We present extensions to discrete-time MIP model that allow to address realistic instances. We show how advanced solution methods can be extended and combined to address a wide range of problems. The proposed method yield (near) optimal solutions in time frames that can be used in practice. a b s t r a c tIn this paper, we show how four recently developed modeling and solution methods can be integrated to address mixed integer programs for the scheduling of large-scale chemical production systems. The first method uses multiple discrete time grids. The second adds tightening constraints that lower bound the total production and number of batches for each task and material based on the customer demand, while the third generates upper bounding constraints based on inventory and resource availability. The final method is a reformulation that introduces a new integer variable representing the total number of batches of a task. We apply the aforementioned methods to large-scale problems with a variety of processing features, including variable conversion coefficients, changeovers, various storage policies, continuous processing tasks, setups, and utilities, using a discrete-time model. We illustrate how these methods lead to significant improvements in computational performance.
We address the problem of production scheduling in multi-product multistage batch plants. Unlike most of the previous works, which propose continuoustime models, we study discrete-time mixed-integer programming models and solution methods. Specifically, we discuss two models based on network representations of the facility and develop two new models inspired by the Resource-Constrained Project Scheduling Problem. Furthermore, we propose different solution methods, including tightening methods based on processing unit availability, a reformulation based on processing unit occupancy, and an algorithm to refine approximate solutions for large-scale instances. Finally, we present a comprehensive computational study, which shows that speedups of up to four orders of magnitude are observed when our models and methods are compared to existing approaches.
SignificanceImportant advances in modeling chemical production scheduling problems have been made in recent years, yet effective solution methods are still required. We use an algorithm that uses process network and customer demand information to formulate powerful valid inequalities that substantially improve the solution process. In particular, we extend the ideas recently developed for discrete-time formulations to continuous-time models and show that these tightening methods lead to a significant decrease in computational time, up to more than three orders of magnitude for some instances. Keywords: Mixed-integer programming, demand propagation, valid inequalities Introduction R esearch efforts in the area of chemical production scheduling have been primarily focused on the development of alternative formulations to ensure both generality and computational efficiency.1,2 Starting from the work of Pantelides and coworkers, 3-5 several general mixed-integer programming (MIP) models, relying on material balances and time grids, have been proposed to (1) reduce computational requirements, 6-14 and (2) account for constraints on storage, utilities, changeovers, connectivity, material transfers, material-handling restrictions, and combined production environments. [15][16][17][18][19] Nevertheless, significantly less attention has been directed to solution methods for general MIP scheduling models.To address the computational challenge, various researchers have studied the structure of MIP chemical production scheduling models, 20,21 used decomposition-based algorithms, 22-27 exploited parallel computing tools, 28,29 developed reformulations, 30-32 and developed tightening methods based on valid inequalities. 31,[33][34][35] An example of the latter is the work of Maravelias and coworkers 35,36 where process network information (recipes and unit capacities) and customer demand are used to calculate a set of parameters (the minimum amount of each material and the minimum production goal for each task that are required to meet the given demand), which are then used to generate strong valid inequalities. This strategy was implemented in discrete-time models leading to dramatic computational time reductions, up to four orders of magnitude for many instances. Discrete-time models have a number of advantages, including (1) the linear modeling of inventory and utility costs, (2) the treatment of intermediate raw material deliveries and final product orders at no additional computational cost, (3) the straightforward modeling of events during the execution of tasks, and (4) the modeling of time-varying utility availability and pricing using no new variables or constraints. Furthermore, a recent study showed that discrete-time models are in general faster than their continuous-time counterparts. 37 Nevertheless, continuous-time models are likely to be preferred in some specific problems (e.g., in problems with sequence-dependent changeovers), so it is important to develop methods that enhance the solution of this type of mod...
We propose a series of preprocessing algorithms for the generation of strong valid inequalities for time-indexed, discrete and continuous, mixed-integer programming scheduling models for problems in network production environments. Specifically, starting from time-and inventory-related instance data, the proposed algorithms use constraint propagation techniques to calculate parameters that are used to bound the number of times subsets of tasks can be executed in a feasible solution. We also extend some of the propagation ideas to generate three classes of new tightening constraints. The proposed methods result in tightening constraints expressed in terms of assignment binary variables (if task is assigned to start on unit at time point) which are present in all time-indexed MIP models, therefore they are applicable to all time-indexed models accounting for a wide range of processing features. Finally, the methods are shown to lead to up to two orders of magnitude reduction in computational time when optimal solutions are found and significantly improve optimality gap when a time limit is enforced.
Although several optimization models have been proposed for chemical production scheduling, there is still a need for effective solution methods. Accordingly, the goal of this work is to present different reformulations of representative continuous-time models by introducing an explicit variable for the number of batches of a given task. This idea, which has been successfully applied to discrete-time models, results in significant computational enhancement. We discuss how different objective functions benefit from particular reformulations and show significant improvements by means of an extensive computational study that includes several instances containing different process networks and scheduling horizons.
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