## 2 Literature Review
### Solution Approaches and Model Extensions
The authors of [27] apply a combined genetic algorithm and mathematical programming approach to solve the P2 SMM that outperforms the approaches presented in [26]. In [28], the authors adjust the P2 SMM for an application in the brewery industry and solve the problem heuristically by using a constructive relax-and-fix heuristic and several improvement procedures based on fix-and-optimize strategies. Note that these approaches borrow ideas from the much older POPMUSIC approach of [29]. The authors of [30] present a GLSP-based model formulation for a multi-product multi-level job shop production where they subdivide the macro-periods into three types of micro-periods: one type for production, one for setups, and one for idle time. Due to the high complexity of their formulation, only problems with a small number of periods, products, and machines can be solved to optimality. In [31], the authors propose a formulation for lot sizing and scheduling in a flow shop environment with sequence-dependent setups and develop four fix-and-relax heuristics that rely on successive resolutions of reduced size MIP-formulations of the problem. The authors of [32] propose a formulation based on the model of [30] for a flexible flow shop environment with sequence-dependent setups. Additionally, the authors of [33] develop two algorithms based on a rolling horizon approach where first, all binary variables of the problem are relaxed. Then, relaxed binary variables of the current period are divided into the two groups so that the members of the first and second groups get value one or zero, respectively. The authors of [34] present two MIP-formulations for joint lot sizing and scheduling motivated by an animal feed plant. While the first formulation sequences each period independently, the second model takes linking setup states between periods into account. The authors present three relax-and-fix (RF) heuristic approaches where they either apply the RF heuristic for relaxing and fixing the lot sizes or the periods. While the RF heuristic on the integer lot sizes performs best, the authors observed that a forward-oriented RF over the periods acts like a greedy heuristic resulting occasionally in infeasible solutions for instances known to be feasible. In [35], the author presents an extended formulation for the GLSP with multiple production stages where an embedded State-Task-Network is used to model product substitution and flexible Bill-of-Materials by introducing several tasks that produce the same product while using different input products. In [36], the authors consider a GLSP-based model with different machine configurations. Therefore, the authors introduce tools as an additional, capacitated resource in a single-stage, multi-machine problem and model tool changeovers instead of product changeovers. As a specific tool cannot be used on more than one machine at a time, continuous variables for the starting and ending times of tool use are introduced. The authors of [37] present a hybrid mixed-binary model based on the GLSP for a practical problem of the process industry and propose two transportation-based reformulations, namely the quantity-based transportation problem (QTP) and the proportional transportation problem (PTP). In their statistical analysis, they observe that the PTP reformulation performs best on average, but for cases of a high level of minimum production quantities, it is outperformed by the QTP reformulation. In [38], the authors propose three novel mathematical formulations for a two-stage GLSP where multiple products are produced on parallel, non-identical machines inspired by the textile industry and solve them with a MIP-solver. The authors of [39] adapt this model for usage in the yarn production and solve the problem by means of a hybrid method called hamming-oriented partition search, which is a branch-and-bound-based procedure that incorporates a fix-and-optimize improvement method.