需求不确定下炼油企业生产计划优化混合规划模型

Abstract Production planning under uncertainty is considered as one of the most important problems in plant-wide optimization. In this article, first, a stochastic programming model with uniform distribution assumption is developed for refinery production planning under demand uncertainty, and then a hybrid programming model incorporating the linear programming model with the stochastic programming one by a weight factor is proposed. Subsequently, piecewise linear approximation functions are derived and applied to solve the hybrid programming model-under uniform distribution assumption. Case studies show that the linear approximation algorithm is effective to solve.the hybrid programming model, along with an error≤0.5% when the deviatiorgmean≤20%. The simulation results indicate that the hybrid programming model with an appropriate weight factor （0.1-0.2） can effectively improve the optimal operational strategies under demand uncertainty, achieving higher profit than the linear programming model and the stochastic programming one with about 1.3% and 0.4% enhancement, respectavely.     

Stochastic programming models for optimal shale well development and refracturing planning under uncertainty

In this work we present an optimization framework for shale gas well development and refracturing planning. This problem is concerned with if and when a new shale gas well should be drilled at a prospective location, and whether or not it should be refractured over its lifespan. We account for exogenous gas price uncertainty and endogenous well performance uncertainty. We propose a mixed‐integer linear, two‐stage stochastic programming model embedded in a moving horizon strategy to dynamically solve the planning problem. A generalized production estimate function is described that predicts the gas production over time depending on how often a well has been refractured, and when exactly it was restimulated last. From a detailed case study, we conclude that early in the life of an active shale well, refracturing makes economic sense even in low‐price environments, whereas additional restimulations only appear to be justified if prices are high. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

Multistage stochastic programming for the closed-loop supply chain planning with mobile modules under uncertainty

Traditional supply chains usually follow fixed facility designs which coincide with the strategic nature of supply chain management (SCM). However, as the global market turns more volatile, the concept of mobile modularization has been adopted by increasingly more industrial practitioners. In mobile modular networks, modular units can be installed or removed at a particular site to expand or reduce the capacity of a facility, or relocated to other sites to tackle market volatility. In this work, we formulate a mixed-integer linear programming (MILP) model for the closed-loop supply chain network planning with modular distribution and collection facilities. To further deal with uncertain customer demands and recovery rates, we extend our model to a multistage stochastic programming model and efficiently solve it using a tailored stochastic dynamic dual integer programming (SDDiP) with Magnanti-Wong enhanced cuts. Computational experiments show that the added Magnanti-Wong cuts in the proposed algorithm can effectively close the gap between upper and lower bounds, and the benefit of mobile modules is evident when the temporal and spatial variability of customer demand is high.     

考虑需求不确定性的化工生产计划与调度集成

生产计划与调度是化工供应链优化中两个重要的决策问题。为了提高生产决策的效率,不仅要对计划与调度进行集成,而且要考虑不确定性的影响。对于多周期生产计划与调度问题,首先在每个生产周期内,分别建立计划与调度的确定性模型,通过产量关联对二者进行集成。然后考虑需求不确定性,使用有限数量的场景表达决策变量,建立二阶段随机规划模型。最后运用滚动时域求解策略,使计划与调度结果在迭代过程中达到一致。实例结果表明,在考虑需求不确定性时,与传统方法相比,随机规划方法可以降低总费用,结合计划与调度的分层集成策略,实现了生产操作性和经济性的综合优化。     

Robust planning of multisite refinery networks: Optimization under uncertainty

This paper considers the problem of multisite integration and coordination strategies within a network of petroleum refineries under uncertainty and using robust optimization techniques. The framework of simultaneous analysis of process network integration, originally proposed by Al-Qahtani & Elkamel [Al-Qahtani, K., & Elkamel, A. (2008). Multisite facility network integration design and coordination: An application to the refining industry. Computers & Chemical Engineering, 32, 2198], is extended to account for uncertainty in model parameters. Robustness is analyzed based on both model robustness and solution robustness, where each measure is assigned a scaling factor to analyze the sensitivity of the refinery plan and integration network due to variations. Parameters uncertainty considered include coefficients of the objective function and right-hand-side parameters in the inequality constraints. The proposed method makes use of the sample average approximation (SAA) method with statistical bounding techniques. The proposed model was tested on two industrial-scale studies of a single refinery and a network of complex refineries. Modeling uncertainty in the process parameters provided a practical perspective of this type of problems in the chemical industry where benefits not only appear in terms of economic considerations, but also in terms of process flexibility.     

Product tri-section based crude distillation unit model for refinery production planning and refinery optimization

Accuracy of a crude distillation unit (CDU) model has a significant impact on refinery production planning. High accuracy is typically accomplished via nonlinear models which causes convergence difficulties when the entire refinery model is optimized. CDU model presented in this work is a mixed-integer linear model with a modest number of binary variables; its accuracy is on par with rigorous tray to tray CDU models. The model relies on the observation¹² that a line through the middle of the product true boiling point (TBP) curve depends on the crude feed properties and the yields of the adjacent products. Novelty of the product tri-section CDU model is that it does not require models of individual distillation towers comprising the CDU, thereby leading to a much simpler model structure. Significant reduction in the computational effort required for the optimization of nonlinear refinery models is illustrated by comparison with previous work.     

Shale gas pad development planning under price uncertainty

In this article, we study shale gas pad development under natural gas price uncertainty. We optimize the sequence of operations, gas curtailment, and storage on a single pad to maximize the net present value. The optimization problem is formulated as an mixed-integer linear programming model, which is similar to the one proposed by Ondeck et al. We investigate how natural gas price uncertainty affects the operation strategy in the pad development. Both two-stage and multistage stochastic programming are used as the mathematical framework to hedge against uncertainty. Our case study shows that there is value of using stochastic programming when the price variance is high. However, when the variance of the price is low, solving the stochastic programming problems does not create additional value compared with solving the deterministic problem.     

炼厂生产计划优化模型

This article addresses a production planning optimization problem of overall refinery. The authors formulated the optimization problem as mixed integer linear programming. The model considers the main factors for optimizing the production plan of overall refinery related to the use of run-modes of processing units. The aim of this planning is to decide which run-mode to use in each processing unit in each period of a given horizon, to satisfy the demand, such as the total cost of production and inventory is minimized. The resulting model can be regarded as a generalized lot-sizing problem where a run-mode can produce and consume more than one product. The resulting optimization problem is large-sized and NP-hard. The authors have proposed a column generation-based algorithm called branch-and-price （BP） for solving the interested optimization problem. The model and implementation of the algorithm are described in detail in this article. The computational results verify the effectiveness of the proposed model and the solution method.     

A game theoretic framework for petroleum refinery strategic production planning

A game theoretic framework for strategic refinery production planning is presented in which strategic planning problems are formulated as non‐cooperative potential games whose solutions represent Nash equilibria. The potential game model takes the form of a nonconvex nonlinear program (NLP) and we examine an additional scenario extending this to a nonconvex mixed integer nonlinear program (MINLP). Tactical planning decisions are linked to strategic decision processes through a potential game structure derived from a Cournot oligopoly‐type game in which multiple crude oil refineries supply several markets. Two scenarios are presented which illustrate the utility of the game theoretic framework in the analysis of production planning problems in competitive scenarios. Solutions to these problems are interpreted as mutual best responses yielding maximum profit in the competitive planning game. The resulting production planning decisions are rational in a game theoretic sense and are robust to deviations in competitor strategies. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2751–2763, 2017     

A new Lagrangian decomposition approach applied to the integration of refinery planning and crude-oil scheduling

The aim of this paper is to introduce a methodology to solve a large-scale mixed-integer nonlinear program (MINLP) integrating the two main optimization problems appearing in the oil refining industry: refinery planning and crude-oil operations scheduling. The proposed approach consists of using Lagrangian decomposition to efficiently integrate both problems. The main advantage of this technique is to solve each problem separately. A new hybrid dual problem is introduced to update the Lagrange multipliers. It uses the classical concepts of cutting planes, subgradient, and boxstep. The proposed approach is compared to a basic sequential approach and to standard MINLP solvers. The results obtained on a case study and a larger refinery problem show that the new Lagrangian decomposition algorithm is more robust than the other approaches and produces better solutions in reasonable times.     

Risk management for a global supply chain planning under uncertainty: Models and algorithms

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 of shipments, and customer service levels. To investigate the potential improvement by using stochastic programming, we describe a simulation framework that relies on a rolling horizon approach. The studies suggest that at least 5% savings in the total real cost can be achieved compared with the deterministic case. In addition, an algorithm based on the multi‐cut L‐shaped method is proposed to effectively solve the resulting large scale industrial size problems. We also introduce risk management models by incorporating risk measures into the stochastic programming model, and multi‐objective optimization schemes are implemented to establish the tradeoffs between cost and risk. To demonstrate the effectiveness of the proposed stochastic models and decomposition algorithms, a case study of a realistic global chemical supply chain problem is presented. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

An improved decomposition algorithm for optimization under uncertainty

This paper proposes a modification to the decomposition algorithm of Ierapetritou and Pistikopoulos (1994) for process optimization under uncertainty. The key feature of our approach is to avoid imposing constraints on the uncertain parameters, thus allowing a more realistic modeling of uncertainty. A theoretical analysis of the earlier algorithm leads to the development of an improved algorithm which successfully avoids getting trapped in local minima while accounting more accurately for the trade-offs between cost and flexibility. In addition, the improved algorithm is 3–6 times faster, on the problems tested, than the original one. This is achieved by avoiding the solution of feasibility subproblems, the number of which is exponential in the number of uncertain parameters.     

Multisite supply planning for drug products under uncertainty

In the pharmaceutical industry, the goal of a supply planner is to make efficient capacity allocation decisions that ensure an uninterrupted supply of drug products to patients and to maintain product inventory levels close to the target stock. This task can be challenging due to the limited availability of manufacturing assets, uncertainties in product demand, fluctuations in production yields, and unplanned site downtimes. It is not uncommon to observe uneven distribution of product inventories with some products carrying excess inventories, while other products may be close to a stockout. Maintaining high stock levels can have economic repercussions due to the risk of expiration of unused products (whereas products facing a stockout can adversely affect the treatment regimen of patients). The network complexity of pharmaceutical supply-chains coupled with regulatory constraints and siloed planning systems force supply planners to rely on manual (error-prone) decision-making processes. Such an approach results in suboptimal capacity allocation and inventory management decisions. In this work, we propose a stochastic optimization methodology for the production scheduling of multiple drug products in lyophilization units across multiple sites. The framework leverages information obtained from historical and forecast data to generate scenarios of uncertain parameters (e.g., yield, demand, and downtimes) that can realize in the future. The optimization model determines a product filling schedule that maintains product stock levels close to targets under diverse scenarios. We show that this approach helps in avoiding reactive scheduling and in maintaining a more robust production plan than deterministic procedures (which ignore uncertainty). Specifically, planning under a stochastic optimization approach reduces the number of scenarios under which backlogs are observed and also reduces the magnitude of the backlogs.     

A Benders decomposition framework for the optimization of disjunctive superstructures with ordered discrete decisions

This study introduces the logic-based discrete-Benders decomposition (LD-BD) for Generalized Disjunctive Programming (GDP) superstructure problems with ordered Boolean variables. The key idea is to obtain Benders cuts that use neighborhood information of a reformulated version of Boolean variables. These Benders cuts are iteratively refined, which guarantees convergence to a local optimum. A mathematical case study, the optimization of a network with Continuous Stirred-Tank Reactors (CSTRs) in series, and a large-scale problem involving the design of a distillation column are considered to demonstrate the features of LD-BD. The results from these case studies have shown that the LD-BD method exhibited good performance by finding attractive locally optimal solutions relative to existing logic-based solvers for GDP problems. Based on these tests, the LD-BD method is a promising strategy to solve optimal synthesis problems with ordered discrete decisions emerging in chemical engineering applications.     

Joint capacity planning and distribution network optimization of coal supply chains under uncertainty

A two‐stage stochastic integer programming model is developed to address the joint capacity planning and distribution network optimization of multiechelon coal supply chains (CSCs) under uncertainty. The proposed model not only introduces the uses of compound real options in sequential capacity planning, but also considers uncertainty induced by both risks and ambiguities. Both strategic decisions (i.e., facility locations and initial investment, service assignment across the entire CSC, and option holding status) and scenario‐based operational decisions (i.e., facility operations and capacity expansions, outsourcing policy, and transportation and inventory strategies) can be simultaneously determined using the model. By exploiting the nested decomposable structure of the model, we develop a new distributed parallel optimization algorithm based on nonconvex generalized Bender decomposition and Lagrangean relaxation to mitigate the computation resource limitation. One of the main CSCs in China is studied to demonstrate the applicability of the proposed model and the performance of the algorithm. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1246–1261, 2018     

Stochastic blockmodeling for learning the structure of optimization problems

Decomposition-based solution algorithms for optimization problems depend on the underlying latent block structure of the problem. Methods for detecting this structure are currently lacking. In this article, we propose stochastic blockmodeling (SBM) as a systematic framework for learning the underlying block structure in generic optimization problems. SBM is a generative graph model in which nodes belong to some blocks and the interconnections among the nodes are stochastically dependent on their block affiliations. Hence, through parametric statistical inference, the interconnection patterns underlying optimization problems can be estimated. For benchmark optimization problems, we show that SBM can reveal the underlying block structure and that the estimated blocks can be used as the basis for decomposition-based solution algorithms which can reach an optimum or bound estimates in reduced computational time. Finally, we present a general software platform for automated block structure detection and decomposition-based solution following distributed and hierarchical optimization approaches.     

Stochastic pooling problem for natural gas production network design and operation under uncertainty

Product quality and uncertainty are two important issues in the design and operation of natural gas production networks. This paper presents a stochastic pooling problem optimization formulation to address these two issues, where the qualities of the flows in the system are described with a pooling model and the uncertainty in the system is handled with a multi‐scenario, two‐stage stochastic recourse approach. In addition, multi‐objective problems are handled via a hierarchical optimization approach. The advantages of the proposed formulation are demonstrated with case studies involving an example system based on Haverly's pooling problem and a real industrial system. The stochastic pooling problem is a potentially large‐scale nonconvex Mixed‐Integer Nonlinear Program (MINLP), and a rigorous decomposition method developed recently is used to solve this problem. A computational study demonstrates the advantage of the decomposition method over a state‐of‐the‐art branch‐and‐reduce global optimizer, BARON. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Medium-term maintenance turnaround planning under uncertainty for integrated chemical sites

Plant maintenance poses extended disruptions to production. Maintenance effects are amplified when the plant is part of an integrated chemical site, as production levels of adjacent plants in the site are also significantly influenced. A challenge in dealing with turnarounds is the difficulty in predicting their duration, due to discovery work and delays. This uncertainty in duration affects two major planning decisions: production levels and maintenance manpower allocation. The latter must be decided several months before the turnarounds occur. We address the scheduling of a set of plant turnarounds over a medium-term of several months using integer programming formulations. Due to the nature of uncertainty, production decisions are treated through stochastic programming ideas, while the manpower aspect is handled through a robust optimization framework. We propose combined robust optimization and stochastic programming formulations to address the problem and demonstrate, through an industrial case study, the potential for significant savings.