# Push/Pull Parts Production Policy Optimization in the ATO Environment
## 1 Introduction  
Offering differentiated products is essential for many manufacturing companies. To reach high levels of efficiency and throughput, they developed product platforms, implementing product standardization and modularization. These elements offered the possibility to implement the Assembly to Order (ATO) paradigm, permitting low time to market and high level of product personalization [1, 2, 3]. In the ATO context, assembly is performed with a Just in Time (JIT) approach, while the parts manufacturing and procurement lead times are masked by the stock. The ATO production strategy typically uses a Pull-Make to Order in the assembly phase and a Push-Make to Stock strategy before the assembly phase according to forecasts or storage reorder points [4]. The pure Make to Stock (MTS) production strategy aims to preventing stock-out risks, and its main advantage is the reactivity to fulfil the demands. The performance criteria in MTS production planning are usually cost-based [5]. In fact, MTS policy can have a negative impact on many operative aspects: the inventory costs, the space utilization, the production capacity utilization, etc. As consequence, many companies tried to adopt some strategies to mitigate this problem. A possible strategy is to apply for the parts with these attributes an MTO-Pull production policy instead of an MTS-Push policy. The result will be a hybrid Push/Pull policy applied to the internally manufactured parts used in assembly (Figure 1). As demonstrated by many studies in the field [6, 7, 8], in recent years industrial companies are moving toward the implementation of hybrid MTO/MTS production strategies. Technological developments in manufacturing systems increasingly allow companies to manufacture different products on the same production facility with hybrid approaches [9]. For example, low-valued, standardized products will often be made to stock, allowing demand to be satisfied instantly. For high valued products with irregular demand, stocking can be expensive or even impossible, and these are typically produced to order [10]. A proper combination of (Make To Order/Make To Stock) MTO/MTS policies can exploit the advantages of both lower inventory and short delivery time [11]. It needs to be optimized for each part as function of its attributes and in accordance with the production system constraints. From a practical point of view, there are many implications. The proposed approach can be applied to different manufacturing technologies: cutting, bending, welding, painting, machining, etc. Secondly, different parts typologies can be interested in a Pull production policy as an effect of their wide variety, huge storage space utilization, and relevant cost. For example, the product frames, the product structure, the switchboards, the electrical engines, the pumps, the plastic parts, etc. The aim of this paper is to explore the chance of using flexibility in production to cope with the wide product variety by applying a hybrid Push/Pull production for internally produced parts to define the best policy to apply for each of them. The novelty of the paper is represented by the proposed bi-objective mathematical optimization model to properly set for each part the Push or Pull policy to minimize setup time and the inventory used space by using a multiciteria approach. A key element of the research is the adoption of operative objective functions instead of a general cost-based approach. In fact, productive and logistic attribute of the parts are considered because they strongly impact on the process. Consequently, the maximum number of units that can be stacked on a Euro Pallet (EPAL) (logistic parameter) and the agility (production parameter) are considered in the proposed optimization model. A further element of interest of this research is the consideration of the concept of agility in the hybrid Push/Pull policy definition, i.e., the ability of the upstream production system to rapidly cope with a variable market demand [12; 13].