Abstract

Manpower planning models have been extensively researched to gain insights into the workforce. Since 1990, a new type of manpower planning problem with the objective of minimizing manpower costs have been substantially discussed. This will be the research focus of the thesis presented.

The thesis investigates a problem of optimal manpower planning over a long planning horizon, with a minimal contract period and two employee types, Type A and Type B. Type B is able to substitute for Type A when needed, while Type A is not able to cover for Type B. The objective is to minimize costs for the two types of employees, including fixed (recruitment / dismissal) costs and variable (salary) costs.

The problem is first formulated as a dynamic programming model (MPSNC). By deriving several properties and theorems of the problem, an improved dynamic programming approach with O (T) computational complexity is proposed.

By introducing Type Z employees to represent the portion of employees who are Type B but are used to cover for Type A, and Type B’ employees, who are Type B employees excluding Type Z employees. MPSNC is reduced into three sub-problems, namely MPSNC-1, MPSNC-2 and MPSNC-3. MPSNC-1 is a problem with only Type A and Type Z employees to get optimal decisions fore Type A employees and demand for the part of Type B employees who are used to cover for Type A. MPSNC-2 is proposed to minimize cost for Type B’ employees. MPSNC-3 is proposed to minimize cost for Type B employees, who are a combination of Type B’ and Type Z employees.

In order to solve the problem, two algorithms, Algorithm 1 and Algorithm 2, are formulated. Algorithm 1 is proposed to solve an optimal multi-period manpower planning problem with minimal contract period, and only one type of employees. Algorithm 2 is proposed to solve an optimal multi-period manpower planning with minimal contract period and two types of employees, Type A and Type Z.

Numerical results are provided to illustrate the performance of the improved dynamic programming approach. A comparison with no substitution is done to demonstrate the approach’s cost effectiveness. Finally, the thesis is concluded by summarizing contributions of the paper and discussing future research recommendations.