Production planning and control in manufacturing systems cover several aspects, at different hierarchical levels, including decisions on production and inventory quantities, resource acquisition, production allocation and sequencing. We consider a problem that is typical of companies that manufacture products in production plants placed in different production areas worldwide. A solution framework for the production allocation and balancing problems based on mathematical programming is proposed. Its computational efficiency is improved using techniques from constraint programming, in order to make it possible to solve real world instances of the problems. An industrial test case is used as a benchmark to prove the effectiveness of the proposed approach.
Production planning and control in manufacturing systems cover several aspects, at different hierarchical levels, including decisions on production and inventory quantities, resource acquisition, production allocation and sequencing. Consequently, different and often contrasting objectives can be pursued; as well as several constraints may need to be considered. In this paper, we address the case of a manufacturing company with production sites spread on a global scale: once a set of orders is given, each characterized by a certain due date, they must be allocated to the production sites and scheduled over time in order to fulfill both customer satisfaction and technological requirements. We present a decision support system (DSS) being developed to provide production managers with an effective tool for this task. The DSS is a software package based on mathematical programming models defined and solved within a user customizable decision framework. Customer satisfaction aspects include two main issues: respect of the agreed due dates and quality level requirements. The decision system considers the former as a strict constraint, while the latter translates into a set of production sites approved by each customer. Hence, not all production orders can be manufactured in any site. Furthermore, there might be a preference level among the sites allowed for a given order. On the other hand, technological requirements are related to production and logistics-related issues, such as the opportunity to group similar products in a same production site as well as optimize the usage of resources and materials available at each site.
Decision support methods have been developed in the literature over the last years to address the ever-growing need for enterprises to manage worldwide spread activities. Supply chain planning involves several aspects at different hierarchical levels; they have been classified, among the others, in [1] as: strategy, major resources capacity planning, tactical production planning, scheduling, execution and feedback. This work addresses tactical production planning and scheduling issues. Trial-and-error approaches are often adopted in this area, as described in detail in [2]. Mathematical programming techniques in general and linear programming in particular have been widely used for production planning issues since the 1960s, see [3] for instance. Since from those early years, however, it appeared clear how managing the whole production as a single, monolithic problem was not an efficient solution to realize effective decision support systems. In [4], for instance, the problem was already divided into three different levels: strategic planning, management control and operations control. Linear programming-based production planning tools typically operate at a higher, aggregate production level. In order to address production planning problems at a deeper detail, integer and, often, binary variables need to be introduced into the mathematical model. This leads to more complex models such as the ones described in [5]. A thorough analysis of planning and scheduling applications as applied in both manufacturing and services industries can be found in [6].
Several approaches exist to decision-making and DSSs can be adapted to various domains. Hence, a DSS can be defined and developed following different approaches. According to [7], a DSS is simply a computer-based system that aids the process of decision making; in more precise terms, [8] defines a DSS as an interactive, flexible and adaptable computer-based information system, especially developed for supporting the solution of a non-structured management problem for improved decision making. It utilizes data, provides an easy-to-use interface and allows for the decision maker's own insights. We designed a DSS that is intended to help the decision maker take his decisions using results coming from data analysis and mathematical programming-based optimization procedures. The DSS is being tested on actual case studies and promising results are presented in the paper, along with hints for future improvements and investigations.
The paper is organized as follows. Section 2 synthetically describes the addressed problem, along with possible scenarios where such a problem might be encountered. The problem is then decomposed and the proposed approach for the two sub-problems is analyzed in 2.1 and 3.4. The developed decision support system and its application to a test case coming from the furniture manufacturing sector are described in 4 and 5, also providing computational results. Final remarks and possible future developments are shown in Section 6.
We addressed a production planning problem that can be often found in companies that manufacture products on a global scale, with production plants dislocated in different production areas. We proposed a solution method for the problem based on mathematical programming, integrating it with techniques deriving from constraint programming in order to improve the computational efficiency of the proposed solution. We considered an industrial test case coming from a corporation having its headquarters in Italy and we proved the effectiveness of the proposed approach developing a DSS used in the company over a large period in parallel with traditional trial-and-error methods. The proposed solution proved its effectiveness over KPIs indicated by the company.
In the next future, we plan to further improve the proposed approach, including more sector-specific rules as well as improving the DSS implementation in terms of available interfaces towards both the user and MRP systems.
