Arul Sundaramoorthy

An adjustable robust optimization approach to scheduling of continuous industrial processes providing interruptible load

Abstract To ensure the stability of the power grid, backup capacities are called upon when electricity supply does not meet demand due to unexpected changes in the grid. As part of the demand response efforts in recent years, large electricity consumers are encouraged by financial incentives to provide such operating reserve in the form of load reduction capacities (interruptible load). However, a major challenge lies in the uncertainty that one does not know in advance when load reduction will be requested. In this work, we develop a scheduling model for continuous industrial processes providing interruptible load. An adjustable robust optimization approach, which incorporates recourse decisions using linear decision rules, is applied to model the uncertainty. The proposed model is applied to an illustrative example as well as a real-world air separation case. The results show the benefits from selling interruptible load and the value of considering recourse in the decision-making.

Simultaneous Batching and Scheduling Using Dynamic Decomposition on a Grid

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 framework 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 for which the binary decision variables are batch selection, batch-unit assignment, and batch sequencing on units. We present methods to decompose the original problem into a number of subproblems in a dynamic fashion. First, we discuss the generation of subproblems based on fixing the batch-selection variables. Second, we generate subproblems by fixing the batch-unit assignment variables in a bottlenecking stage. Third, we generate subproblems by fixing the last batch in the sequence on each unit of the bottlenecking stage. Furthermore, the second and third methods can be carried out in various combinations. 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 a reasonable computational time.

A discrete-time scheduling model for continuous power-intensive process networks with various power contracts

Abstract Increased volatility in electricity prices and new emerging demand side management opportunities call for efficient tools for the optimal operation of power-intensive processes. In this work, a general discrete-time model is proposed for the scheduling of power-intensive process networks with various power contracts. The proposed model consists of a network of processes represented by Convex Region Surrogate models that are incorporated in a mode-based scheduling formulation, for which a block contract model is considered that allows the modeling of a large variety of commonly used power contracts. The resulting mixed-integer linear programming model is applied to an illustrative example as well as to a real-world industrial test case. The results demonstrate the models capability in representing the operational flexibility in a process network and different electricity pricing structures. Moreover, because of its computational efficiency, the model holds much promise for its use in a real industrial setting.

Risk-based integrated production scheduling and electricity procurement for continuous power-intensive processes

Abstract For optimal operation of power-intensive plants, production scheduling and electricity procurement have to be considered simultaneously. In addition, uncertainty needs to be taken into account. For this purpose, an integrated stochastic mixed-integer linear programming model is developed that considers the two most critical sources of uncertainty: spot electricity price, and product demand. Conditional value-at-risk is incorporated into the model as a measure of risk. Furthermore, scenario reduction and multicut Benders decomposition are implemented to solve large-scale real-world problems. The proposed model is applied to an illustrative example as well as an industrial air separation case. The results show the benefit from stochastic optimization and the effect of taking a risk-averse rather than a risk-neutral approach. An interesting insight from the analysis is that in risk-neutral optimization, accounting for electricity price uncertainty does not yield significant added value; however, in risk-averse optimization, modeling price uncertainty is crucial for obtaining good solutions.

Multiscale production routing in multicommodity supply chains with complex production facilities

In this work, we introduce the multiscale production routing problem (MPRP), which considers the coordination of production, inventory, distribution, and routing decisions in multicommodity supply chains with complex continuous production facilities. We propose an MILP model involving two different time grids. While a detailed mode-based production scheduling model captures all critical operational constraints on the fine time grid, vehicle routing is considered in each time period of the coarse time grid. In order to solve large instances of the MPRP, we propose an iterative MILP-based heuristic approach that solves the MILP model with a restricted set of candidate routes at each iteration and dynamically updates the set of candidate routes for the next iteration. The results of an extensive computational study show that the proposed algorithm finds high-quality solutions in reasonable computation times, and in large instances, it significantly outperforms a standard two-phase heuristic approach and a solution strategy involving a one-time heuristic pre-generation of candidate routes. Similar results are achieved in an industrial case study, which considers a real-world industrial gas supply chain. HighlightsIntroduces the multiscale production routing problem (MPRP).Proposes an MILP model that incorporates two different time grids.Proposes an iterative heuristic solution method for solving large instances.Computational study demonstrates the effectiveness of the proposed framework.Same conclusion is confirmed in a real-world industrial gas supply chain case study.

Solution methods for vehicle-based inventory routing problems

Abstract A novel method for solving vehicle-based inventory routing problems (IRPs) under realistic constraints is presented. First, we propose a preprocessing algorithm that reduces the problem size by eliminating customers and network arcs that are irrelevant for the current horizon. Second, we develop a decomposition method that divides the problem into two subproblems. The upper level subproblem considers a simplified vehicle routing problem to minimize the distribution cost while satisfying minimum demands, which are calculated based on consumption rate, initial inventory and safety stock. In the lower level, a detailed schedule with drivers is acquired using a continuous-time MILP model, by adopting the routes selected from the upper level. Finally, an iterative approach based on the upper and lower levels is presented, including the addition of different types of integer cuts and parameter updates. Different options of implementing this iterative approach are discussed, and computational results are presented.

Optimal Scheduling of Air Separation with Cryogenic Energy Storage

Abstract The idea of cryogenic energy storage (CES), which is to store energy in the form of liquefied gas, has gained increased interest in recent years. Although CES at an industrial scale is a relatively new approach, the technology used for CES is well-known and essentially part of any cryogenic air separation unit (ASU). In this work, we assess the operational benefits of adding CES to an existing air separation plant. Three potential new opportunities are investigated: (1) increasing the plant’s flexibility for load shifting, (2) storing purchased energy and selling it back to the market during higher-price periods, (3) creating additional revenue by providing operating reserve capacity. We develop a mixed-integer linear programming (MILP) scheduling model for an ASU- CES plant and apply a robust optimization approach to model the uncertainty in reserve demand. Results from an industrial case study show that the amount of wasted products can be considerably reduced and significant cost savings can be achieved by utilizing the CES.

Nonconvex Generalized Benders Decomposition

This chapter gives an overview of an extension of Benders decomposition (BD) and generalized Benders decomposition (GBD) to deterministic global optimization of nonconvex mixed-integer nonlinear programs (MINLPs) in which the complicating variables are binary. The new decomposition method, called nonconvex generalized Benders decomposition (NGBD), is developed based on convex relaxations of nonconvex functions and continuous relaxations of non-complicating binary variables in the problem. NGBD guarantees finding an e-optimal solution or indicates the infeasibility of the problem in a finite number of steps. A typical application of NGBD is to solve large-scale stochastic MINLPs that cannot be solved via the decomposition procedures of BD and GBD. Case studies of several industrial problems demonstrate the dramatic computational advantage of NGBD over state-of-the-art commercial solvers.

Capacity Planning for Continuous Pharmaceutical Manufacturing Facilities

Abstract In this work, we develop an integrated optimization under uncertainty framework to address the problem of capacity planning in pharmaceutical supply chains that employ novel integrated continuous production schemes. Since the outcomes of clinical trials are uncertain, the problem naturally leads to a stochastic programming problem, which is formulated as a scenario-based multi-period mixed-integer linear programming (MILP) model. The number of scenarios grows exponentially with the number of potential products, resulting in large-scale MILP models that are intractable with standard solvers. We propose a novel solution method to solve the above industrial-scale problems that contain up to 10 potential products and nearly 60,000 scenarios.

Using Grid Computing to Solve Hard Planning and Scheduling Problems

Production planning and scheduling problems routinely arise in process industries. In spite of extensive research work to develop efficient scheduling methods, existing approaches are inefficient in solving industrial-scale problems in reasonable time. In this paper we develop a dynamic decomposition scheme that exploits the structure of the problem and facilitates grid computing. We consider the problem of simultaneous batching and scheduling of multi-stage batch processes. The proposed method can be used to solve hard problems on a grid computer to optimality in reasonable time.