An approach to solving a scheduling problem arising in industry

• Main Author: Stoltz, Adham Raymond
• Format: Others
• Language: en
• Published: 2018
• Online Access: https://hdl.handle.net/10539/25625

A dissertation submitted to the Faculty of Science, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, November 2017. === This work is a result of the necessity to resolve a real world problem: a call centre capacity problem. The result of the capacity challenge is a high cost of operations and large number of disgruntled customers. The research comprises two components: developing a new mathematical model as an extension to existing scheduling problems and then also the industrial engineering component of implementing this new scheduling model into the call centre operation in which the problem was identi ed. The real world problem is introduced and discussed in detail, with particular emphasis placed on the unique features and events which give rise to the capacity problem. The problem is shown to share many features with the class of problems known as Scheduling Problems. Particular attention is paid to the sub classes of Resource Constrained Project Scheduling (RCPSP) and Resource Levelling Problems (RLP). A review of the literature relating to these classes of problems, as well as the extensions and features that are relevant to the real world problem, is presented. The real world problem is discussed in more detail and framed in terms of the conventions that have been established for RCPSP and RLP. Similarities and di erences between the real world problem and established models from literature are discussed. The special and unique features of this problem are then shown to be: the need to perform scheduling on a batch basis every day, without knowledge of what will occur the following day and also the requirement that resources (call centre capacity) are fully utilized and not exceeded. There is also no terminal state which can be planned for, batch scheduling continues inde nitely. The result of the research is that a new mathematical model called the Critical Time Window Resource Levelling Problem (CTWRLP) with the Continual Rescheduling method is developed and proposed as a method for solving the real world scheduling problem. This method addresses all the requirements of the real world problem. An approach to solving the model in the practical environment is also presented. This involves additional pre-processing required to prepare all inputs for the scheduling model, namely creating sub-models for calculating resource consumption and resource availability. The global optimization technique of Simulated Annealing is then introduced as this is the method chosen to solve the optimization component of the CTWRLP. The CTWRLP model is implemented in the call centre. The practical algorithm, numerical solution technique, results and success of the model are presented. === LG2018