Model and analysis of integrated production–inventory system: The case of steel production

The study originated from an industrial case study in the field of steel production, but it presents a larger interest, as many other manufacturing fields have similar concerns (e.g. foundries, food, textile and paper industries). A significant phase of steel manufacturing is the product cooling (likewise, drying in paper and textile production, or maturing in food production). This phase may be completed in different ways, but (1) it must be carried out in the finished product warehouse and (2) it must meet both production optimisation and customer needs. The latter requirement acquires a strategic relevance in JIT environments. The present study proposes a mathematical model to find the optimal production schedule of steel billets, based on the relevant parameters of the productive system (set-up and processing times, demand profile). In the industrial case examined, the negative impact of holding costs on cash flows is also linked to the space required by the cooling process, which depends on the production schedule adopted. In other words, the finished product storage can be considered a part of the manufacturing cycle and impacts on it. In the case of steel plants operating in JIT environments, the warehouse must be promptly emptied and carefully managed to exploit the available space. Thus, the effect of inventory costs is examined in a production–inventory system with finite capacity, where products are made to order and share the same manufacturing facility. The study is completed by an experimental analysis to investigate the effect of variations in the relevant parameters of the problem.