Carlos A. Méndez

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.

Scope for industrial applications of production scheduling models and solution methods

Abstract This paper gives a review on existing scheduling methodologies developed for process industries. Above all, the aim of the paper is to focus on the industrial aspects of scheduling and discuss the main characteristics, including strengths and weaknesses of the presented approaches. It is claimed that optimization tools of today can effectively support the plant level production. However there is still clear potential for improvements, especially in transferring academic results into industry. For instance, usability, interfacing and integration are some aspects discussed in the paper. After the introduction and problem classification, the paper discusses some lessons learned from industry, provides an overview of models and methods and concludes with general guidelines and examples on the modeling and solution of industrial problems.

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.

A simultaneous optimization approach for off-line blending and scheduling of oil-refinery operations

This paper presents a novel MILP-based method that addresses the simultaneous optimization of the off-line blending and the short-term scheduling problem in oil-refinery applications. Depending on the problem characteristics as well as the required flexibility in the solution, the model can be based on either a discrete or a continuous time domain representation. In order to preserve the models linearity, an iterative procedure is proposed to effectively deal with non-linear gasoline properties and variable recipes for different product grades. Thus, the solution of a very complex MINLP formulation is replaced by a sequential MILP approximation. Instead of predefining fixed component concentrations for products, preferred blend recipes can be forced to apply whenever it is possible. Also, different alternatives for coping with infeasible problems are presented. Sufficient conditions for convergence for the proposed approach are presented as well as a comparison with NLP and MINLP solvers to demonstrate that the method provides an effective integrated solution method for the blending and scheduling of large-scale problems. The new method is illustrated with several real world problems requiring very low computational requirements.

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.

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.

MIP-based decomposition strategies for large-scale scheduling problems in multiproduct multistage batch plants: A benchmark scheduling problem of the pharmaceutical industry

An efficient systematic iterative solution strategy for solving real-world scheduling problems in multiproduct multistage batch plants is presented. Since the proposed method has its core a mathematical model, two alternative MIP scheduling formulations are suggested. The MIP-based solution strategy consists of a constructive step, wherein a feasible and initial solution is rapidly generated by following an iterative insertion procedure, and an improvement step, wherein the initial solution is systematically enhanced by implementing iteratively several rescheduling techniques, based on the mathematical model. A salient feature of our approach is that the scheduler can maintain the number of decisions at a reasonable level thus reducing appropriately the search space. A fact that usually results in manageable model sizes that often guarantees a more stable and predictable optimization model behavior. The proposed strategy performance is tested on several complicated problem instances of a multiproduct multistage pharmaceuticals scheduling problem. On average, high quality solutions are reported with relatively low computational effort. Authors encourage other researchers to adopt the large-scale pharmaceutical scheduling problem to test on it their solution techniques, and use it as a challenging comparison reference.

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.