Sequencing a generalized two-stage flowshop with finite intermediate storage

The scheduling of batch chemical facilities may be modeled as a generalized flowshop problem, for which the objective is to minimize the products' completion time. In particular, this paper examines the scheduling difficulties that arise if interstage storage is used within the production facility. A branch and bound solution procedure is presented which uses a simulation model to evaluate sequence compeltion times. An initial upper bound completion time is determined based on a heuristic scheduling rule.     

Scheduling of serial multiproduct batch processes via simulated annealing

We present an in-depth study of the simulated annealing approach to the scheduling of serial multiproduct batch processes under the assumption of a permutation schedule. Four versions of the simulated annealing algorithm are studied based on two move acceptance criteria, the Metropolis algorithm and the Glauber algorithm, and two annealing schedules, the exponential schedule and the Aarts and van Laarhoven schedule. Makespan minimization is performed for unlimited intermediate storage (UIS), no intermediate storage (NIS), zero wait (ZW), finite intermediate storage (FIS) and mixed intermediate storage (MIS) flowshop problems using simulated annealing and also the idle matrix search (IMS) heuristic. Of the four versions of the simulated annealing algorithm studied, the Metropolis algorithm with the Aarts and van Laarhoven annealing schedule is found to give the best results, with all four versions giving significantly better results than the IMS heuristic. The Metropolis algorithm with the Aarts and van Laarhoven annealing schedule is studied in more detail for further comparison with the IMS heuristic in terms of the computational effort expended by the simulated annealing algorithm and the solution quality obtained.     

Genetic algorithm for short-term scheduling of make-and-pack batch production process

This paper considers a scheduling problem in industrial make-and-pack batch production process. This process equips with sequence-dependent changeover time, multipurpose storage units with limited capacity, storage time, batch splitting, partial equipment connectivity and transfer time. The objective is to make a production plan to satisfy al constraints while meeting demand requirement of packed products from various product fam-ilies. This problem is NP-hard and the problem size is exponentially large for a realistic-sized problem. Therefore, we propose a genetic algorithm to handle this problem. Solutions to the problems are represented by chromo-somes of product family sequences. These sequences are decoded to assign the resource for producing packed products according to forward assignment strategy and resource selection rules. These techniques greatly reduce unnecessary search space and improve search speed. In addition, design of experiment is carefully utilized to de-termine appropriate parameter settings. Ant colony optimization and Tabu search are also implemented for com-parison. At the end of each heuristics, local search is applied for the packed product sequence to improve makespan. In an experimental analysis, al heuristics show the capability to solve large instances within reason-able computational time. In al problem instances, genetic algorithm averagely outperforms ant colony optimiza-tion and Tabu search with slightly longer computational time.     

Continuous-time approaches for short-term scheduling of network batch processes: Small-scale and medium-scale problems

Two time representation approaches, discrete-time and continuous-time approaches, have been developed for short-term scheduling of batch process in small-scale and medium-scale during the last two decades. As usually establishing advantages over discrete-time approaches in the scheduling problems, continuous-time approaches have gained increasing attention in the last 10 years. The reported continuous-time approaches can be divided into four categories: global event-based, unit-specific event-based, slot-based and precedence-based models. In this paper, more complex processes, network batch processes in small and medium scales, are considered. Six models based on different continuous-time representations are compared in several benchmark examples from the literature. The compared items include problem size, computational times and model convergence. Moreover, two intermediate storage policies (limited and unlimited intermediate storage) and two objective functions (maximization of profit and minimization of makespan) are addressed.     

A novel constraint programming model for large-scale scheduling problems in multiproduct multistage batch plants: Limited resources and campaign-based operation

This contribution introduces an efficient constraint programming (CP) model that copes with large-scale scheduling problems in multiproduct multistage batch plants. It addresses several features found in industrial environments, such as topology constraints, forbidden product-equipment assignments, sequence-dependent changeover tasks, dissimilar parallel units at each stage, limiting renewable resources and multiple-batch orders, among other relevant plant characteristics. Moreover, the contribution deals with various inter-stage storage and operational policies. In addition, multiple-batch orders can be handled by defining a campaign operating mode, and lower and upper bounds on the number of batches per campaign can be fixed. The proposed model has been extensively tested by means of several case studies having various problem sizes and characteristics. The results have shown that the model can efficiently solve medium and large-scale problems with multiple constraining features. The approach has also rendered good quality solutions for problems that consider multiple-batch orders under a campaign-based operational policy.     

Practical infeasibility of cross-transfer in batch plants with complex recipes: S-graph vs MILP methods

Multipurpose batch processes entail various operational policies that have been widely investigated in published literature. In this paper, no-intermediate-storage (NIS), zero-wait (ZW) and common-intermediate-storage (CIS) operational policies are of particular interest. In all these policies, no dedicated storage facility is available between two consecutive units. Unlike the other operational policies, these particular policies bear some subtle practical infeasibility that has gone unnoticed in literature. In essence, this infeasibility has been reported as optimal, thus assumed to be feasible, by various authors using mathematical programming techniques. It pertains to a unit transferring product to one or more units whilst simultaneously receiving feed from another, which is practically infeasible and as such need not be considered as a possible solution. This feature is particularly conspicuous in batch processes with complex recipes wherein production paths can be in opposite directions. This paper presents the unique feature of the S-graph framework to isolate cross-transfer during optimization, whereas the available mathematical programming methods inherently fail neither to detect nor to eliminate this infeasibility. A few examples taken from published literature are presented for demonstration purposes.     

Multiobjective evolutionary optimization of batch process scheduling under environmental and economic concerns

The simultaneous consideration of economic and environmental objectives in batch production scheduling is today a subject of major concern. However, it constitutes a complex problem whose solution necessarily entails production trade‐offs. Unfortunately, a rigorous multiobjective optimization approach to solve this kind of problem often implies high computational effort and time, which seriously undermine its applicability to day‐to‐day operation in industrial practice. Hence, this work presents a hybrid optimization strategy based on rigorous local search and genetic algorithm to efficiently deal with industrial scale batch scheduling problems. Thus, a deeper insight into the combined environmental and economic issues when considering the trade‐offs of adopting a particular schedule is provided. The proposed methodology is applied to a case study concerning a multiproduct acrylic fiber production plant, where product changeovers influence the problem results. The proposed strategy stands for a marked improvement in effectively incorporating multiobjective optimization in short‐term plant operation. © 2012 American Institute of Chemical Engineers AIChE J, 59: 429–444, 2013     

Efficient multi-product multi-BOM batch scheduling for a petrochemical blending plant with a shared pipeline network

We present an effective scheduling heuristic for realistic production planning in a petrochemical blending plant. The considered model takes into account orders spanning a multi-product portfolio with multiple bills of materials per product, that need to be scheduled on shared production facilities including a complex pipeline network. Capacity constraints, intermediate storage restrictions, due dates, and the dedication of resources to specific product families have to be respected. The primary objective of the heuristic is to minimize the total order tardiness. Secondary objectives include the minimization of pipeline cleaning operations, the minimization of lead times, and the balanced utilization of filling units.The developed algorithm is based on a dynamic prioritization-based greedy search that schedules the orders sequentially. The proposed method can schedule short to mid-term operations and evaluate different plant configurations or production policies on a tactical level. We demonstrate its performance on various real-world inspired scenarios for different scheduling strategies.Our heuristic was used during the construction phase of a new blending plant and was instrumental in the optimal design of the plant.     

Multi‐stage adjustable robust optimization for process scheduling under uncertainty

Variations in parameters such as processing times, yields, and availability of materials and utilities can have a detrimental effect in the optimality and/or feasibility of an otherwise “optimal” production schedule. In this article, we propose a multi‐stage adjustable robust optimization approach to alleviate the risk from such operational uncertainties during scheduling decisions. We derive a novel robust counterpart of a deterministic scheduling model, and we show how to obey the observability and non‐anticipativity restrictions that are necessary for the resulting solution policy to be implementable in practice. We also develop decision‐dependent uncertainty sets to model the endogenous uncertainty that is inherently present in process scheduling applications. A computational study reveals that, given a chosen level of robustness, adjusting decisions to past parameter realizations leads to significant improvements, both in terms of worst‐case objective as well as objective in expectation, compared to the traditional robust scheduling approaches. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1646–1667, 2016     

Optimal scheduling and minimum storage tank capacities in a process system with parallel batch units

It is first presumed that a chemical process system is operated continuously as a whole, but some part of the system is composed of a parallel batch section and intermediate storage tanks. The problem of determining the scheduling of the parallel batch operations and the tank capacities is discussed here. For the case where a batch section is composed of parallel identical units, optimal scheduling is obtained analytically. Then the case in which each batch section has different operation times is dealt with. For this case, it is shown that the search domain necessary can be reduced to an extremely small size.     

Scheduling of displacement batch digesters using discrete time formulation

This paper provides mathematical programming based optimization model and computational results for short-term scheduling of displacement batch digesters in a pulp industry. The scheduling problem involves development of an optimal solution that yields the best sequence of operations in each of the parallel batch digesters sharing common resources. The constraints are imposed on meeting the demand of pulp of different qualities within a specified time horizon. The problem comprises of both fixed-time and variable time durations of the tasks, different storage policies, zero-wait and finite wait times, and handling of shared resources. The scheduling problem is formulated using a state-task-network (STN) representation of production recipes, based on discrete time representation resulting in a mixed-integer linear programming (MILP) problem which is solved using GAMS software. The basic framework is adapted from the discrete-time model of Kondili et al. (Comput. Chem. Eng., 1993, 17, 211–227). Different case studies involving parallel digesters in multiple production lines are considered to demonstrate the effectiveness of the proposed formulation using two different objective functions.     

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

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.     

Optimal scheduling of continuous plants with energy constraints

This work addresses the scheduling of continuous single stage multiproduct plants with parallel units and shared storage tanks. Processing tasks are energy intensive and we consider time-dependent electricity pricing and availability together with multiple intermediate due dates, handled as hard constraints. A new discrete-time aggregate formulation is proposed to rapidly plan the production levels. It is combined with a continuous-time model for detailed scheduling as the essential part of a rolling-horizon algorithm. Their computational performance is compared to traditional discrete and continuous-time full-space formulations with all models relying on the Resource-Task Network (RTN) process representation. The results show that the new models and algorithm can generate global optimal schedules much more efficiently than their counterparts in problems involving unlimited power availability. Under restricted power, the aggregate model underestimates the electricity cost, which may cause the rolling-horizon approach to converge to a suboptimal solution, becoming the discrete-time model a better approach.     

Ordonnancement à court-terme d'un atelier discontinu de chimie fine

The objective of this paper is to use production engineering concepts to solve scheduling problems encountered in chemical engineering. The studied case is the multipurpose (or job-shop) chemical batch plant involving the most complex specific constraints which can be found practically: various products to be manufactured, different synthesis sequences, presence of intermediate products, various storage policies, mass balances, utilities, effluent limitation,… The development of a discrete-event simulation model of a fine chemistry plant is proposed in this paper. Use of the model and simulation results are then analyzed. Attention is focused on applications which seem interesting from a production management viewpoint but also from chemical engineering concepts (plant design, effluent treatment, stability et storage of reaction intermediates…).     

The heterogeneous vehicle routing and truck scheduling problem in a multi-door cross-dock system

Cross-docking is a logistics technique applied by many industrial firms to get substantial savings in two warehousing costly functions like storage and order picking. Incoming shipments are unloaded from inbound trucks on a cross-dock terminal with minimal storage space and directly transferred to outbound vehicles that carry them to their destinations. The major decisions at the operational level are the vehicle routing and scheduling, the dock door assignment and the truck scheduling at the cross-dock. Because such decisions are interdependent, all of them are simultaneously considered in the so-called vehicle routing problem with cross-docking (VRPCD). Previous contributions on VRPCD assume that pickup and delivery tasks are accomplished by a homogeneous vehicle fleet, and they mostly ignore the internal transportation of goods through the cross-dock. This work introduces a new rigorous mixed-integer linear programming (MILP) formulation for the VRPCD problem to determine the routing and scheduling of a mixed vehicle fleet, the dock door assignment, the truck docking sequence and the travel time required to move the goods to the assigned stack door all at once. To improve the computational efficiency of the branch-and-cut search, an approximate sweep-based model is developed by also considering a set of constraints mimicking the sweep algorithm for allocating nodes to vehicles. Numerous heterogeneous VRPCD examples involving up to 50 transportation requests and a heterogeneous fleet of 10 vehicles with three different capacities were successfully solved using the proposed approaches in acceptable CPU times.     

Continuous-time scheduling formulation for multipurpose batch plants

Short-term scheduling of batch processes is a complex combinatorial problem with remarkable impact on the total revenue of chemical plants. It consists of the optimal allocation of limited resources to tasks over time in order to manufacture final products following given batch recipes. This article addresses the short-term scheduling of multipurpose batch plants, using a mixed integer linear programming formulation based on the state-task network representation. It employs both single-grid and multi-grid continuous-time representations, derived from generalized disjunctive programming. In comparison to other multigrid scheduling models in the literature, the proposed multi-grid model uses no big-M constraints and leads to more compact mathematical models with strong linear relaxations, which often results in shorter computational times. The single-grid counterpart of the formulation is not as favorable, as it leads to weaker linear relaxations than the multi-grid approach and is not capable of handling changeover time constraints.     

An MILP-based reordering algorithm for complex industrial scheduling and rescheduling

The challenging structure as well as the extensive economical potential of solving various scheduling problems has fascinated numerous researchers during the recent decades. Despite the significant progress made in the fields of operations research and process systems engineering (Puigjaner, Comp. Chem. Eng., 23 (1999): S929–S943; Shah, Proceedings of FOCAPO'98, Snowbird, Utah, USA, 1998) the complexity of many industrial-size scheduling problems means that a global optimal solution cannot be reached within a reasonable computational time. In these cases, the production schedule must be generated using e.g. some kind of sophisticated heuristics, which can often lead to suboptimal solutions. In this paper, we introduce a Mixed Integer Linear Programming (MILP) based algorithm, which can be efficiently used to improve an existing feasible, but non-optimal, production schedule or to reschedule jobs in the case of changed operational parameters. The algorithm has been successfully applied to certain scheduling problems in both the paper-converting and pharmaceutical industry.     

A monolithic approach to vehicle routing and operations scheduling of a cross-dock system with multiple dock doors

Cross-docking is a logistic strategy for moving goods from suppliers to customers via a cross-dock terminal with no permanent storage. The operational planning of a cross-dock facility involves different issues such as vehicle routing, dock door assignment and truck scheduling. The vehicle routing problem seeks the optimal routes for a homogeneous fleet of vehicles that sequentially collects goods at pickup points and delivers them to their destinations. The truck scheduling problem deals with the timing of unloading and reloading operations at the cross-dock. This work introduces a mixed-integer linear programming formulation for the scheduling of single cross-dock systems that, in addition to selecting the pickup/delivery routes, simultaneously decides on the dock door assignment and the truck scheduling at the cross-dock. The proposed monolithic formulation is able to provide near-optimal solutions to medium-size problems involving up to 70 transportation orders, 16 vehicles and 7 strip/stack dock doors at acceptable CPU times.     

Short-term scheduling and recipe optimization of blending processes

The main objective of this paper is to develop an integrated approach to coordinate short-term scheduling of multi-product blending facilities with nonlinear recipe optimization. The proposed strategy is based on a hierarchical concept consisting of three business levels: Long-range planning, short-term scheduling and process control. Long-range planning is accomplished by solving a large-scale nonlinear recipe optimization problem (multi-blend problem). Resulting blending recipes and production volumes are provided as goals for the scheduling level. The scheduling problem is formulated as a mixed-integer linear program derived from a resource-task network representation. The scheduling model permits recipe changeovers in order to utilize an additional degree of freedom for optimization. By interpreting the solution of the scheduling problem, new constraints can be imposed on the previous multi-blend problem. Thus bottlenecks arising during scheduling are considered already on the topmost long-range planning level. Based on the outlined approach a commercial software system has been designed to optimize the operation of in-line blending and batch blending processes. The application of the strategy and software is demonstrated by a detailed case study.     

A novel search framework for multi‐stage process scheduling with tight due dates

This article improves the original genetic algorithm developed by He and Hui (Chem Eng Sci. 2007; 62:1504–1527) and proposes a novel global search framework (GSF) for the large‐size multi‐stage process scheduling problems. This work first constructs a comprehensive set of position selection rules according to the impact factors analysis presented by He and Hui (in this publication in 2007), and then selects suitable rules for schedule synthesis. In coping with infeasibility emerging during the search, a penalty function is adopted to force the algorithm to approach the feasible solutions. The large‐size problems with tight due dates are challenging to the current solution techniques. Inspired by the gradient used in numerical analysis, we treat the deviation existing among the computational tests of the algorithm as evolutionary gradient. Based on this concept, a GSF is laid out to fully utilize the search ability of the current algorithm. Numerical experiments indicate that the proposed search framework solves such problems with satisfactory solutions. © 2010 American Institute of Chemical Engineers AIChE J, 2010