Optimization of workers quantity using mathematical model

Abstract

Production and maintenance processes are inherent in the life cycle of every product. Despite great efforts to automate these processes, a great deal of human resources are still required, which represent a significant part of the financial costs. Each process is composed of sub-tasks that require certain specifics in terms of the number of staff, their expertise, qualifications and experience. It is assumed that the staff are divided according to specifics into different groups with differing wages. Workers' wages are reflected in the final financial cost of the product, its life cycle and its return. Reducing labour costs in a production or maintenance process can be achieved by reducing the total number of staff deployed in the process and by appropriately composing groups of workers. Reducing labour costs leads to increased competitiveness in the market. The main tools of competitiveness are price, speed and range of services offered. This paper examines a strategy that uses price as the main tool for competitiveness in the market. One way to reduce the final price of the product for the customer is to optimise the costs of human resources. This can be achieved through appropriate planning of staff shifts. The specifics of the deployment of staff in a production or maintenance process depend on the requirements of the process sub-tasks. This means that each group of workers can only handle a certain group of tasks according to their qualifications. A Binary Programming Problem with Linear Bonds will be used to plan the deployment of staff, aiming to minimize the number of workers needed in a production or maintenance process within a predefined timeframe.