Model of Integrated Production-Inventory- Distribution System: The Case of Billet Steel Manufacturing Parwadi Moengin and Rina Fitriana, Member, IAENG Abstract—A significant phase of billet steel manufacturing is the cooling process. This phase may be completed in the finished goods warehouse and it must meet both production optimization and customer needs. The fluctuation of customer demand and production process in this phase may cause some problems of production schedule and inventory of billet steel. The decreasing of customer demand can increase the inventory level in finished goods warehouse. Therefore, the company need to consider a production planning that gives an optimum decision of billet steel production schedule. In this paper, a mathematical model of integrated production-inventory- distribution system of billet steel will be proposed. The model is used to find the optimal production schedule of billet steel, based on the relevant parameters of the productive system, such as: set-up time, processing times, and demand profile. The study is completed by a case study to investigate the proposed model. Index Terms—production-inventory-distribution system, scheduling, linear programming, mathematical model. I. INTRODUCTION This paper discusses the optimal method of production scheduling in billet steel products ordered by consumers considering the limitations of space in the warehouse. Fluctuations in consumer demand can be considered as one of the causes of some problems in the production and supply company. Increased demand led to problems concerning storage capacity cooling billet steel products and raw material supply of iron ore. Decline in demand cause overproduction and excessive accumulation of finished goods. This poses particular problems in the cooling warehouse capacity of billet steel products. Observing this, companies need to consider the production planning so that activities are carried out more optimal production to meet market demand. Production planning concerns the tactical planning provides optimum decisions based on the availability of time and the capacity of the company's inventory to overcome problems related to the production process. Utilization of mathematical model for the optimization of production, especially the production of billet steels has been done by many researchers, including Chen and Wang (1997) which uses linear programming models for production planning and distribution of steel, Kapusinski and Tayur (1998) model the production system limited to periodic demand and Kalagnanam et al. (2000) addressed the issue of excess inventory in the process industry. Manuscript is submitted on March 8, 2015. This research was supported and funded by the Ministry of Education and Culture, Republic of Indonesia.. Parwadi Moengin and Rina Fitriana are with the Department of Industrial Engineering, Faculty of Industrial Technology, Trisakti University, Jakarta 11440, Indonesia. (email: parwadi@trisakti.ac.id). Several other authors such as Lally et al. (1997) have made a model of sequencing a continuous casting operation in order to minimize costs, Mohanty and Singh (1998) using a hierarchical approach to planning system steel manufacturing, Tang et al. (2000) using a mathematical programming model for scheduling the production of continuous casting of steel and Tang et al. (2001, 2002) have discussed the problem of production planning and scheduling using Lagrange relaxation. Zanoni et. al. latter. (2005) discuss the optimization of the production system of billet steel products. In general, the billet steel production process starting from (1) the process of melting and cooking through the stages: filling and blending sponge iron, iron and hot scrap bracket iron in the bucket; smelting in the Electric Arc Furnace; Oxidation processes Refining & Electric Arc Furnace; (2) Ladle Refining Furnace process on, and ends with (3) a process in Continuous Casting Machine. This paper is structured as follows. Writing begins from the introduction that discusses the optimization of production associated with distribution, scheduling and inventory that has been done by some previous authors; followed by the proposal of a model of integer linear programming for integrated production-inventory-distribution systems of billet steel products. A case study in PT. XYZ is used to apply the proposed model. II. MODEL FORMULATION FOR INTEGRATED PRODUCTION-INVENTORY-DISTRIBUTION SYSTEM The model is formulated to focus on the optimization of production planning, i.e. the amount of production in the planning horizon. The mathematical model is focused on sustainable production, where finished goods warehouse capacity becomes an important part in the production cycle. To solve this problem, an integer linear programming models is introduced by taking into account the capacity of finished goods warehouse in continuous production planning. In continuous production, initially satisfied the market demand of finished goods inventory in the warehouse, then just do the next planning to meet the rest of the reservation. In this case the integer linear programming models are used, has a goal to maximize profits at the end of the sale of products incorporating the costs saved in the finished goods warehouse, and also pay attention to the cost penalty as the costs incurred because the manufacturer cannot meet the market reservations on time. Basically the integer linear programming model of this paper, consider three kinds of costs, namely: Proceedings of the World Congress on Engineering 2015 Vol II WCE 2015, July 1 - 3, 2015, London, U.K. ISBN: 978-988-14047-0-1 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online) WCE 2015