Jaime Cerdá

State-of-the-art review of optimization methods for short-term scheduling of batch processes

There has been significant progress in the area of short-term scheduling of batch processes, including the solution of industrial-sized problems, in the last 20 years. The main goal of this paper is to provide an up-to-date review of the state-of-the-art in this challenging area. Main features, strengths and limitations of existing modeling and optimization techniques as well as other available major solution methods are examined through this paper. We first present a general classification for scheduling problems of batch processes as well as for the corresponding optimization models. Subsequently, the modeling of representative optimization approaches for the different problem types are introduced in detail, focusing on both discrete and continuous time models. A comparison of effectiveness and efficiency of these models is given for two benchmarking examples from the literature. We also discuss two real-world applications of scheduling problems that cannot be readily accommodated using existing methods. For the sake of completeness, other alternative solution methods applied in the field of scheduling are also reviewed, followed by a discussion related to solving large-scale problems through rigorous optimization approaches. Finally, we list available academic and commercial software, and briefly address the issue of rescheduling capabilities of the various optimization approaches as well as important extensions that go beyond short-term batch scheduling.

A cluster-based optimization approach for the multi-depot heterogeneous fleet vehicle routing problem with time windows

This paper presents a novel three-phase heuristic/algorithmic approach for the multi-depot routing problem with time windows and heterogeneous vehicles. It has been derived from embedding a heuristic-based clustering algorithm within a VRPTW optimization framework. To this purpose, a rigorous MILP mathematical model for the VRPTW problem is first introduced. Likewise other optimization approaches, the new formulation can efficiently solve case studies involving at most 25 nodes to optimality. To overcome this limitation, a preprocessing stage clustering nodes together is initially performed to yield a more compact cluster-based MILP problem formulation. In this way, a hierarchical hybrid procedure involving one heuristic and two algorithmic phases was developed. Phase I aims to identifying a set of cost-effective feasible clusters while Phase II assigns clusters to vehicles and sequences them on each tour by using the cluster-based MILP formulation. Ordering nodes within clusters and scheduling vehicle arrival times at customer locations for each tour through solving a small MILP model is finally performed at Phase III. Numerous benchmark problems featuring different sizes, clustered/random customer locations and time window distributions have been solved at acceptable CPU times.

An MILP continuous-time approach to short-term scheduling of resource-constrained multistage flowshop batch facilities

Abstract This work presents a new MILP mathematical formulation for the resource-constrained short-term scheduling of flowshop batch facilities with a known topology and limited supplies of discrete resources. The processing structure is composed of multiple stages arranged in series and several units working in parallel at each one. All production orders consist of a single batch and follow the same processing sequence throughout the plant. The proposed MILP approach is based on a continuous time domain representation that relies on the notion of order predecessor and accounts for sequence-dependent setup times. Assignment and sequencing decisions are independently handled through separate sets of binary variables. A proper formulation of the sequencing constraints provides a substantial saving in sequencing variables and constraints. By postulating a pair of conditions for the simultaneous execution of processing tasks, rather simple resource constraints requiring a few extra binary variables are derived. The proposed MILP scheduling approach shows a remarkable computational efficiency when applied to real-world problems.

Optimal scheduling of multiproduct pipeline systems using a non-discrete MILP formulation

Abstract Multiproduct pipelines permit to transport large volumes of a wide range of refined petroleum products from major supply sources to distribution centers near market areas. Batches of refined products and grades are pumped back-to-back in the same pipeline, often without any separation device between batches. The sequence and lengths of such pumping runs should be carefully selected in order to meet market demands at the promised dates while satisfying many pipeline operational constraints. This paper deals with the scheduling of a multiproduct pipeline system receiving a number of liquid products from a single refinery source to distribute them among several depots. A novel MILP continuous mathematical formulation that neither uses time discretization nor division of the pipeline into a number of single-product packs is presented. By developing a more rigorous problem representation, the quality of the pipeline schedule is significantly improved. Moreover, a severe reduction in binary variables and CPU time with regards to previous approaches is also achieved. To illustrate the proposed approach, a pair of real-world case studies was solved. Both involve the scheduling of a single pipeline carrying four oil derivatives from an oil refinery to five distribution depots. Higher pumping costs at daily peak periods were also considered. Compared with previous work, better solutions were found at much lower computational time.

Dynamic scheduling in multiproduct batch plants

This work introduces a novel MILP formulation for reactive scheduling of multiproduct batch plants to optimally generate updated schedules due to the occurrence of unforeseen events. It can also be used to improve a non-optimal production schedule before it is executed. The approach is based on a continuous-time problem representation that takes into account the schedule in progress, the updated information on the batches still to be processed, the present plant state and the time data. To limit the changes on the current schedule, rescheduling operations involving local reordering and unit reallocation of old batches as well as the insertion of new batches are just permitted. In contrast to previous contributions, multiple rescheduling operations can be performed at the same time. The MILP problem formulation is iteratively solved until no further improvement on the current schedule is obtained. Three large-size example problems were successfully solved with low computational cost.

Optimal scheduling of batch plants satisfying multiple product orders with different due-dates

Abstract In most multiproduct batch plants, the short-term planning activity starts by considering the set of product orders to be filled during the scheduling period. Each order specifies the product and the amount to be manufactured as well as the promised due date and the release time. Several orders can be related to the same product, though featuring different quantities and due-dates. The initial task to be accomplished by the scheduler is the so-called batching process that transforms the product orders to fill into equivalent sets of batches to be scheduled and subsequently assigns a due date to each one. To execute the batching procedure for a particular product, the scheduler should not only account for the preferred unit sizes but also for all the orders related to such a product and their corresponding deadlines. Frequently, a batch is shared by several orders with the earliest one determining the batch due-date. In this paper, a new two-step systematic methodology for the scheduling of single-stage multiproduct batch plants is presented. In the first phase, the product batching process is accomplished to minimize the work-in-process inventory while meeting the orders’ due-dates. The set of batches so attained is then optimally scheduled to meet the product orders as close to their due dates as possible. New MILP continuous-time models for both the batching and the scheduling problems were developed. In addition, widely known heuristic rules can be easily embedded in the scheduling problem formulation to get a faster convergence to near-optimal schedules for ‘real-world’ industrial problems. Three example problems involving up to 29 production orders have been successfully solved in low computational time.

Dynamic scheduling of multiproduct pipelines with multiple delivery due dates

Abstract Scheduling product batches in pipelines is a very complex task with many constraints to be considered. Several papers have been published on the subject during the last decade. Most of them are based on large-size MILP discrete time scheduling models whose computational efficiency greatly diminishes for rather long time horizons. Recently, an MILP continuous problem representation in both time and volume providing better schedules at much lower computational cost has been published. However, all model-based scheduling techniques were applied to examples assuming a static market environment, a short single-period time horizon and a unique due-date for all deliveries at the horizon end. In contrast, pipeline operators generally use a monthly planning horizon divided into a number of equal-length periods and a cyclic scheduling strategy to fulfill terminal demands at period ends. Moreover, the rerouting of shipments and time-dependent product requirements at distribution terminals force the scheduler to continuously update pipeline operations. To address such big challenges facing the pipeline industry, this work presents an efficient MILP continuous-time framework for the dynamic scheduling of pipelines over a multiperiod moving horizon. At the completion time of the current period, the planning horizon moves forward and the re-scheduling process based on updated problem data is triggered again over the new horizon. Pumping runs may extend over two or more periods and a different sequence of batches may be injected at each one. The approach has successfully solved a real-world pipeline scheduling problem involving the transportation of four products to five destinations over a rolling horizon always comprising four 1-week periods.

An efficient MILP continuous-time formulation for short-term scheduling of multiproduct continuous facilities

Abstract This paper presents a new MILP mathematical formulation for the scheduling of resource-constrained multiproduct plants involving continuous processes. In such facilities, a sequence of continuous processing steps is usually carried out to produce a significant number of final products and required intermediates. In order to reduce equipment idle time due to unbalanced stage capacities, storage tanks are available for temporary inventory of intermediates. The problem goal is to maximize the plant economic output while satisfying specified minimum product requirements. The proposed approach relies on a continuous time domain representation that accounts for sequence-dependent changeover times and storage limitations without considering additional tasks. The MILP formulation was applied to a real-world manufacturing facility producing seven intermediates and fifteen final products. Compared with previous scheduling methodologies, the proposed approach yields a much simpler problem representation with a significant saving in 0–1 variables and sequencing constraints. Moreover, it provides a more realistic and profitable production schedule at lower computational cost.

An MILP Continuous-Time Framework for Short-Term Scheduling of Multipurpose Batch Processes Under Different Operation Strategies

This work introduces a novel MILP continuous-time framework to the optimal short-term scheduling of non-sequential multipurpose batch processes with intermediate storage vessels. It is based on a problem representation that describes the batch sequence at any processing/storage unit by providing the full set of predecessors for every batch. Different operation modes can be considered by making minor changes in the problem model. The proposed framework can also handle sequence-dependent changeovers as well as multiple storage tanks available to receive material from one or several processing units. Three example problems involving up to fifteen batches and six processing tasks were successfully solved. Compared with previous work, a drastic reduction in both problem size and CPU time has been achieved.

The multi-echelon vehicle routing problem with cross docking in supply chain management

Multi-echelon distribution networks are quite common in supply chain and logistics. Deliveries of multiple items from factories to customers are managed by routing and consolidating shipments in warehouses carrying on long-term inventories. On the other hand, cross-docking is a logistics technique that differs from warehousing because products are no longer stored at intermediate depots. Instead, cross-dock facilities consolidate incoming shipments based on customer demands and immediately deliver them to their destinations. Hybrid strategies combining direct shipping, warehousing and cross-docking are usually applied in real-world distribution systems. This work deals with the operational management of hybrid multi-echelon multi-item distribution networks. The goal of the N-echelon vehicle routing problem with cross-docking in supply chain management (the VRPCD-SCM problem) consists of satisfying customer demands at minimum total transportation cost. A monolithic optimization framework for the VRPCD-SCM based on a mixed-integer linear mathematical formulation is presented. Computational results for several problem instances are reported.