Modeling lotsizing and scheduling problems with sequence dependent setups Luis Guimar˜ aes a , Diego Klabjan b , Bernardo Almada-Lobo a a INESC TEC, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal b Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL, USA Abstract Several production environments require simultaneous planing of sizing and scheduling of sequences of pro- duction lots. Integration of sequencing decisions in lotsizing and scheduling problems has received an increased attention from the research community due to its inherent applicability to real world problems. A two-dimensional classification framework is proposed to survey and classify the main modeling approaches to integrate sequencing decisions in discrete time lotsizing and scheduling models. Computational experiments are conducted to assess the performance of various models, in terms of running times and upper bounds, when solving real-word size instances. We also present a new formulation for the problem using commodity flow based subtour elimination constraints. Keywords: Production Planning, Lotsizing and Scheduling, Mixed-Integer Programming, Sequence-dependent Setups, Non-triangular Setups, Computational Benchmark 1. Introduction Several companies face the problem of timing and sizing production lots over a given planning horizon. Addi- tionally, in many of these production environments, switching between production lots of two different products triggers operations, such as machine adjustments and cleansing procedures. These setup operations, which are dependent on the sequence, consume scarce production time and may cause additional costs due to, for example, losses in raw materials or intermediate products. Consequently, the production sequence must be explicitly em- bedded in the lot definition and scheduling. Lot sizing determines the timing and level of production to satisfy deterministic product demand over a finite planning horizon. Sequencing establishes the order in which lots are executed within a time period, accounting for the sequence–dependent setup times and costs. Integration of these two problems enables the creation of better production plans than those obtained when solving the two problems hierarchically by inducing the solution of the lotsizing problem in the scheduling level. Production plans are created with the objective of minimizing the overall costs consisting mainly of stock holding and setups, while satisfying the available capacity in each time period from which the expenditure in setup times is deducted. This production scenario is present in many process industries, in which an efficient use of the available ca- pacity is key to stay competitive in the current market environment. In the beverage industry sequence dependent Email addresses: guimaraes.luis@fe.up.pt (Luis Guimar˜ aes), d-klabjan@northwestern.edu (Diego Klabjan), almada.lobo@fe.up.pt (Bernardo Almada-Lobo) Preprint submitted to European Journal of Operations Research May 18, 2013