John M. Wassick

Carnegie Mellon University | CMU · Department of Chemical Engineering

Background: We address in this paper linear programming (LP) models in which it is desired to find alternate optima. An LP may have multiple alternate solutions with the same objective value or with increasing objective values. For many real life applications, it can be interesting to have a pool of solutions to compare what operations should be e...

This paper discusses the broad challenges shared by e-commerce and the process industries operating global supply chains. Specifically, we discuss how process industries and e-commerce differ in many aspects but have similar challenges ahead of them in order to remain competitive, keep up with the always increasing requirements of the customers and...

We present an integrated digital twin framework for supply chain business processes. The framework combines models supply chain processes as queueing networks where agents perform tasks on orders flowing through the process. The modeling approach captures the routing dynamics and stochasticity in both the task durations and order arrivals that are...

The Resource-Task Network (RTN) model is a major contribution of Process Systems Engineering to the general area of scheduling optimization. The RTN representation models processes as bipartite graphs comprising two types of vertices: resources and tasks. A resource is general and includes all entities that are involved in the process steps (e.g.,...

A scheduling model is proposed to schedule order transactions and manufacturing operations in the order-to-cash process of a digital supply chain. The proposed model is compared to scheduling models that focus on either the order transactions or the manufacturing operations. The advantage of the integrated approach is found in the accuracy of the s...

In this paper we present a methodology, by utilizing a nonparametric multivariate cumulative sum control chart and data envelopment analysis in tandem, to evaluate and monitor distribution network performance by simultaneously considering multiple performance factors and their interrelationships. While these methods were previously applied individu...

We propose a mathematical programming approach to optimize the business process transactions in digital supply chains. Five scheduling models from the Process Systems Engineering (PSE) area are applied to schedule the processing of orders in a simplified Order-To-Cash (OTC) business process, which is modeled as a multistage network with parallel un...

An integrated framework for building a virtual replica of business transactional processes in supply chains is presented. The framework consists of two main components: a simulation module and an optimization module. Business processes are modeled as networks of queues through which requests (internal or external to the enterprise) can flow. The di...

We discuss the implementation of a deep reinforcement learning based agent to automatically make scheduling decisions for a continuous chemical reactor currently in operation. This model is tasked with scheduling the reactor on a daily basis in the face of uncertain demand and production interruptions. The reinforcement learning model has been trai...

Reinforcement learning (RL) has been widely applied to game-playing and surpassed the best human-level performance in many domains, yet there are few use-cases in industrial or commercial settings. We introduce OR-Gym, an open-source library for developing reinforcement learning algorithms to address operations research problems. In this paper, we...

The optimization of batch processes usually relies on the availability of a detailed knowledge-driven model. However, because of the great varieties of industrial batch processes and their small production rates, a knowledge-driven model might not always be available. In such a case, a data-driven model, developed after a limited number of experime...

This work examines applying deep reinforcement learning to a chemical production scheduling process to account for uncertainty and achieve online, dynamic scheduling, and benchmarks the results with a mixed-integer linear programming (MILP) model that schedules each time interval on a receding horizon basis. An industrial example is used as a case...

A new continuous time multistage scheduling Mixed-Integer Linear Programming (MILP) model is proposed to optimize the business transactional processes in supply chains. The novelty of this approach is in using techniques from the Process Systems Engineering (PSE) and Operations Research (OR) communities to address a side of supply chain optimizatio...

Four of the main modeling frameworks for batch scheduling are compared and extended to include quality-based changeovers (QBC), a procedure in which the equipment cleaning operation in between batches can be avoided given that enough batches of the second product are performed in a row. QBC has been ignored up to this point in scheduling models. Th...

The problem of integrating planning and scheduling models is addressed. Many of the previous models proposed in the literature assume that both models need to be solved over the same time horizon, leading to intractable models. Integrated models with shorter scheduling horizons are considered. To maintain the trade-o balance between the decision le...

Unknown parameters in batch process models can be estimated as uncertainties owing to model mismatch, measurement errors and even the absence of variable measurements. Applying a model-based dynamic optimization with the estimated parameter values is likely to violate path and end-point constraints. This work aims at developing a robust off-line op...

In this paper, we address the problem of incorporating knowledge of the automation system in a chemical plant into the online scheduling problem. Optimization models for online scheduling necessarily omit some of the plant dynamics to ensure sufficiently fast solution times for use in online rescheduling. This can result in the computed schedules n...

Process optimization and control rely highly on system modeling. A reliable model must be formulated with estimable parameters in order to closely predict system behavior in the operating domain. This paper focuses on the modeling and parameter estimation of organic solid-liquid reactions in batch reactors with limited lab-scale experimental data a...

We present an approach to online scheduling of chemical plant operations that incorporates precise knowledge of the dynamics enforced by the automation system. The scheduling problem is solved using a discrete-time state-space resource task network formulation. Rescheduling is triggered when the schedule currently being executed conflicts with the...

Supply chains (SC) span many geographies, modes and industries and involve several phases where data flows in both directions from suppliers, manufacturers, distributors, retailers, to customers. This data flow is necessary to support critical business decisions that may impact product cost and market share. Current SC information systems are unabl...

In this paper, we apply formal verification and falsification of temporal logic specifications to analyze chemical plant automation systems. We present new results, obtained by applying a recently-developed approach to handle combined invariance and reachability requirements. In addition, we develop a set of tests that can be generated automaticall...

Supply-chain management problems are common to most industries and they involve a hierarchy of subtasks, which must be coordinated well to arrive at an overall optimal solution. Such problems involve a hierarchy of decision-makers, each having its own objectives and constraints, but importantly requiring a coordination of their actions to make the...

This paper shows that we can use the backstepping method for semi-batch reactor temperature control. The system studied has relative degree higher than one. We show that the feedback system can be written in its error dynamic model form, which is shown to be passive. Input strictly passive feedback controllers render the origins of the passive erro...

A Mixed-integer Linear Programming model is proposed to determine the optimal number, location and capacity of the warehouses required to support a long-term forecast with seasonal demand. Discrete transportation costs, dynamic warehouse contracting, and the handling of safety stock are the three main distinctive features of the problem. Four alter...

Plant maintenance turnarounds constitute a large fraction of all maintenance activities in the process industries. We consider turnaround planning problems over large networks of interconnected plants. The network interactions provide an opportunity to plan and coordinate the different turnaround activities to save on annual downtime and recover th...

Commodity conversion assets play important economic roles. It is well known that the market value of these assets can be maximized by managing them as real options on the prices of their inputs and/or outputs. In particular, when futures on these inputs and outputs are traded, managing such real options, that is, valuing, hedging, and exercising th...

This work shows that kinetic information is not needed to estimate states (compositions) and control continuous stirred tank reactors (CSTRs). An asymptotic observer is developed using reaction invariants to provide on-line estimates of unmeasured compositions. The estimates are used in a feedback controller, based on inventory control theory, to c...

We first review advances in rescheduling, traditionally viewed as an approach to tackle uncertainty, including methods that rely on recourse through feedback as well as methods that account for uncertainty a priori. Then, we show that traditional event-triggered rescheduling has some shortcomings which can be addressed if rescheduling is approached...

Model-based dynamic optimization is an effective tool for control and optimization of chemical processes, especially during transitions in operation. This study considers the dynamic optimization of grade transitions for a solution polymerization process. Here, a detailed dynamic model comprises the entire flowsheet and includes a method-of-moments...

We address the inventory planning problem in process networks under uncertainty through stochastic programming models. Inventory planning requires the formulation of multiperiod models to represent the time-varying conditions of industrial process, but multistage stochastic programming formulations are often too large to solve. We propose a policy-...

In this paper a method for detecting errors in the discrete logic of hybrid systems is applied to chemical plant automation systems. The method relies on the application of supervisory control theory to a discrete abstraction of the hybrid system that models the plant and controller. A set of general operability requirements are also presented that...

We propose two data-driven, optimization-based frameworks (simulation-optimization and bi-objective optimization) to account for production variability in the operations planning stage of the sales and operations planning (S&OP) of an enterprise. Production variability is measured as the deviation between historical planned (target) and actual (ach...

We propose a model-based optimization approach for the integration of production scheduling and dynamic process operation for general continuous/batch processes. The method introduces a discrete time formulation for simultaneous optimization of scheduling and operating decisions. The process is described by the resource task network (RTN) represent...

We propose a data-driven, nonparametric approach to reformulate (conditional) individual and joint chance constraints with right-hand side uncertainty into algebraic constraints. The approach consists of using kernel smoothing to approximate unknown true continuous probability density/distribution functions. Given historical data for continuous uni...

Production-inventory systems model the interaction of manufacturing processes with internal and external customers. The role of inventory in these systems is to buffer mismatches between production and demand caused by process uncertainty. Often, production and demand variability is described using simplified probabilistic models that ignore underl...

An integrated chemical site involves a complex network of chemical plants. Typically, these plants interact closely, are dependent on each other for raw materials and demand for their products, and have the provision of intermediate storage tanks to help manage inventory at strategic points in the network. Disruptions in the operation of these plan...

A supply chain is a network of entities involving an interplay of different individual behaviors. For an industrial scale supply chain, this network can be very complex. For a large scale supply chain, the structure is usually distributed with the different functions being performed both synchronously and asynchronously. A supply chain may consist...

The industrial production of chemicals is characterized by complex networks of unit operations that transform raw materials into products. In these networks, material flows are constrained by the production capacity of the processing units, and the performance of the whole system often depends on the capacity of some limiting processes. The rigorou...

The design of resilient supply chains under the risk of disruptions at candidate locations for distribution centers (DCs) is formulated as a two-stage stochastic program. The problem involves selecting DC locations, determining storage capacities for multiple commodities, and establishing the distribution strategy in scenarios that describe disrupt...

A mixed integer linear programming (MILP) model is developed for the optimal reactive scheduling of a mixed batch/continuous process, based on the discrete time resource task network (RTN) representation and extensions. The scheduling task is complicated with the mixed process units and network structure, as well as operation rules such as product...

For manufacturers operating batch plants, production scheduling is a critical and challenging problem. A thorough understanding of the problem and the variety of solutions approaches is needed to achieve a successful application. This entry will present a brief overview of batch operations and the state of the art of batch plant scheduling for none...

This paper brings systematic methods for scenario tree generation to the attention of the Process Systems Engineering community. We focus on a general, data-driven optimization-based method for generating scenario trees that does not require strict assumptions on the probability distributions of the uncertain parameters. Using as a basis the Moment...

Sustainability plays a key role in the management of a successful and responsible business. When trying to improve the sustainability performance of a business, there are three major challenges that need to be addressed. First, assessment of sustainability requires consideration of not just economic, but also environmental and social impacts. Secon...

We propose a hybrid method integrating agent-based modeling and heuristic tree search to solve complex batch scheduling problems. Agent-based modeling describes the batch process and constructs a feasible schedule. To overcome myopic decisions of agents, the agent-based simulation is embedded into a heuristic search algorithm. The heuristic algorit...

A specification expressed in computation tree logic (CTL) that enforces safety and reachability requirements in discrete event systems is proposed. It is shown that the specification has a unique minimal control strategy that maximizes the set of states that satisfy the specification, and an algorithm is provided to calculate the control strategy....

This paper gives a review on existing scheduling methodologies developed for process industries. Above all, the aim of the paper is to focus on the industrial aspects of scheduling and discuss the main characteristics, including strengths and weaknesses of the presented approaches. It is claimed that optimization tools of today can effectively supp...

We propose a hybrid method integrating agent-based modeling and heuristic tree search to solve complex batch scheduling problems. Agent-based modeling describes the batch process and constructs a feasible schedule under various constraints. To overcome myopic decisions of agents, the agent-based simulation is embedded into a heuristic search algori...

Commodity conversion assets play important economic roles. It is well known that the market value of these assets can be maximized by managing them as real options on the prices of their inputs and/or outputs. In particular, when futures on these inputs and outputs are traded, managing such real options, that is, valuing, hedging, and exercising th...

The design of efficient supply chains is a major challenge for companies in the process industry. Supply chain performance is subject to different sources of uncertainty including reliability of the facilities. Facility disruptions are among the most critical events that supply chains can experience. In order to reduce the undesirable effects of di...

This paper addresses reactor modeling and recipe optimization of semibatch ring-opening polymerization processes for making block copolymers. Two rigorous reactor models are developed on the basis of the population balance and method of moments, respectively. The complete polymerization process model also includes vapor–liquid equilibrium equations...

Production planning decisions usually span multiple time periods and generally involve, but are not limited to, determining the amount of raw materials to be purchased by each plant, the production and inventory levels at each plant, the transportation of intermediate and finished products between different locations, and meeting the forecast deman...

The impact of supply chain disruptions in the performance of companies has received increasing attention in recent years. The management of disruptions is an important topic for every company with a complex supply chain. Intuitively, it is well understood that reactive measures are not enough to deal with disruptive events. Therefore, the design of...

This paper addresses reactor modeling and recipe optimization of semi-batch polyether polyol processes, extending our previous results on homopolymerization to polyoxyalkylene copolymers. We first develop a rigorous first-principles reactor model based on the population balance, heat balance, reaction kinetics, and vapor-liquid equilibria (VLE) etc...

A novel efficient agent‐based method for scheduling network batch processes in the process industry is proposed. The agent‐based model is based on the resource‐task network. To overcome the drawback of localized solutions found in conventional agent‐based methods, a new scheduling algorithm is proposed. The algorithm predicts the objective function...

The reactor modeling and recipe optimization of conventional semibatch polyether polyol processes, in particular for the polymerization of propylene oxide to make polypropylene glycol, is addressed. A rigorous mathematical reactor model is first developed to describe the dynamic behavior of the polymerization process based on first‐principles inclu...

Motivated by a real-world industrial problem, this work deals with the integration of planning and scheduling in the operation of a network of batch plants. The network consists of single-stage, multiproduct batch plants located in different sites, which can exchange intermediate products in order to blend them to obtain finished products. The time...

The challenges of supplying advanced materials and performance products are very different from those associated with commodity chemicals. Yet these challenges are well addressed by enterprise-wide optimization techniques. This paper discusses the nature of advanced materials and some challenges and solutions related to product design, production s...

We propose a novel agent-based method for real-time scheduling of network batch processes. The agent architecture is formulated based on the resource-task network (RTN) or state-task network (STN) representation so it is applicable to a wide range of network batch scheduling problems. A scheduling algorithm is developed based on the predicted objec...

A systematic framework for the integration of short-term scheduling and dynamic optimization (DO) of batch processes is described. The state equipment network (SEN) is used to represent a process system, where it decomposes the process into two basic kinds of entities: process materials and process units. Mathematical modeling based on the SEN fram...

Scheduling is a crucial decision-making in batch processes [1]. Optimization methods provide a systematic approach to the scheduling problem and the optimality of the solution is guaranteed [2, 3]. However, due to the combinatorial nature of the resulting mixed-integer programming (MIP) problems, the computational complexity is still a main challen...

Dynamic Modeling and Recipe Optimization of Semibatch Polymerization Processes Y. Nie L.T. Biegler Department of Chemical Engineering Carnegie Mellon University C.M. Villa J.M. Wassick The Dow Chemical Company Dynamic modeling and optimization techniques offer advantages for the design and improvement of process recipes. In this study, a...

This paper presents a novel mixed-integer linear programming (MILP) formulation for the tank farm operation problem (TFOP), which involves the simultaneous scheduling of continuous multiproduct processing lines and the assignment of dedicated storage tanks to finished products. The objective of the problem is to minimize blocking of the finished li...

The objective of this work was to develop and demonstrate batch process optimization tools that can be deployed for use in a manufacturing environment. The work specifically addresses the lack of tangible re-al time performance measures for batch process operations in literature and industry. Such performance measures need to account for real time...

A generic model is a model that is built for a class of system and can be implemented for a specific system through changes in input data alone, without any structural changes to the model. In this paper, we propose a framework for building such generic model for non-steady state process networks, which are characterized by flow of materials betwee...

The discrete time resource-task network (RTN) model is a generalized mixed-integer linear programming model used in scheduling optimization problems. This paper presents several extensions to the RTN that have been used at The Dow Chemical Company. One RTN extension allows for more realistic demand fulfillment: customer orders can be filled in thei...

Integrated sites are tightly interconnected networks of large-scale chemical processes. Given the large-scale network structure of these sites, disruptions in any of its nodes, or individual chemical processes, can propagate and disrupt the operation of the whole network. Random process failures that reduce or shut down production capacity are amon...

Since plants that form the process network are subjected to fluctuations in product demand or random mechanical failures, design decisions such as adding redundant units and increasing storage between units can increase the flexibility and reliability of an integrated site. In this paper, we develop a bi-criterion optimization model that captures t...

We propose a multiperiod mixed-integer linear programming (MILP) model for the simultaneous capacity, production, and distribution planning for a multisite system including a number of production sites and markets. Multiple products are produced in several production trains that are located in different sites. The unique feature of the proposed mod...

An integrated chemical production complex provides a rich environment for the application of enterprise-wide optimization techniques. A world scale site can be composed of dozens of production plants manufacturing hundreds of products. This paper discusses the nature of an integrated chemical production site to identify the opportunities for enterp...

In this article, we consider the risk management for mid-term planning of a global multi-product chemical supply chain under demand and freight rate uncertainty. A two-stage stochastic linear programming approach is proposed within a multi-period planning model that takes into account the production and inventory levels, transportation modes, times...

Global supply chains in the process industries are usually very large scale systems that can be comprised of up to hundreds of or even thousands of production facilities, distribution centers and customers. Due to competition in the global marketplace, process industries are facing increasing pressure to manage their supply chains so as to reduce c...

Chemical supply chain networks provide large opportunities for cost reductions through the redesign of the flow of material from producer to customer. In this paper we present a mixed-integer linear program (MILP) capable of optimizing a multi-product supply chain network made up of production sites, an arbitrary number of echelons of distribution...

We address the problem of short-term scheduling of parallel batch reactors followed by continuously operating finishing trains to form workgroups which is motivated by a real world problem at the Dow Chemical Co. The proposed MILP formulation is based on the recent planning model of Erdirik-Dogan and Grossmann ( AIChE J.2007, 53, 2284−2300) and fea...

We address the simultaneous planning and scheduling of parallel multi-product batch reactors, a challenging problem that has been motivated by a real world application at the Dow Chemical Company. We propose a novel continuous time MILP model for the simultaneous planning and scheduling that is based on slot representation. While effective for shor...

In this paper we propose a multiperiod nonlinear programming (NLP) formulation that incorporates empirical process models for the optimal planning of a multi-plant production site. Using as a basis a real world application of a polymer plant that produces 27 products, a model is developed for predicting the detailed production using actual plant da...

Model-based control algorithms generally use a model of the process with fixed parameters in the synthesis of the control law and implicitly account for uncertainty in those parameters in the selection of tunable parameters in the feedback path. In this work, a notion of set-based control is introduced for SISO processes, in order to explicitly acc...

A theoretical formulation of the deadtime window approach to deadtime compensation is presented and investigated. The central idea in this approach is to use a specified uncertainty band in the deadtime to create a time domain uncertainty window. The feedback signal is changed only if the measurement is outside the expected region. Simulations resu...

The control of pH is widely recognized as a difficult problem. The Strong Acid Equivalent approach for control of pH processes consists of defining an alternate equivalent control objective, the Strong Acid Equivalent, and using a linear control law in terms of this new control objective. The Strong Acid Equivalent is calculated on line from pH mea...

A multivariable internal model control system was developed for a full-scale distillation column. The basis for the design of the control is a two-input/two-output matrix of linear transfer functions describing column dynamics. The control system is designed to perform dual composition control of the overhead and bottom products. Hardware constrain...

This paper describes the successful application of state estimation in the control of commercial chemical process operations. From a theoretical standpoint, it appears straightforward to use state estimation for detecting faulty measurements, for estimating unmeasured variables, and for obtaining improved estimates when redundant information is ava...

For some industrial extruders it is difficult to maintain constant torque on the screw. One cause of this control problem is the highly non-linear dynamic behavior exhibited by these extruders. This paper describes the design and production experience of a non-linear Internal Model Controller for torque control. The controller is based on a non-lin...

In this paper we propose a multiperiod nonlinear programming (NLP) formulation that incorporates empirical process models for the optimal planning of a multi-plant production site. Using as a basis a real world application of a polymer plant that produces 27 products, a model is developed for predicting the detailed production using actual plant da...