A proposed mathematical model for production planning problem in the brewing industry

Production planning is a continuous process that aims to achieve particular production amount at the right time while keeping the system resources' utilization at a target level and guaranteeing the satisfaction of the market demand. This study addresses the production planning problem in a brewing department while considering quality control inspections and rejection percentages. In this paper, a mathematical optimization model is proposed for the brewing company under the study. The targeted production, according to the estimated demand, could be less or more than the planned production volume. The brewing department consists of a series of stages which produces a set of product types at each shift. The objective function aims to minimize the disparity between planned production volume and targeted production volume, where the former represents the amount of planned production volume of each product type on each day, and the latter represents the targeted volume of each product type on day. The model decision variables calculate the optimal volume that should be targeted at each stage while considering the stages' maximum capacity and quality defect allowance of 90%. The proposed model is validated based on real data from a brewing manufacturing system located in Gauteng Province, South Africa. The model is solved optimally considering an 8 hours-shift time unit, and a three-weeks (63 shifts) planning horizon. The proposed model is generic and can be applied for production planning of any brewing manufacturing system. Based on the inputs, the processes in the brewing department under the study are not capable of achieving the volume they are expected to achieve. Stage one, stage two and stage three can only achieve a maximum volume of 3600 HL, 3780 HL and 5760 HL respectively in an eight-hours shift.