A multi-level simulation approach for the crude oil loading/unloading scheduling problem

An integrated approach for refinery production scheduling and unit operation optimization problems is presented. Each problem is at a different decision making layer and has an independent objective function and model. The objective function at the operational level is an on-line maximization of the difference between the product revenue and the energy and environmental costs of the main refinery units. It is modeled as an NLP and is constrained by ranges on the unit's operating condition as well as product quality constraints. The production scheduling layer is modeled as an MILP with the objective of minimizing the logistical costs of unloading the crude oil over a day-to-week time horizon. The objective function is a linear sum of the unloading, sea waiting, inventory, and setup costs. The nonlinear simulation model for the process units is used to find optimized refining costs and revenue for a blend of two crudes. Multiple linear regression of the individual crude oil flow rates within the crude oil percentage range allowed by the facility is then used to derive linear refining cost and revenue functions. Along with logistics costs, the refining costs or revenue are considered in the MILP scheduling objective function. Results show that this integrated approach can lead to a decrease of production and logistics costs or increased profit, provide a more intelligent crude schedule, and identify production level scheduling decisions which have a tradeoff benefit with the operational mode of the refinery.     

Scheduling multi-product tree-structure pipelines

The problem discussed in this paper is short-term scheduling of distribution of petroleum derivatives from a single oil refinery to a number of depots through a tree-structure pipeline. Scheduling product batches in pipelines is a very complex task with many constraints to be considered. Batches of refined products and grades are pumped back-to-back in the pipeline, often with no separation device between batches. In this work a continuous-time, MILP problem representation for tree-structure pipelines is proposed. The approach is successfully applied to a number of pipeline scheduling problems, including a real-world problem. The data and experimental results are reported.     

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.     

An MILP continuous-time approach to short-term scheduling of resource-constrained multistage flowshop batch facilities

This work presents a new MILP mathematical formulation for the resource-constrained short-term scheduling of flowshop batch facilities with a known topology and limited supplies of discrete resources. The processing structure is composed of multiple stages arranged in series and several units working in parallel at each one. All production orders consist of a single batch and follow the same processing sequence throughout the plant. The proposed MILP approach is based on a continuous time domain representation that relies on the notion of order predecessor and accounts for sequence-dependent setup times. Assignment and sequencing decisions are independently handled through separate sets of binary variables. A proper formulation of the sequencing constraints provides a substantial saving in sequencing variables and constraints. By postulating a pair of conditions for the simultaneous execution of processing tasks, rather simple resource constraints requiring a few extra binary variables are derived. The proposed MILP scheduling approach shows a remarkable computational efficiency when applied to real-world problems.     

印染车间作业计划优化调度

由于基于统一离散时间表示的生产过程优化模型的约束和变量多,基于连续时间的批处理短期调度在近10年得到了广泛的重视和研究。本文简略介绍了生产过程调度模型的情况,通过对生产过程优化调度模型和印染生产工艺的研究,建立了基于连续时间印染生产过程优化调度MILP模型。然后,通过把数学模型转换成IL-OG OPL语言描述的模型,以浙江省某印染企业2个案例为数据,利用ILOG CPLEX进行求解,调度结果以甘特图的形式表达。结果表明印染生产连续时间MILP调度模型的有效性,优化了车间生产资源的配置。     

A continuous-time formulation for refinery production scheduling problems involving operational transitions in mode switching

In the refinery scheduling, operational transitions in mode switching are of great significance to formulate dynamic nature of production and obtain efficient schedules. The discrete-time formulation meets two main challenges in modeling:discrete approximation of time and large size of mixed-integer linear problem (MILP). In this article, a continuous-time refinery scheduling model, which involves transitions of mode switching, is presented due to these challenges. To reduce the difficulty in solving large scale MILPs resulting from the sequencing constraints, the global event-based formulation is chosen. Both transition constraints and production transitions are introduced and the numbers of key variables and constraints in both of the discrete-time and continuous-time formulations are analyzed and compared. Three cases with different lengths of time horizons and different numbers of orders are studied to show the efficiency of the proposed model.     

An efficient MILP continuous-time formulation for short-term scheduling of multiproduct continuous facilities

This paper presents a new MILP mathematical formulation for the scheduling of resource-constrained multiproduct plants involving continuous processes. In such facilities, a sequence of continuous processing steps is usually carried out to produce a significant number of final products and required intermediates. In order to reduce equipment idle time due to unbalanced stage capacities, storage tanks are available for temporary inventory of intermediates. The problem goal is to maximize the plant economic output while satisfying specified minimum product requirements. The proposed approach relies on a continuous time domain representation that accounts for sequence-dependent changeover times and storage limitations without considering additional tasks. The MILP formulation was applied to a real-world manufacturing facility producing seven intermediates and fifteen final products. Compared with previous scheduling methodologies, the proposed approach yields a much simpler problem representation with a significant saving in 0–1 variables and sequencing constraints. Moreover, it provides a more realistic and profitable production schedule at lower computational cost.     

考虑不确定汽电需求的蒸汽动力系统优化设计

蒸汽动力系统优化设计不仅要保证系统全周期总费用最小,还要保证系统具有一定可操作性应对各种不确定变工况影响。本文提出了同时考虑汽电需求确定性多周期变化以及燃料、电力价格,汽电需求不确定性变化的蒸汽动力系统优化设计策略,专门提出不确定变化参数对优化目标及约束的影响以及数学表达,建立混合整数线性规划(MILP)优化模型进行求解,并应用于某石化企业蒸汽动力系统优化设计。实例设计结果表明,与按照传统策略设计结果相比,应用本文提出的考虑不确定参数的设计策略获得的优化方案,具体设计了针对不确定因素实现而对应的运行调度安排,降低年总费用,保证系统安全稳定运行,实现经济性和可操作性综合最优。     

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).     

Scheduling a multi-product pipeline network

Daily some millions barrels of oil are moved around the world in imports and exports and domestically within countries. While ships are the main mode for intercontinental transport, pipelines are the chief form of transcontinental transport, while regional and local transports is performed by trains and trucks. Despite high installation costs, pipelines are considered highly efficient as a mode for transporting large amounts of oil and oil products over long distances, because they offer lower operation costs, higher reliability rates, lower product loss rates, less environmental impact, and less susceptibility to adverse weather conditions than other modes. This study deals with a multi-product pipeline system that transports a set of oil products (diesel, gasoline and kerosene, for example), which have to be moved from points (operating areas) where they are produced or stored (refineries, terminals) to points where they are needed (other refineries, distribution centers, terminals, ports, customers) through a pipeline or set of pipelines.The present study contributes primarily by offering an efficient tool for the problem of scheduling multi-product pipeline networks. The methodology proposed takes the approach of discretizing both pipelines and planning horizon and combines an efficient MILP model with a post-processing heuristic. When compared with previous models, we propose a more efficient one in which the set of volumetric constraints is modeled in the form of knapsack cascading constraints and constraints on products in pipeline sections, which made for significantly improved performance in the experiments that were conducted. The proposed methodology thus constitutes an advance in terms of modeling the problem, making it feasible to solve problems increasingly close to the realities confronting oil industry operators.     

Optimal management of logistic activities in multi-site environments

The new emerging area of Enterprise Wide Optimization (EWO) has focused the attention in effectively solving the combined production/distribution scheduling problem. The importance of logistic activities performed in multi-site environments comes from the relative magnitude of the associated transportation costs and the good chance of getting large savings on such expenses. This paper first develops an exact MILP mathematical formulation for the multiple vehicle time-window-constrained pickup and delivery (MVPDPTW) problem. The approach is able to account for many-to-many transportation requests, pure pickup and delivery tasks, heterogeneous vehicles and multiple depots. Optimal solutions for a variety of benchmark problems with cluster/random distributions of pickup and delivery locations and limited sizes in terms of customer requests and vehicles have been discovered. However, the computational cost exponentially grows with the number of requests. For large-scale m-PDPTW problems, a local search improvement algorithm steadily providing a better solution through two evolutionary steps is also presented. A neighborhood structure around the starting solution is generated by first allowing multiple request exchanges among nearby trips and then permitting the reordering of nodes on every individual route. If a better set of routes is found, both steps are repeated until no improved solution is discovered. Compact MILP mathematical formulations for both sub-problems have been developed and solved through an efficient branch-and-bound algorithm. A significant number of large-scale m-PDPTW benchmark problems, some of them including up to 100 transportation requests, were successfully solved in reasonable CPU times.     

A discretization-based approach for the optimization of the multiperiod blend scheduling problem

In this paper, we introduce a new generalized multiperiod scheduling version of the pooling problem to represent time varying blending systems. A general nonconvex MINLP formulation of the problem is presented. The primary difficulties in solving this optimization problem are the presence of bilinear terms, as well as binary decision variables required to impose operational constraints. An illustrative example is presented to provide unique insight into the difficulties faced by conventional MINLP approaches to this problem, specifically in finding feasible solutions. Based on recent work, a new radix-based discretization scheme is developed with which the problem can be reformulated approximately as an MILP, which is incorporated in a heuristic procedure and in two rigorous global optimization methods, and requires much less computational time than existing global optimization solvers. Detailed computational results of each approach are presented on a set of examples, including a comparison with other global optimization solvers.     

Batch selection,assignment and sequencing in multi-stage multi-product processes

The scheduling of multi-product, multi-stage batch processes is industrially important because it allows us to utilize resources that are shared among competing products in an optimal manner. Previously proposed methods consider problems where the number and size of batches is known a priori. In many instances, however, the selection and sizing (batching) of batches is or should be an optimization decision. To address this class of problems we develop a novel mixed-integer linear programming (MILP) formulation that involves three levels of discrete decisions: selection of batches, assignment of batches to units and sequencing of batches in each unit. Continuous decision variables include sizing and timing of batches. We consider various objective functions: minimization of makespan, earliness, lateness and production cost, as well as maximization of profit, an objective not addressed by previous multi-stage scheduling methods. To enhance the solution of the proposed MILP model we propose symmetry breaking constraints, develop a preprocessing algorithm for the generation of constraints that reduce the number of feasible solutions, and fix sequencing variables based upon time window information. The model enables the optimization of batch selection, assignment and sequencing decisions simultaneously and is shown to yield solutions that are better than those obtained by existing sequential optimization methods.     

An improvement-based MILP optimization approach to complex AWS scheduling

The automated wet-etch station (AWS) is one of the most critical stages of a modern semiconductor manufacturing system (SMS), which has to simultaneously deal with many complex constraints and limited resources. Due to its inherent complexity, industrial-sized automated wet-etch station scheduling problems are rarely solved through full rigorous mathematical formulations. Decomposition techniques based on heuristic, meta-heuristics and simulation-based methods have been traditionally reported in literature to provide feasible solutions with reasonable CPU times.This work introduces an improvement MILP-based decomposition strategy that combines the benefits of a rigorous continuous-time MILP (mixed integer linear programming) formulation with the flexibility of heuristic procedures. The schedule generated provides enhanced solutions over time to challenging real-world automated wet etch station scheduling problems with moderate computational cost. This methodology was able to provide more than a 7% of improvement in comparison with the best results reported in literature for the most complex problem instances analyzed.     

Multi-period scheduling of a multi-stage multi-product bio-pharmaceutical process

There have been several works in the literature for scheduling of multi-product continuous processes with significant attention laid on short-term scheduling. This work presents a continuous-time model for multi-period scheduling of a multi-stage multi-product process from bio-pharmaceutical industry. The overall model is a mixed-integer linear programming (MILP) formulation based on state-task-network (STN) representation of the process using unit-specific event-based continuous-time representation. The proposed model is an extension of model by Shaik and Floudas (2007, Industrial & Engineering Chemistry Research, 46, 1764) with several new constraints to deal with additional features such as unit and sequence dependent changeovers, multiple intermediate due dates, handling of shelf-life and waste disposal, and penalties on backlogs and late deliveries. Improved tightening and sequencing constraints have been presented. The validity of the proposed model has been illustrated through an example from the literature.     

一种改进的顺序型多目的间歇工厂生产调度的MILP模型

分析了顺序型多目的工厂间歇生产的特点,建立了一种新的混合整数线性规划（MILP）模型.该模型以操作活动序列作为建模的依据,将整个间歇生产过程分解成若干个子系统.在对各子系统建模的基础上,实现了顺序型多目的工厂间歇调度的全局性优化.并通过算例验证了该模型求解结果的正确性和可行性.然后将新模型运用到更大规模的调度问题上,均求解出了有效的调度方案.     

Multi-week MILP scheduling for an ice cream processing facility

This paper presents a multi-week mixed integer linear programming (MILP) scheduling model for an ice cream processing facility. The ice cream processing is a typical complex food manufacturing process and a simplified version of this processing has been adapted to investigate scheduling problems in the literature. Most of these models only considered the production scheduling for a week. In this paper, multi-week production scheduling is considered. The problem has been implemented as an MILP model. The model has been tested on a set of cases from the literature, and its results were compared to the results of problems solved using hybrid MILP-heuristics methods in the literature. The inclusion of clean-up session, weekend break and semi-processed product from previous week were also assessed with two additional sets of experiments. The experiments result show that the proposed MILP is able to handle multi-week scheduling efficiently and effectively within a reasonable time limit.     

The heterogeneous vehicle routing and truck scheduling problem in a multi-door cross-dock system

Cross-docking is a logistics technique applied by many industrial firms to get substantial savings in two warehousing costly functions like storage and order picking. Incoming shipments are unloaded from inbound trucks on a cross-dock terminal with minimal storage space and directly transferred to outbound vehicles that carry them to their destinations. The major decisions at the operational level are the vehicle routing and scheduling, the dock door assignment and the truck scheduling at the cross-dock. Because such decisions are interdependent, all of them are simultaneously considered in the so-called vehicle routing problem with cross-docking (VRPCD). Previous contributions on VRPCD assume that pickup and delivery tasks are accomplished by a homogeneous vehicle fleet, and they mostly ignore the internal transportation of goods through the cross-dock. This work introduces a new rigorous mixed-integer linear programming (MILP) formulation for the VRPCD problem to determine the routing and scheduling of a mixed vehicle fleet, the dock door assignment, the truck docking sequence and the travel time required to move the goods to the assigned stack door all at once. To improve the computational efficiency of the branch-and-cut search, an approximate sweep-based model is developed by also considering a set of constraints mimicking the sweep algorithm for allocating nodes to vehicles. Numerous heterogeneous VRPCD examples involving up to 50 transportation requests and a heterogeneous fleet of 10 vehicles with three different capacities were successfully solved using the proposed approaches in acceptable CPU times.     

改进PSO算法在蒸汽动力系统多周期运行优化中的应用

为了满足石化企业工艺过程对蒸汽和电力不断变化的要求,实现企业降低成本、节能降耗的目的,必须保证蒸汽动力系统在最优的状态下运行。针对这一问题在以往研究的基础上提出了包括设备维护和启停费用的改进的混合整数线性规划模型,利用改进的PSO算法对其求解,并通过实例证明了利用该模型、使用改进的PSO算法能很快得到最优的方案,并节省了大量的运行成本。     

A rule-based genetic algorithm for the scheduling of single-stage multi-product batch plants with parallel units

This paper presents a heuristic rule-based genetic algorithm (GA) for large-size single-stage multi-product scheduling problems (SMSP) in batch plants with parallel units. SMSP have been widely studied by the researchers. Most of them used mixed-integer linear programming (MILP) formulation to solve the problems. With the problem size increasing, the computational effort of MILP increases greatly. Therefore, it is very difficult for MILP to obtain acceptable solutions to large-size problems within reasonable time. To solve large-size problems, the preferred method in industry is the use of scheduling rules. However, due to the constraints in SMSP, the simple rule-based method may not guarantee the feasibility and quality of the solution. In this study, a random search based on heuristic rules was proposed first. Through exploring a set of random solutions, better feasible solutions can be achieved. To improve the quality of the random solutions, a genetic algorithm-based on heuristic rules has been proposed. The heuristic rules play a very important role in cutting down the solution space and reducing the search time. Through comparative study, the proposed method demonstrates promising performance in solving large-size SMSP.