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STATEOFTHEART REVIEW OF OPTIMIZATION METHODS FOR SHORTTERM SCHEDULING OF BATCH PROCESSES
, 2005
"... There has been significant progress in the area of shortterm scheduling of batch processes, including the solution of industrialsized problems, in the last 20 years. The main goal of this paper is to provide an uptodate review of the stateoftheart in this challenging area. Main features, stre ..."
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Cited by 30 (9 self)
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There has been significant progress in the area of shortterm scheduling of batch processes, including the solution of industrialsized problems, in the last 20 years. The main goal of this paper is to provide an uptodate review of the stateoftheart 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 realworld 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 largescale 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.
A Hybrid MILP/CP Decomposition Approach for the Continuous Time Scheduling of . . .
, 2003
"... A hybrid MixedInteger Linear Programming (MILP)/Constraint Programming (CP) decomposition algorithm is proposed for the shortterm scheduling of batch plants that rely on the State Task Network representation. The decisions about the type and number of tasks performed, as well as the assignment ..."
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Cited by 24 (12 self)
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A hybrid MixedInteger Linear Programming (MILP)/Constraint Programming (CP) decomposition algorithm is proposed for the shortterm scheduling of batch plants that rely on the State Task Network representation. The decisions about the type and number of tasks performed, as well as the assignment of units to tasks are made by the MILP master problem. The CP
An Efficient MILP Model for the ShortTerm Scheduling of Single Stage Batch Plants
"... This paper presents a multiple time grid continuous time MILP model for the shortterm scheduling of single stage, multiproduct batch plants where the objective is the minimization of total cost or total earliness. It can handle both release and due dates and it can determine the products delivery d ..."
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Cited by 5 (3 self)
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This paper presents a multiple time grid continuous time MILP model for the shortterm scheduling of single stage, multiproduct batch plants where the objective is the minimization of total cost or total earliness. It can handle both release and due dates and it can determine the products delivery dates explicitly if these need to be considered in the objective function. This formulation is compared to other mixedinteger linear programming approaches that have appeared in the literature, to a constraint programming model, and to a hybrid mixed integer linear/constraint programming algorithm. The results show that the proposed formulation is significantly more efficient than the MILP and CP models and comparable to the hybrid model when the objective is the minimization of total cost. For one large instance, both methods exceeded the time limit but the hybrid method failed to find a feasible solution. The results also show that a discretetime formulation performs very efficiently even when a large number of time intervals are used.
Optimization of timed automata models using mixedinteger programming
 In Formal Modeling And Analysis of Timed Systems, volume 2791 of LNCS
, 2004
"... Abstract. Research on optimization of timed systems, as e.g. for computing optimal schedules of manufacturing processes, has lead to approaches that mainly fall into the following two categories: On one side, mixed integer programming (MIP) techniques have been developed to successfully solve schedu ..."
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Cited by 5 (1 self)
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Abstract. Research on optimization of timed systems, as e.g. for computing optimal schedules of manufacturing processes, has lead to approaches that mainly fall into the following two categories: On one side, mixed integer programming (MIP) techniques have been developed to successfully solve scheduling problems of moderate to medium size. On the other side, reachability algorithms extended by the evaluation of performance criteria have been employed to optimize the behavior of systems modeled as timed automata (TA). While some successful applications to realworld examples have been reported for both approaches, industrial scale problems clearly call for more powerful techniques and tools. The work presented in this paper aims at combining the two types of approaches: The intention is to take advantage of the simplicity of modeling with timed automata (including modularity and synchronization), but also of the relaxation techniques and heuristics that are known from MIP. As a first step in this direction, the paper describes a translation procedure that automatically generates MIP representations of optimization problems formulated initially for TA. As a possible use of this translation, the paper suggests an iterative solution procedure, that combines a tree search for TA with the MIP solution of subproblems. The key idea is to use the relaxations in the MIP step to guide the tree search for TA in a branchandbound fashion.
New ContinuousTime MILP Model for the ShortTerm Scheduling of Multistage Batch
, 2005
"... This paper presents a new multiple time grid continuous time MILP model for the shortterm scheduling of multistage, multiproduct plants. It can handle both release and due dates and different objective functions efficiently, such as the minimization of total cost, total earliness or makespan. This ..."
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Cited by 4 (2 self)
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This paper presents a new multiple time grid continuous time MILP model for the shortterm scheduling of multistage, multiproduct plants. It can handle both release and due dates and different objective functions efficiently, such as the minimization of total cost, total earliness or makespan. This formulation is compared to other existing mixedinteger linear programming approaches and to a constraint programming model. The results show that the proposed formulation is much more efficient than its uniform time grid counterpart and is comparable to a continuoustime formulation that uses global precedence sequencing variables. Discretetime formulations are preferred for larger scheduling problems where a reasonable number of time points are enough to consider the exact problem data. The results also show that the constraint programming model is the best approach for makespan minimization.
Singlefacility scheduling over long time horizons by logicbased benders decomposition
 Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, LNCS 6140
, 2010
"... Abstract. Logicbased Benders decomposition can combine mixed integer programming and constraint programming to solve planning and scheduling problems much faster than either method alone. We find that a similar technique can be beneficial for solving pure scheduling problems as the problem size sca ..."
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Cited by 4 (1 self)
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Abstract. Logicbased Benders decomposition can combine mixed integer programming and constraint programming to solve planning and scheduling problems much faster than either method alone. We find that a similar technique can be beneficial for solving pure scheduling problems as the problem size scales up. We solve singlefacility nonpreemptive scheduling problems with time windows and long time horizons that are divided into segments separated by shutdown times (such as weekends). The objective is to find feasible solutions, minimize makespan, or minimize total tardiness. 1
Generalized Disjunctive Programming as a Systematic Modeling Framework to Derive Scheduling Formulations
"... We propose generalized disjunctive programming models for the shortterm scheduling problem of single stage batch plants with parallel units. Three different concepts of continuoustime representation are explored, immediate and general precedence, as well as multiple time grids. The GDP models are ..."
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Cited by 3 (3 self)
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We propose generalized disjunctive programming models for the shortterm scheduling problem of single stage batch plants with parallel units. Three different concepts of continuoustime representation are explored, immediate and general precedence, as well as multiple time grids. The GDP models are then reformulated using both bigM and convex hull reformulations, and the resulting mixedinteger linear programming models compared to the solution of a set of example problems. We show that two general precedence models from the literature can be derived using a bigM reformulation for a set of disjunctions and a convex hull reformulation for another. The best performer is, however, a multiple time grid model which can be derived from the convex hull reformulation followed by simple algebraic manipulations to eliminate the disaggregated variables and reduce the sets of constraints, thus leading to a more compact and efficient formulation.
Mixed Integer Programming vs. Logicbased Benders Decomposition for Planning and Scheduling ⋆
"... Abstract. A recent paper by Heinz and Beck (CPAIOR 2012) found that mixed integer software has become competitive with or superior to logicbased Benders decomposition for the solution of facility assignment and scheduling problems. Their implementation of Benders differs, however, from that describ ..."
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Cited by 2 (1 self)
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Abstract. A recent paper by Heinz and Beck (CPAIOR 2012) found that mixed integer software has become competitive with or superior to logicbased Benders decomposition for the solution of facility assignment and scheduling problems. Their implementation of Benders differs, however, from that described in the literature they cite and therefore results in much slower performance than previously reported. We find that when correctly implemented, the Benders method remains 2 to 3 orders of magnitude faster than the latest commercial mixed integer software on larger instances, thus reversing the conclusion of the earlier paper. 1
Simultaneous batching and scheduling using dynamic decomposition on a grid
, 2008
"... Scheduling problems arise in many applications in process industries. However, despite various efforts to develop efficient scheduling methods, current approaches cannot be used to solve instances of industrial importance in reasonable time frames. The goal of this paper is the development of a dyna ..."
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Cited by 2 (2 self)
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Scheduling problems arise in many applications in process industries. However, despite various efforts to develop efficient scheduling methods, current approaches cannot be used to solve instances of industrial importance in reasonable time frames. The goal of this paper is the development of a dynamic decomposition scheme that exploits the structure of the problem and is well suited for grid computing. The problem we study is the simultaneous batching and scheduling of multistage batch processes. The algorithm first decomposes the original problem into 1 stlevel subproblems based on batching decisions. The subproblems that remain unsolved within a resource limit are then dynamically decomposed into 2 ndlevel subproblems based on batchunit assignment decisions in one stage. The process can be repeated in a dynamic fashion by identifying subproblems that cannot be solved within a given resource limit and decomposing them by batchunit assignment, until all subproblems are solved. Alternatively, a problem can be decomposed into a number of promising subproblems using an automatic strong branching scheme. Our results show that the proposed method can be used on a grid computer to solve large problems to optimality in reasonable computational time.
Two New Continuoustime Models for the Scheduling of Multistage Batch Plants with Sequence Dependent
"... This paper presents two new multipletime grid, continuoustime mixed integer linear program (MILP) models for the shortterm scheduling of multistage, multiproduct plants featuring equipment units with sequence dependent changeovers. Their main difference results from the explicit consideration of ..."
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This paper presents two new multipletime grid, continuoustime mixed integer linear program (MILP) models for the shortterm scheduling of multistage, multiproduct plants featuring equipment units with sequence dependent changeovers. Their main difference results from the explicit consideration of changeover tasks as model variables rather than implicitly through model constraints. The former approach is more versatile in terms of type of objective function that can be efficiently handled (minimization of total cost, total earliness and makespan) and, despite generating larger mathematical problems, it is also a better performer in single stage problems. The latter is better suited for multistage problems, where the former approach has some difficulties even in finding feasible solutions, particularly as the number of stages increases. The performance of both formulations is compared to other mixed integer linear program and constraint programming models. The results show that multiple time grid models are better suited for single stage problems or when minimizing total earliness, that the constraint programming model is the best approach for