Multi-bucket optimization for integrated planning and scheduling in the perishable dairy supply chain

This paper considers a dairy industry problem on integrated planning and scheduling of set yoghurt production. A mixed integer linear programming formulation is introduced to integrate tactical and operational decisions and a heuristic approach is proposed to decompose time buckets of the decisions. The decomposition heuristic improves computational efficiency by solving big bucket planning and small bucket scheduling problems. Further, mixed integer linear programming and constraint programming methodologies are combined with the algorithm to show their complementary strengths. Numerical studies using illustrative data with high demand granularity (i.e., a large number of small-sized customer orders) demonstrate that the proposed decomposition heuristic has consistent results minimizing the total cost (i.e., on average 8.75% gap with the best lower bound value found by MILP) and, the developed hybrid approach is capable of solving real sized instances within a reasonable amount of time (i.e., on average 92% faster than MILP in CPU time).     

A new continuous-time formulation for scheduling crude oil operations

In today's competitive business climate characterized by uncertain oil markets, responding effectively and speedily to market forces, while maintaining reliable operations, is crucial to a refinery's bottom line. Optimal crude oil scheduling enables cost reduction by using cheaper crudes intelligently, minimizing crude changeovers, and avoiding ship demurrage. So far, only discrete-time formulations have stood up to the challenge of this important, nonlinear problem. A continuous-time formulation would portend numerous advantages, however, existing work in this area has just begun to scratch the surface. In this paper, we present the first complete continuous-time mixed integer linear programming (MILP) formulation for the short-term scheduling of operations in a refinery that receives crude from very large crude carriers via a high-volume single buoy mooring pipeline. This novel formulation accounts for real-world operational practices. We use an iterative algorithm to eliminate the crude composition discrepancy that has proven to be the Achilles heel for existing formulations. While it does not guarantee global optimality, the algorithm needs only MILP solutions and obtains excellent maximum-profit schedules for industrial problems with up to 7 days of scheduling horizon. We also report the first comparison of discrete- vs. continuous-time formulations for this complex problem.     

Integrated production planning and scheduling using a decomposition framework

To ensure the consistency between planning and scheduling decisions, the integrated planning and scheduling problem should be addressed. Following the natural hierarchy of decision making, integrated planning and scheduling problem can be formulated as bilevel optimization problem with a single planning problem (upper level) and multiple scheduling subproblems (lower level). Equivalence between the proposed bilevel model and a single level formulation is proved considering the special structure of the problem. However, the resulting model is still computationally intractable because of the integrality restrictions and large size of the model. Thus a decomposition based solution algorithm is proposed in this paper. In the proposed method, the production feasibility requirement is modeled through penalty terms on the objective function of the scheduling subproblems, which is further proportional to the amount of unreachable production targets. To address the nonconvexity of the production cost function of the scheduling subproblems, a convex polyhedral underestimation of the production cost function is developed to improve the solution accuracy. The proposed decomposition framework is illustrated through examples which prove the effectiveness of the method.     

Multi-mode resource constrained project scheduling under resource disruptions

Over the last few decades, research on resource constrained project scheduling has focused on the development of mathematical programming based approaches for the generation of a nominal schedule under a deterministic environment. During the implementation phase, however, the nominal schedule may need to be revised when one or more resources are disrupted for a length of time. In this paper, we formulate two discrete time based models to deal with two different disruption scenarios for multi-mode resource constrained problems. We propose a reactive re-scheduling procedure for a single, as well as a series of disruptions, without having any disruption information in advance. To test the proposed approaches, sets of ten, twenty and thirty-activity multi-mode test instances from Project Scheduling Library (PSLIB) were used after introducing randomly generated disruption events. The experimental studies were also carried out to determine the effect of different factors related to the disruption recovery process.     

An MILP Model for Optimal Scheduling of the Lubricant Production Plant

In this article we are developing a model that can be used for determining the optimal production schedule in a lubricant production plant. The model includes all the main stages in the lubricant production process, contains both continuous and binary variables, and results in the formulation of a mixed integer linear programming (MILP) problem that is solved using standard optimization techniques. The model can be easily adapted to any lube production facility, thus providing a valuable tool to refineries in their effort to automate the production scheduling process. The proposed tool can save valuable time and resources by eliminating the time-consuming search for a feasible production plan that production engineers go through in order to meet production demands.     

Proactive scheduling of batch processes by a combined robust optimization and multiparametric programming approach

We address short‐term batch process scheduling problems contaminated with uncertainty in the data. The mixed integer linear programming (MILP) scheduling model, based on the formulation of Ierapetritou and Floudas, Ind Eng Chem Res. 1998; 37(11):4341–4359, contains parameter dependencies at multiple locations, yielding a general multiparametric (mp) MILP problem. A proactive scheduling policy is obtained by solving the partially robust counterpart formulation. The counterpart model may remain a multiparametric problem, yet it is immunized against uncertainty in the entries of the constraint matrix and against all parameters whose values are not available at the time of decision making. We extend our previous work on the approximate solution of mp‐MILP problems by embedding different uncertainty sets (box, ellipsoidal and budget parameter regulated uncertainty), and by incorporating information about the availability of uncertain data in the construction of the partially robust scheduling model. For any parameter realization, the corresponding schedule is then obtained through function evaluation. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4184–4211, 2013     

Optimal maintenance scheduling of a gas engine power plant using generalized disjunctive programming

A new continuous‐time model for long‐term scheduling of a gas engine power plant with parallel units is presented. Gas engines are shut down according to a regular maintenance plan that limits the number of hours spent online. To minimize salary expenditure with skilled labor, a single maintenance team is considered which is unavailable during certain periods of time. Other challenging constraints involve constant minimum and variable maximum power demands. The objective is to maximize the revenue from electricity sales assuming seasonal variations in electricity pricing by reducing idle times and shutdowns in high‐tariff periods. By first developing a generalized disjunctive programming model and then applying both big‐M and hull reformulation techniques, we reduce the burden of finding the appropriate set of mixed‐integer linear constraints. Through the solution of a real‐life problem, we show that the proposed formulations are very efficient computationally, while gaining valuable insights about the system. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2083–2097, 2014     

An MILP formulation for the synthesis of protein purification processes

This paper presents a mixed integer linear programming (MILP) model for the optimal synthesis of chromatographic protein purification processes including the time line in which our target protein product is collected. The model is linearised using piecewise linear approximation strategies and tested on three example protein mixtures, containing up to 13 contaminants and selecting from a set of up to 21 candidate steps. The results are also compared with previous literature models attempting to solve the same problem and show that the proposed approach offers significant gains in computational efficiency without compromising the quality of the solution.     

批处理过程优化调度研究综述——2.MILP调度

详细阐述MILP建模的关键技术和现有的有关参考文献,同时给出MILP调度实施框架和已经报道的成功应用。在此基础上,指出进一步的研究方向。     

Simultaneous mixed-integer dynamic scheduling of processes and their energy systems

Increasingly volatile electricity prices make simultaneous scheduling optimization desirable for production processes and their energy systems. Simultaneous scheduling needs to account for both process dynamics and binary on/off-decisions in the energy system leading to challenging mixed-integer dynamic optimization problems. We propose an efficient scheduling formulation consisting of three parts: a linear scale-bridging model for the closed-loop process output dynamics, a data-driven model for the process energy demand, and a mixed-integer linear model for the energy system. Process dynamics is discretized by collocation yielding a mixed-integer linear programming (MILP) formulation. We apply the scheduling method to three case studies: a multiproduct reactor, a single-product reactor, and a single-product distillation column, demonstrating the applicability to multiple input multiple output processes. For the first two case studies, we can compare our approach to nonlinear optimization and capture 82% and 95% of the improvement. The MILP formulation achieves optimization runtimes sufficiently fast for real-time scheduling.     

Integration of scheduling and control for batch processes using multi‐parametric model predictive control

Integration of scheduling and control results in Mixed Integer Nonlinear Programming (MINLP) which is computationally expensive. The online implementation of integrated scheduling and control requires repetitively solving the resulting MINLP at each time interval. (Zhuge and Ierapetritou, Ind Eng Chem Res. 2012;51:8550–8565) To address the online computation burden, we incorporare multi‐parametric Model Predictive Control (mp‐MPC) in the integration of scheduling and control. The proposed methodology involves the development of an integrated model using continuous‐time event‐point formulation for the scheduling level and the derived constraints from explicit MPC for the control level. Results of case studies of batch processes prove that the proposed approach guarantees efficient computation and thus facilitates the online implementation. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3169–3183, 2014     

批处理过程优化调度研究综述--1.MILP调度方法的描述框架

综述化工批处理过程调度建模研究及其实际应用。计划／调度在企业生产管理中起着承上启下的作用，合理的计划调度不但能提高企业的服务水平、降低存储费用，而且还能提高企业的生产能力、加深对过程机制及关键数据的理解。整数规划方法应用于批处理过程计划调度，具有较好的适用性和扩展性，解的性质良好，在批处理过程调度研究得到广泛的应用。     

抗生素发酵过程优化调度模型的研究

对抗生素多罐并行发酵过程进行了分析,将任务、设备和事件之间的分配关系表达为两类0-1变量,建立了一个基于连续时间的抗生素多罐并行发酵过程优化调度的M ILP(混合整数线性规划)模型。该模型整数变量少,求解速度快,并给出了最短生产时间和罐批最优生产序列。最后以头孢菌素发酵过程为例证明了此调度模型的可行性和有效性。     

Air separation with cryogenic energy storage: Optimal scheduling considering electric energy and reserve markets

The concept of cryogenic energy storage (CES) is to store energy in the form of liquid gas and vaporize it when needed to drive a turbine. Although CES on an industrial scale is a relatively new approach, the technology is well known and essentially part of any air separation unit that utilizes cryogenic separation. In this work, the operational benefits of adding CES to an existing air separation plant are assessed. Three new potential 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, and (3) creating additional revenue by providing operating reserve capacity. A mixed‐integer linear programming scheduling model is developed and a robust optimization approach is applied to model the uncertainty in reserve demand. The proposed model is applied to an industrial case study, which shows significant potential economic benefits. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1547–1558, 2015     

考虑能耗影响的多产品间歇化工过程优化排序

提出一种用于间歇生产的多产品化工厂排序的多目标优化的混合整数非线性规划(MINLP)模型,其目标函数同时考虑了总生产时间最短和能耗最小的影响,定义了关于过程能耗的影响因子及决策因子,用以对总生产时间和能耗的影响进行权衡。采用改进的模拟退火算法(SA)对具有不同决策因子和能耗影响因子情况下的算例进行了求解,结果表明,该模型能够较好地反映能耗因素在多产品厂排序问题中的影响,使排序结果达到生产时间和能耗影响的综合最优。     

A new approach for scheduling of multipurpose batch processes with unlimited intermediate storage policy

The increasing demand of goods, the high competitiveness in the global marketplace as well as the need to minimize the ecological footprint lead multipurpose batch process industries to seek ways to maximize their productivity with a simultaneous reduction of raw materials and utility consumption and efficient use of processing units. Optimal scheduling of their processes can lead facilities towards this direction. Although a great number of mathematical models have been developed for such scheduling, they may still lead to large model sizes and computational time. In this work, we develop two novel mathematical models using the unit-specific event-based modelling approach in which consumption and production tasks related to the same states are allowed to take place at the same event points. The computational results demonstrate that both proposed mathematical models reduce the number of event points required. The proposed unit-specific event-based model is the most efficient since it both requires a smaller number of event points and significantly less computational time in most cases especially for those examples which are computationally expensive from existing models.     

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。     

Integrated planning and scheduling under production uncertainties: Bi-level model formulation and hybrid solution method

We propose a novel method for integrating planning and scheduling problems under production uncertainties. The integrated problem is formulated into a bi-level program. The planning problem is solved in the upper level, while the scheduling problems in the planning periods are solved under uncertainties in the lower level. The planning and scheduling problems are linked via service level constraints. To solve the integrated problem, a hybrid method is developed, which iterates between a mixed-integer linear programming solver for the planning problem and an agent-based reactive scheduling method. If the service level constraints are not met, a cutting plane constraint is generated by the agent-based scheduling method and appended to the planning problem which is solved to determine new production quantities. The hybrid method returns an optimality gap for validating the solution quality. The proposed method is demonstrated by two complicated problems which are solved efficiently with small gaps less than 1%.     

Continuous‐time modeling and global optimization approach for scheduling of crude oil operations

Scheduling of crude oil operations is a critical and complicated component of overall refinery operations, because crude oil costs account for about 80% of the refinery turnover. Moreover, blending with less expensive crudes can significantly increase profit margins. The mathematical modeling of blending different crudes in storage tanks results in many bilinear terms, which transforms the problem into a challenging, nonconvex, and mixed‐integer nonlinear programming (MINLP) optimization model. Two primary contributions have been made. First, the authors developed a novel unit‐specific event‐based continuous‐time MINLP formulation for this problem. Then they incorporated realistic operational features such as single buoy mooring (SBM), multiple jetties, multiparcel vessels, single‐parcel vessels, crude blending, brine settling, crude segregation, and multiple tanks feeding one crude distillation unit at one time and vice versa. In addition, 15 important volume‐based or weight‐based crude property indices are also considered. Second, they exploited recent advances in piecewise‐linear underestimation of bilinear terms within a branch‐and‐bound algorithm to globally optimize the MINLP problem. It is shown that the continuous‐time model results in substantially fewer bilinear terms. Several examples taken from the work of Li et al. are used to illustrate that (1) better solutions are obtained and (2) ε‐global optimality can be attained using the proposed branch‐and‐bound global optimization algorithm with piecewise‐linear underestimations of the bilinear terms. © 2011 American Institute of Chemical Engineers AIChE J, 2012