A Zero-One Integer Programming Model for the Optimum Workforce Capacity Planning with Workload Constraints

S.A. Hassan (Egypt) and I.A. Al-Darrab (Saudi Arabia)


Human resource management; Workforce capacityplanning; Integer programming; Optimization


Workforce planning is an essential activity that is required to optimally utilize human resources in an organization, work center or service facility. The assignment problem, which is a special case of the transportation problem, is an example of optimally and uniquely allocating each resource (e.g., an employee, machine or time slot) to a particular activity (e.g., a task, site or event). Another problem in workforce planning arises when management needs to employ the right number of people to perform daily tasks such as in a reception department. Each employee is weekly required to work a certain number of days (not necessarily consecutive) and the number of required employees varies from day to day according to demand. In particular, if every employee is required to work five days a week and takes any two days off, then scheduling employees to meet daily requirements becomes a formidable task for management. This problem is harder than when the two off-days are consecutive. This paper addresses the problem of finding the optimal number of employees to be assigned each day of the week and determining the weekly schedule of each employee given that on each day at least a certain number of employees must be used to meet job or project requirements. The approach presented here is to solve the problem in two stages. The first stage solves the problem with two consecutive off-days using a linear integer programming model. The second stage uses a zero-one integer programming model utilizing results of the first stage. Both mathematical formulation and solution to the problem are developed, and the LINDO computer package is used to solve an illustrative example. The optimum daily workforce size and schedule of every employee are thus obtained.

Important Links:

Go Back