مسئله مقدار تولید اقتصادی فازی چند-آیتمی با نرخ تولید محدود

Inventory Management and production planning are essential tasks for every company in the industry. Therefore, the development of a large set of Economic Order Quantity (EOQ) models is needed. In this paper, a fuzzy multi-item Economic Production Quantity (EPQ) model is developed. This paper contributes to the state-of-the-art with a theoretical study of a problem, where a company has to decide the size of some production batches under uncertain cycle times. The uncertainty will be handled with triangular fuzzy numbers and an analytical solution will be found to the optimization problem.

In the early 20th century, the first models for the combined optimization of the batch-production and inventory level problem were derived from the basic Economic Order Quantity (EOQ) model. Before this, mathematical methods had started emerging to optimize the size of inventory and orders (the EOQ-model in Harris, 1913) and since then, there has been an increasing number of contributions, which have improved and extended the basic model in many ways. One of these extensions allows for a finite production rate. The different EOQ-models are most often used in a continuous-review setting and it is assumed that the inventory can be monitored every moment in time. It is imperative to acknowledge the importance of production aspects in supply chain management, especially in process-based industries. For these applications, it is important to find solutions that allow the production to be efficient while keeping inventory low (Björk and Carlsson, 2007). This tradeoff problem is found in many supply chains. A specific application that inspired the author to conduct this research is found in the paper industry supply chains in the Nordic countries. These supply chains consist of a few, large paper producing companies and quite many distributors that operate independently from the producers. Typically a large paper machine is producing several products in large quantities. There are often substantial uncertainties found in these supply chains and these cannot be captured by probabilistic measures, cf. Björk and Carlsson (2005) and Carlsson and Fuller (1999). The cycle time (or equivalently the production batch sizes) is often not exact. There are substantial uncertainties in the market conditions (there has been overcapacity on the European fine paper market during the past years, Björk and Carlsson, 2007). This may result in a situation, where management wants to increase batch sizes in order to produce to stock. There are also other reasons for the uncertainty in the batch sizes. All these uncertainties will lead to uncertain cycle time. Therefore, an EPQ-model that models a production process, with several different products, is developed in this paper.