Planning and scheduling of the make-and-pack dairy production under lifetime uncertainty

Abstract

• We consider a planning and scheduling problem in the make-and-pack production. • We propose a chance constrained linear programming model. • The model minimizes the makespan and accounts for the uncertainty in quality decay. • The numerical study reflects real settings from a yoghurt production case. • The proposed production schedule is evaluated by a simulation model. In the dairy processing, the rapid quality decay of milk-based intermediate mixture to make and pack restricts productivity and, forces organizations to carefully plan and schedule their production. Hereby, in this study, we consider a planning and scheduling problem encountered in the dairy industry and propose a chance-constrained programming model accounting for uncertainty in quality decay of intermediate mixture. The aim of the model is to find the optimal lot sizes and production schedule with minimum makespan (total time needed to finish the daily production). The proposed schedule allows the storage duration of intermediate mixture to be within a stochastic lifetime. A case study is presented to illustrate the typical structure of the two-stage semi-continuous make-and-pack production process. The numerical study reflects real settings from a set (Balkan type) yoghurt production process. Accordingly, a simulation of the production process is introduced to evaluate the proposed production plan and schedule in terms of product waste. The model is examined with 32 scenarios consisting of different distribution parameters, confidence levels and demand patterns. Overall in the scenarios, the proposed plan and schedule result in decreasing 2693 l of product waste with 3.24 h increase of makespan in total.