# Push/Pull Parts Production Policy Optimization in the ATO Environment
## 2 Literature Review  
Reduced product life cycles, dynamic market demand, and flexible production cycles are rising as crucial challenges for most industrial companies [2]. In such a context, the assignment of the best production strategy, i.e., Pull-MTO or Push-MTS to each item within the production mix is a strategic issue. Table 1 represents a schematic representation of some recent and important contributions on hybrid MTS/MTO policy definition with the aim of highlighting the objective,  
Figure 1: Reference example of hybrid Push/Pull production strategy in an assembly to order (ATO) environment. the proposed method, and the reported case study. Even if a wide set of researchers and industrial practitioners investigates hybrid MTS/MTO production systems, so far, a limited number of studies was published in this field [14]. Moreover, the few published papers do not focus on manufacturing within an ATO environment. A relevant contribution on hybrid MTS/MTO was the study proposed by [PERSON] [15], which focused on one-stage systems with stochastic demands and capacity constraints through queuing theory. The main goal of the proposed algorithm was to select the items to be managed with MTS production strategy. Furthermore, in this field, other relevant studies were proposed with different goals. According to Table 1, the main optimization objectives are related to:  
* the determination of the decoupling point between MTO and MTS, i.e., by analyzing the flow of the different production stages, the goal is to find separation point between the upstream MTS strategy and the downstream MTO strategy where the generic products are post manufactured and customized [8; 10; 11; 16; 17; 18; 19]. * Optimization of the production planning & scheduling phases by applying a suitable MTS/MTO strategy [5; 14; 20; 21; 22; 23; 24; 25; 26; 27]. * Order acceptance and capacity requirement, including production resource constraints, material supplies, and dynamic changes in the market context [4; 6; 20; 23]
* Inventory management according to the MTS policy [14; 16; 19; 22; 28; 29; 30; 31; 32; 33]. The presence of different objectives explored by researchers in the MTO/MTS policy definition stresses the complexity and relevance of the problem. On the other hand, just a few authors propose multiobjective models, addressing multiple goals simultaneously. As an example, [PERSON] et al. [22] propose a hybrid algorithm for order acceptance and scheduling problem in MTO/MTS industries. [PERSON] and [PERSON] [24] introduce a batch ordering policy to permit economies of scale. [PERSON] et al. [29] propose an optimization model to find the optimal intermediate buffer size considering earliness/tardiness penalty, inventory cost, production penalty, inventory matching, and order cancellation penalty. Moreover, as by the Table 1, different approaches were proposed, e.g., mathematical single- or multiobjective optimization models, heuristic algorithms, decision process models based on Markov chains, or on decisional frameworks, simulation models, etc. The use of industrial case studies is not often present and well-described in the existing research. In fact, the use of numerical analysis is widespread to test the proposed methodologies. The case studies reported by some authors belong to different industrial sectors, demonstrating the cross-interest of this research topic. The literature review highlights that authors focus on defining single-objective models, even if in the hybrid Push/Pull policy definition problem a set of objectives exists, which need to be managed and best balanced. On the other hand, the few contributions proposing multiobjective formulations do not propose a robust multicriteria approach. According to this background, this paper aims at proposing a bi-objective mathematical optimization model supporting the hybrid Push/Pull policy definition to jointly minimize the setup time and the storage used space, getting the final Pareto frontier of the optimal solutions [31]. As demonstrated by [PERSON] et al.