A mixed integer programming problem in the pharmaceutical industry

Abstract

This dissertation deals with an optimization problem which appears in the context of scheduling pharmaceutical quality control tests. Scheduling such tests, which are mandatory to approve the safety, purity and efficacy of pharmaceutical product families, is a very challenging task given the limited resource availability and the fact that a single product family must undergo multiple tests. The aim of this study is to develop an original mixed integer linear programming (MILP) model for scheduling these laboratory tests within the pharmaceutical company Aurobindo Pharma (Malta) Limited. Each week the company needs to plan tests for approximately 40 different product families, with each family requiring at least 5 different tests. Effective plans are thus essential for increasing efficiency of the laboratory and improving utilization of resources (employees/machines). The proposed model determines a schedule over a given planning horizon by minimizing the makespan. It encompasses constraints such as assignment constraints of different stages of tests to resources and timing constraints between tests pertaining to the same product family. Having formulated the model, theoretical background on the existence and uniqueness of optimal solutions to MILP problems is studied and exemplified. The proposed model has been implemented in GAMS and solved by CPLEX/GUROBI via a Branch-and-Cut solution approach. Computational experiments were run on real data provided by the company over different planning horizons. The success of obtained results is reported via Gantt charts.