Gabriela P. Henning

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 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.

A constraint programming model for the scheduling of flexible manufacturing systems with machine and tool limitations

This contribution presents an integrated constraint programming (CP) model to tackle the problems of tool allocation, machine loading, part routing, and scheduling in a flexible manufacturing system (FMS). The formulation, which is able to take into account a variety of constraints found in industrial environments, as well as several objective functions, has been successfully applied to the solution of various case studies of different sizes. Though some of the problem instances have bigger sizes than the examples reported to date in literature, very good-quality solutions were reached in quite reasonable CPU times. This good computational performance is due to two essential characteristics of the proposed model. The most significant one is the use of two sets of two-index variables to capture manufacturing activities instead of having just one set of four indexes. Thus, dimensionality is greatly reduced. The other relevant feature is the fact that the model relies on an indirect representation of tool needs by means of tool types, thus avoiding the consideration of tool copies.

Knowledge-based predictive and reactive scheduling in industrial environments

Abstract Real-world scheduling problems are intrinsically complex because of the dynamic nature of industrial environments, conflicting organizational goals, the existence of operational constraints and preferences that are difficult to represent in a computational model. In addition, plant capacity and bottleneck stages are generally not known ahead of time since they depend upon the product mixture. Therefore, rigid scheduling procedures, designed to provide optimal or near-optimal solutions under particular circumstances, will not always be satisfactory. Moreover, purely automatic scheduling is not realistic because it neglects the important role of the human expert, who has the ultimate responsibility for all decisions and wants to be engaged in the solution process. To overcome these difficulties, many authors have adopted knowledge-based approaches. This contribution presents a knowledge-based framework, based on the object oriented technology, for building scheduling systems aimed at solving real-world problems. The paper points out the most relevant aspects of the proposed framework architecture that supports both predictive and reactive scheduling. It has been designed to enhance the problem solving capabilities of human schedulers and has been abstracted after the successful implementation of three different scheduling systems, two of which have entered into everyday industrial use. The most important lessons that were learned during the design of these systems are outlined in the paper.

Production Scheduling in the Process Industries: Current Trends, Emerging Challenges and Opportunities

Abstract This paper discusses the current trends and defies associated with production scheduling, both from an industrial and academic perspective. First, the new challenges that appear in the context of globalized and competitive economies are addressed. They stem from the need of considering scheduling as a building block of the Advanced Planning Systems (APSs) that nowadays participate in Supply Chain Management (SCM) functions. They are primarily associated with business process coordination and information integration requirements. Then, main features, strengths and limitations of current academic proposals are briefly addressed. Finally, some of the reasons for the slow acceptance and modest penetration of these research results are highlighted. Thus, challenges and opportunities to be faced in order to alleviate the miscommunication of the academic and industrial worlds are pointed out.

Parametric sensitivity in fixed-bed catalytic reactors

Abstract This paper introduces a criterion for runaway in fixed-bed catalytic reactors based on the behaviour of sensitivity coefficients along the reactor. The criterion can be used when the temperature variation in a co-current cooling medium is taken into account; and also, it is not restricted to simple kinetics. In addition, multiple reactions may be analysed. Some examples of industrial significance are studied and the results are compared with those obtained by other authors.

Design and planning of multipurpose plants involving nonlinear processing networks

Abstract An efficient algorithmic approach to the design and campaign planning of multipurpose plants performing nonlinear batch processes is presented. Nonlinear sequences of processing tasks involving batch mixing and splitting as well as multiple outputs from certain production steps are usually found in real industrial problems. Through the proper allocation of storage capacity, this work shows that a nonlinear batch network can be transformed into an equivalent set of simpler task sequences, called stages, as long as the stage precedence relationships are all fully satisfied. The proposed design procedure consists of the successive solution of the following three optimization problems: 1. (1) a nonlinear mathematical programming (NLP) problem accounting for the stage precedence constraints and providing the set of multistage campaigns to be run, their lengths and the equipment capacity for each processing task all at once. Multiple execution of every single/multistage campaign is permitted by the formulation. Though the existence of a feasible sequencing of such campaigns is guaranteed by the problem, a linear STRIPS-like planner has subsequently been applied to efficiently find it. 2. (2) a small-size mixed-integer linear programming (MILP) problem assigning a sufficient number of standard-size units working in-phase to each processing task. 3. (3) a slightly modified version of the NLP-formulation adjusting stage batch sizes to save some of the assigned smaller units. Three example problems all involving nonlinear batch structures have successfully been solved using GAMS/MINOS 2.25 PC/386 version in a reasonable CPU time.

A knowledge-based approach to production scheduling for batch processes

Abstract Scheduling problem solving has escaped its initial attention on mathematical programming approaches and it is gaining benefits from other fields such as Discrete-Event simulation and Artificial Intelligence (AI). The AI community has investigated the problem and most of its research focuses on the use of dispatching heuristic rules and constraint-satisfaction. This paper presents a different perspective. The similarities between the design and the multiproduct batch plant scheduling problems are analyzed, stressed and exploited; and a methodology based on a task-oriented approach is introduced. The scheduler is viewed as the “designer” of a production plan. Similar to the design problem, the “final artifact” is not known in advance and the complexity of the overall problem is tackled by means of decomposition. To accomplish it, the structure of the solution methodology is identified and explicitly conceptualized. The approach relies on the appropriate modeling of the scheduling scenario. An object-oriented modeling language is presented.

A comprehensive CP approach for the scheduling of resource-constrained multiproduct multistage batch plants

Abstract This work presents a novel, efficient and expressive Constraint Programming (CP) approach to the short-term scheduling problem of multistage batch plants. The CP model accounts for many features found in industrial settings and allows modeling operational policies that group batches of the same product into campaigns. Product campaigns simplify the plant operation and allow reducing scrap and changeover times. The formulation has been extensively tested with various examples, including large-scale ones, and different objective functions. Comparisons with results reported in recent contributions are also presented and discussed.

An Ontological Approach to Integration of Planning and Scheduling Activities in Batch Process Industries

Abstract In the last decades, the integration of informatic applications supporting planning, scheduling and control has been a serious concern of the industrial community. Many standards have been developed to tackle this issue by addressing the exchange of data between the scheduling function and its immediate lower and upper levels in the planning pyramid. However, a more comprehensive approach is required to tackle integration problems, since this matter entails much more than data exchange. So, this article presents an ontological framework that provides the foundations to reach an effective interoperability among the various applications linked to scheduling activities.