A model of optimization for the integrated problem of sizing of lots and production programming in factories of soft drinks

The present paper establishes, describes mathematically and solves a multi-level lot sizing and scheduling problem in an industrial set with parallel machines and sequence-dependent setup cost and time. The problem is motivated by real situations found in some industrial settings mainly the soft drink industry. In this kind of industry, the production involves two interdependent levels with decisions about raw material storage and soft drink bottling. The several raw materials are stored in tanks from which they flow to the bottling lines. The challenge is to determine simultaneously the minimum cost lot sizing and scheduling of raw material in tanks and also in the bottling lines, where setup costs and time depend on the previous items stored and bottled. A mixed-integer mathematical model with several combined constraints that used to be handled apart in the literature is proposed. The lack of similar models led us to create a set of instances to evaluate the model and the solution techniques developed. The instances were optimally solved by the GAMS/Cplex software. Due to the problem complexity, it is demonstrated that the use of this optimization package is only viable for small-sized instances. The computational results are shown and analyzed.