Formulation and Solution ofTwo-Level Capacitated Lot-Sizing Problem

The integration of sequencing decisions in lot-sizing and scheduling problems has received an increased attention from the research community due to its inherent applicability to the real-world problems. In this paper, we develop and solve a synchronized and integrated two-level lot-sizing and scheduling problem motivated by a real-world problem arisen in the soft drink production. The soft drink production process has two main stages: flavor preparation (Stage1) and bottling (Stage2). In Stage 1, the liquid flavor (concentrated syrup plus some water) is prepared in tanks with various capacities. In Stage 2 in which the liquid flavors are bottled at the filling lines. we considered stock capacityconstraint, and shortages of the combination(shortages backlog and lost sales) added to the model. The aim is to determine the lot-sizing and scheduling raw materials and products so that the soft drink flavors and bottle types are assigned to the tanks and bottling lines, respectively, in order to meet a known weekly product demand. Finally, we implement LINGO solver to solve this model.