Integration of generative and evaluative models for production scheduling of lube oil plants in a petroleum refinery

A study was made on the existing practices of production planning, scheduling and prevailing constraints in the six plants of a lube oil section in a petroleum refinery. Based on the data collected from these plants, some generative and evaluative models were developed. The generative models developed were flow network optimisation (FNO) model and binary integer linear programming (BILP) model. The evaluative model developed was simulation. The optimal results obtained from the generative model were fed to the evaluative model to derive the measure of performance. This integration of generative and evaluative models offers an opportunity for better understanding of the subsystem and appropriate decision making.     

Application of fuzzy linear programming to aggregate production plan of a refinery industry in Taiwan

After the oil market in Taiwan has been opened to private enterprise, the oil refinery industries in Taiwan have not only entered a completely free market; but also faced the challenge from world competition. In such an environment, there exist varieties of uncertain factors, which have caused the failure of traditional production planning models. Therefore, in this study we develop a responsive and flexible production planning system to cope with uncertain manufacturing factors. On the basis of fuzzy set theory, the uncertain demand and cost are clarified, and a fuzzy linear programming model is proposed to find a maximal profit production strategy with degree of satisfaction. The proposed model has been applied to CPC Corporation, Taiwan. The results show that the developed model is able to provide useful information for developing profit-effective oil refinery strategies in an uncertain environment.     

Planning logistics operations in the oil industry

In this paper we apply stochastic programming modelling and solution techniques to planning problems for a consortium of oil companies. A multiperiod supply, transformation and distribution scheduling problem—the Depot and Refinery Optimization Problem (DROP)—is formulated for strategic or tactical level planning of the consortium's activities. This deterministic model is used as a basis for implementing a stochastic programming formulation with uncertainty in the product demands and spot supply costs (DROPS), whose solution process utilizes the deterministic equivalent linear programming problem. We employ our STOCHGEN general purpose stochastic problem generator to ‘recreate’ the decision (scenario) tree for the unfolding future as this deterministic equivalent. To project random demands for oil products at different spatial locations into the future and to generate random fluctuations in their future prices/costs a stochastic input data simulator is developed and calibrated to historical industry data. The models are written in the modelling language XPRESS-MP and solved by the XPRESS suite of linear programming solvers. From the viewpoint of implementation of large-scale stochastic programming models this study involves decisions in both space and time and careful revision of the original deterministic formulation. The first part of the paper treats the specification, generation and solution of the deterministic DROP model. The stochastic version of the model (DROPS) and its implementation are studied in detail in the second part and a number of related research questions and implications discussed.     

Integrating operations research in constraint programming

This paper presents constraint programming (CP) as a natural formalism for modelling problems, and as a flexible platform for solving them. CP has a range of techniques for handling constraints including several forms of propagation and tailored algorithms for global constraints. It also allows linear programming to be combined with propagation and novel and varied search techniques which can be easily expressed in CP. The paper describes how CP can be used to exploit linear programming within different kinds of hybrid algorithm. In particular it can enhance techniques such as Lagrangian relaxation, Benders decomposition and column generation.     

成品油调和配方优化研究

成品油调和是石油炼制过程中的重要环节,直接影响炼油企业的经济效益。本文以石化行业为背景,针对成品油调和配方优化问题进行了研究,在满足成品油质量指标约束的条件下,以最小化企业生产成本为目标,建立了混合整数规划模型,提出了基于遗传算法的有效求解策略,并根据某炼油厂的实际生产数据进行了仿真实验,计算结果反映了库存成本与启动成本之间的平衡关系,即:当单位库存成本不变,单位启动成本逐渐变大时,库存总成本随之增大,启动次数随之减少。反之,当单位启动成本不变,单位库存成本逐渐变大时,启动次数随之增大,库存总成本随之减少。     

A two-stage approach to multi-period allocation of savings among investment plans

This paper presents a two-stage multi-period decision model for allocation of the individual's savings into several investment plans. Although the U.S. economy is used as the background, the modelling methods are general enough to accommodate any tax law. The first stage of the model uses an asset-allocation method based on the single-index model. Because this method is static and does not provide for tax considerations and other constraints, it alone is not enough. The output of this optimal selection is used as exogenous parameters and controls for the second stage of the model which is an integer program. The IP includes fixed charges, statutory and budgetary constraints, a discount rate, and the risk level. We provide an example of this approach to illustrate how an individual can achieve his goals of terminal accumulations while maintaining the risk level, measured by the aggregate beta, he prefers. A linear programming relaxation of the IP model is utilized for sensitivity analysis to examine whether future adjustments in investment strategies are required. The model remains tractable enough for implementation by individuals who may not be experts in mathematical programming and financial planning.     

A clone-based graphical modeler and mathematical model generator for optimal production planning in process industries

This paper outlines a visually interactive graphical modeling approach for process type production systems, with hidden generation of complex optimization models for production planning. The proposed system lets the users build a graphical model of the production system with one-to-one clones of its production units through its interactive visual interface, accepts production-specific data for its components, and finally, internally generates and solves its mathematical programming model without any interaction from the user. This “clone-based” modeling approach allows the continued use of optimization models with minimal mathematical programming understanding, as generation of mathematical model by clones is hidden and automatic, therefore maintenance-free: Updating graphical production system models is enough for renewing internal optimization models. The concept is demonstrated in this paper with a linear programming prototype developed for a petroleum refinery.     

Computer-assisted Modelling and Analysis of Linear Programming Problems: Towards a Unified Framework

A framework for model formulation and analysis to support operationsand management of large-scale linear programs is developed fromthe combined capabilities of CAMPS and ANALYZE. Both the systemsare reviewed briefly and the interface which integrates thetwo systems is then described. The model formulation, matrixgeneration, and model management capability of CAMPS and thecomplementary model and solution analysis capability of ANALYZEare presented within a unified framework. Relevant generic functionsare highlighted, and an example is presented in detail to illustratethe level of integration achieved in the current prototype system.Some new results on discourse models and model management supportare given in a framework designed to move toward an ‘intelligent’system for linear programming modelling and analysis.     

A Partioning Technique for Leontief Type Linear Programming Production Models

This paper studies the application of linear programming to the class of production planning problems which maximise profit subject to constraints on interacting production processes which can be represented by a static Leontief model. The method partitions the matrices involved in the solution process which enables the matrices involved in the computational process to become smaller at each iteration. Preliminary computational results show that the partitioning technique is quite efficient in solving such problems and should prove to be very effective on large-scale problems.     

Linear polynomial constraints inferencing algorithm

This paper propose the inference mechanism for handling linear polynomial constraints called consistency checking algorithm based on the feasibility checking algorithm borrowed from linear programming. In contrast with other approaches, proposed algorithm can efficiently and coherented by linear polynomial forms. The developed algorithm is successfully applied to the symbolic simulation that offers a convenient means to conduct multiple, simultaneous exploration of model behaviors.     

Sensitivity analysis in linear programming: just be careful!

In this paper we review the topic of sensitivity analysis in linear programming. We describe the problems that may occur when using standard software and advocate a framework for performing complete sensitivity analysis. Three approaches can be incorporated within it: one using bases, an approach using the optimal partition and one using optimal values. We elucidate problems and solutions with an academic example and give results from an implementation of these approaches to a large practical linear programming model of an oil refinery. This shows that the approaches are viable and useful in practice.     

Linear programming on a micro computer: An application in refinery modelling

Given the complexity of refinery modelling, linear programming for this application has until now been developed essentially on mainframes. New developments in microcomputer LP software now allow us to handle real life problems. This paper will describe the process of a general refinery, and how a micro based model has been designed to study its economics.     

Multi-parallel work centers scheduling optimization with shared or dedicated resources in low-volume low-variety production systems

A new methodology for modeling large-scale scheduling problems in low-volume low-variety production systems is proposed through this paper. Such scheduling problems are constrained by limited time and resources, where each work center is assigned a unique statement of work, to be completed on-time with the budgeted number of resources. Products assembled in low-volume low-variety production systems are processed through a series of stations referred to as work centers, where varying levels and classifications of resources are deployed onto the product. Aircraft, heavy aero-structures, and heavy military equipment are examples of products assembled in low-volume low-variety production systems. To ensure products are delivered on-time and on-budget, it is crucial to execute to a detailed schedule, such that all precedence, resource, zonal, and other constraints and characteristics inherent in such production systems are successfully satisfied. Despite the criticality of detailed schedules in delivering products on-time and on-budget, limited research is reported on mixed-integer programming approaches for scheduling optimization of activities in low-volume low-variety production systems. The discrete-time linear mixed-integer mathematical programming model developed in this paper fills the gap in the current literature with a direct impact on the organizations’ service levels and bottom line. The proposed mathematical programming models are validated through a real-world case-study of the assembly process of a narrow body aircraft to ensure compatibility in the modeling of large-scale industrial problems.     

Chance constrained programming models for refinery short-term crude oil scheduling problem

The main objective of this work is to put forward chance constrained mixed-integer nonlinear stochastic and fuzzy programming models for refinery short-term crude oil scheduling problem under demands uncertainty of distillation units. The scheduling problem studied has characteristics of discrete events and continuous events coexistence, multistage, multiproduct, nonlinear, uncertainty and large scale. At first, the two models are transformed into their equivalent stochastic and fuzzy mixed-integer linear programming (MILP) models by using the method of Quesada and Grossmann [I. Quesada, I E. Grossmann, Global optimization of bilinear process networks with multicomponent flows, Comput. Chem. Eng. 19 (12) (1995) 1219–1242], respectively. After that, the stochastic equivalent model is converted into its deterministic MILP model through probabilistic theory. The fuzzy equivalent model is transformed into its crisp MILP model relies on the fuzzy theory presented by Liu and Iwamura [B.D. Liu, K. Iwamura, Chance constrained programming with fuzzy parameters, Fuzzy Sets Syst. 94 (2) (1998) 227–237] for the first time in this area. Finally, the two crisp MILP models are solved in LINGO 8.0 based on scheduling time discretization. A case study which has 267 continuous variables, 68 binary variables and 320 constraints is effectively solved with the solution approaches proposed.     

Formulating diets for growing pigs: economic and?environmental considerations

We look at the environmental impact of formulating diets for an animal production system, namely the case of growing pigs. The classic approach in animal production is to use a growth model based on the least-cost diet formulation. This optimal diet is generally established by linear programming. Such an approach can lead to adverse environmental effects in the form of nitrogen and phosphorus excretions. Multi-criteria (two and three criteria) models are proposed with the aim of addressing both economic and environmental considerations. We apply the models to two real-life contexts: Qu??bec (Canada) and France, and make some comparisons. We show that important reductions in nitrogen and phosphorus excretions can be achieved at relatively low costs in both contexts.     

A mathematical programming model and solution for scheduling production orders in Shanghai Baoshan Iron and Steel Complex

In this paper, we investigate the production order scheduling problem derived from the production of steel sheets in Shanghai Baoshan Iron and Steel Complex (Baosteel). A deterministic mixed integer programming (MIP) model for scheduling production orders on some critical and bottleneck operations in Baosteel is presented in which practical technological constraints have been considered. The objective is to determine the starting and ending times of production orders on corresponding operations under capacity constraints for minimizing the sum of weighted completion times of all orders. Due to large numbers of variables and constraints in the model, a decomposition solution methodology based on a synergistic combination of Lagrangian relaxation, linear programming and heuristics is developed. Unlike the commonly used method of relaxing capacity constraints, this methodology alternatively relaxes constraints coupling integer variables with continuous variables which are introduced to the objective function by Lagrangian multipliers. The Lagrangian relaxed problem can be decomposed into two sub-problems by separating continuous variables from integer ones. The sub-problem that relates to continuous variables is a linear programming problem which can be solved using standard software package OSL, while the other sub-problem is an integer programming problem which can be solved optimally by further decomposition. The subgradient optimization method is used to update Lagrangian multipliers. A production order scheduling simulation system for Baosteel is developed by embedding the above Lagrangian heuristics. Computational results for problems with up to 100 orders show that the proposed Lagrangian relaxation method is stable and can find good solutions within a reasonable time.     

Shortening cycle times in multi-product,capacitated production environments through quality level improvements and setup reduction

This paper addresses the issue of investing in reduced setup times and defect rates for a manufacturer of several products operating in a JIT environment. Production cycle times can be shortened by investing in setup time and defect rate reductions, respectively. The objective is to determine optimal levels of setup time and defect rate reductions along with the corresponding optimal levels of investments respectively, and the optimal production cycle time for each product. The problem is constrained by demand requirements, process improvement budget limitations, and manufacturing and warehousing capacity constraints. We consider the cases of product-specific quality improvements and joint-product quality improvements. A general nonlinear optimization models of these problems are formulated. A convex geometric programming approximation of these models is developed respectively, in order to solve them. The approximation can be made to any desired degree of accuracy. Our empirical findings provide insights into a number of managerial issues surrounding investment decisions in product-specific quality improvements and setup reductions due to a product redesign as well as in joint-product improvements due to a process redesign.     

Multi-product production planning: A goal programming approach

Cost minimization multi-product production problems with static production resource usage and internal product flow requirements have been solved by linear programming (LP) with input/output analysis. If the problem is complicated by interval resource estimates, interval linear programming (ILP) can be used. The solution of realistic problems by the above method is cumbersome. This paper suggests that linear goal programming (LGP) can be used to model a multi-product production system. LGP's unique modeling capabilities are used to solve a production planning problem with variable resource parameters. Input/output analysis is used to determine the technological coefficients for the goal constraints and is also used to derive an information sub-model that is used to reduce the number of variable resource goal constraints. Preliminary findings suggest that the LGP approach is more cost-efficient (in terms of CPU time) and in addition provides valuable information for aggregate planning.     

Developments in linear and integer programming

In this review we describe recent developments in linear and integer (linear) programming. For over 50 years Operational Research practitioners have made use of linear optimisation models to aid decision making and over this period the size of problems that can be solved has increased dramatically, the time required to solve problems has decreased substantially and the flexibility of modelling and solving systems has increased steadily. Large models are no longer confined to large computers, and the flexibility of optimisation systems embedded in other decision support tools has made on-line decision making using linear programming a reality (and using integer programming a possibility). The review focuses on recent developments in algorithms, software and applications and investigates some connections between linear optimisation and other technologies.