A New Continuous-Time Scheduling Formulation for Continuous Plants under Variable Electricity Cost

This work addresses the scheduling of continuous plants subject to energy constraints related to time-dependent electricity pricing and availability. Discrete and continuous-time formulations are presented that can address these issues together with multiple intermediate due dates. Both formulations rely on the resource-task network process representation. Their computationally performance is compared for the objective of total electricity minimization with the results favoring the discrete-time model due to the more natural way of handling such a wide variety of discrete events. In particular, it can successfully handle problems of industrial size. Nevertheless, the new continuous-time model is a major breakthrough since it is the first model of its type that is able to effectively incorporate time-variable utility profiles. When compared to a simple manual scheduling procedure, the proposed scheduling approaches can lead to potential electricity savings around 20% by switching production from periods of high to low electricity cost. * To whom correspondence should be addressed. Tel.: +351-210924643. Fax: +351-217167016. Email: [email protected]. 2 1. Motivation Enterprises are currently under pressure to produce at the lowest possible cost within continuously changing economic constraints. To achieve this goal, they must actively look at the best operating practices and optimize these both globally and locally. Within this overall goal, scheduling plays an important part. This work is motivated by a real industrial problem that we cannot disclose for confidentiality reasons. It involves the final stage of a multiproduct plant with electricity intensive parallel equipment units, where scheduling involves deciding when each unit has to produce a certain product. Most of the times, this is made manually by the operator according to heuristic rules. The products are then sent to storage units, where they are stored until dispatching takes place. Meeting customer demands on time is vital, and for this reason, in some plants, no other factors are taken into account besides trying to keep the storage units full in order to be able to fulfill the orders. Plant scheduling is difficult due to the following factors: large combinatorial size arising from the number of equipment units, products and storage units; various operating and contractual constraints; liberalized electricity market with nontransparent billing practices. Due to the inherent complexity, the operator scheduling choices may be far from the optimal ones. The most challenging aspect of plant scheduling is undoubtedly the incorporation of energy constraints related to electricity pricing and availability. We consider in this paper the case where in the planning stage, contracts are agreed between the electricity supplier and the plant, which often specifies maximum levels of power usage. If electricity consumption exceeds this threshold, the plant incurs in stiff penalties, whereas underproduction costs the same as planned production. Even for normal production, electricity cost varies significantly throughout the day, and this must be taken into consideration within the modeling framework. Another important aspect, concerns meeting the sales forecasts, which represent the minimum amount of products that has to be available in the storage units, during the time horizon. These are typically considered to occur at the end of each day. Accounting for events that occur at predetermined points of time, for instance at a specific hour of a given day, being either a change in electricity cost level or the occurrence of a demand point, may