Tightening methods for continuous‐time mixed‐integer programming models for chemical production scheduling

Abstract

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...

On the solution of large-scale mixed integer programming scheduling models

“…We focus on problems in network production environments, that is, environments where a task can consume or produce multiple materials, the output of multiple batches of the same task can be mixed (batch mixing), the output of a single batch can be consumed by multiple downstream batches of the same or different task (batch splitting), and there are recycle streams. While methods (2)-(4) are applicable to both discrete-time and continuous-time models (Merchan et al, 2013;Merchan and Maravelias, 2014), we focus on the former because they are more general, can be readily extended to account for a number of processing constraints, and were recently shown to be computationally superior to continuous-time models for problems in network environments .…”

Systematic generation of alternative production schedules

“…To facilitate the solution process, tightening constraints and valid inequalities, decomposition methods, reformulations, and parallel solution algorithms have been developed.…”

“…In terms of model development, the introduction of innovative concepts enabled development of smaller scheduling models and models with mathematical structures that can be exploited by decomposition and parallel computing strategies: models based on multiple unit-specific continuous-time grids, 7-10 models employing mixed time representation, 11,12 as well as multiple nonuniform discrete-time grids. 13,14 To facilitate the solution process, tightening constraints and valid inequalities, [15][16][17][18] decomposition methods, [19][20][21] reformulations, [22][23][24] and parallel solution algorithms [24][25][26][27][28] have been developed.…”

An economic model predictive control approach to integrated production management and process operation

“…Production management subject to demand changes plays a crucial role in industry . Shifts in demand and supply of certain products occur constantly and finding reliable methods to achieve the desired production has become necessary .…”

“…Production management subject to demand changes plays a crucial role in industry. [5][6][7][8] Shifts in demand and supply of certain products occur constantly and finding reliable methods to achieve the desired production has become necessary. 9,10 It has become common in the chemical industry to produce multiple products from the same plant in both batch and continuous processes 6,8,11 such as the production of multiple grades of polyethylene.…”