基于可信性理论的生产计划期望值模型

基于可信性理论,提出一类新的模糊生产计划期望值模型.然后,讨论这个模糊生产计划模型的基本性质.最后,利用这个模糊模型的基本性质我们可以把模糊生产计划期望值模型转化为一个线性规划模型并且设计相应的算法求解模糊生产计划问题的一个数值例子.     

Long term planning of a major national sector using a linear programming model

This article discusses a linear programming model for the long term planning of the Turkish iron and steel industry. Iron and steel industry is a complicated industry. It is rich in terms of products and production technologies, and has a large transportation problem associated with it. The model is formulated as a cost minimization problem and is solved in terms of several scenarios, each representing a different strategy for capacity expansion, using a mathematical programming package.     

Production planning under uncertainty in textile manufacturing

Textile manufacturing consists of yarn production, fabric formation, and finishing and dyeing stages. The subject of this paper is the yarn production planning problem, although the approach is directly applicable to the fabric production planning problem due to similarities in the respective models. Our experience at an international textile manufacturer indicates that demand uncertainty is a major challenge in developing yarn production plans. We develop a stochastic programming model that explicitly includes uncertainty in the form of discrete demand scenarios. This results in a large-scale mixed integer model that is difficult to solve with off-the-shelf commercial solvers. We develop a two-step preprocessing algorithm that improves the linear programming relaxation of the model and reduces its size, consequently improving the computational requirements. We illustrate the benefits of a stochastic programming approach over a deterministic model and share our initial application experience.     

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.     

Integrated production scheduling and distribution planning in dairy supply chain by hybrid modelling

In this paper we address the production scheduling and distribution planning problem in a yoghurt production line of the multi-product dairy plants. A mixed integer linear programming model is developed for the considered problem. The objective function aims to maximize the benefit by considering the shelf life dependent pricing component and costs such as processing, setup, storage, overtime, backlogging, and transportation costs. Key features of the model include sequence dependent setup times, minimum and maximum lot sizes, overtime, shelf life requirements, machine speeds, dedicated production lines, typically arising in the dairy industry. The model obtains the optimal production plan for each product type, on each production line, in each period together with the delivery plan. The hybrid modelling approach is adopted to explore the dynamic behavior of the real world system. In the hybrid approach, operation time is considered as a dynamic factor and it is adjusted by the results of the simulation and optimization model iteratively. Thus, more realistic solutions are obtained for the scheduling problem in yoghurt industry by using the iterative hybrid optimization-simulation procedure. The efficiency and applicability of the proposed model and approach are demonstrated in a case study for a leading dairy manufacturing company in Turkey.     

VMI策略下的综合生产计划研究

本重点研究了在供应链环境下，基于供应商管理客户库存(VMI)策略的供应商综合生产计划问题。模型综合考虑了供应链的存储费用、缺货损失和生产费用，提出供应链总成本最小目标模型，并采用搜索法结合线性规划给出了算例求解和分析结论。     

An Interactive Production Planning System in the Chemical Industry

This paper offers an example of a practical production planning system as used routinely by BP Chemicals Ltd. It is based on the interactive control of a linear programming model embedded in a system for data collection and report production. The model solves a "product mix" type of problem with a multi-criteria objective function.     

A lexicographic approach to bi-objective scheduling of single-period orders in make-to-order manufacturing

This paper presents a lexicographic approach and integer programming formulations for a dual-objective, long-term production scheduling in make-to-order manufacturing environment. The problem objective is to assign single-period customer orders for various product types to planning periods to complete all the orders with minimum number of tardy orders as a primary criterion and to level the aggregate production or the total capacity utilization over a planning horizon as a secondary criterion. Each order must be completed during one planning period. The basic integer programming formulation has been strengthened by the addition of some cutting constraints derived by relating the demand on required capacity to available capacity for each subset of orders with the same due date. The approach has been applied to optimize production schedules in a flexible flowshop made up of several processing stages in series, with identical, parallel machines, and an output buffer of limited capacity for holding completed products before delivery to the customers. Numerical examples modeled after a real-world make-to-order flexible assembly line in the electronics industry are provided and some computational results are reported.     

Capacity planning with working time accounts in services

This paper presents, formalizes and classifies working time accounts (WTAs), a means of achieving flexible production capacity through the flexible organization of working time. We propose linear programming models to plan working time, using WTA, at companies in the service industry. A computational experiment shows that the models can be solved for any capacity planning problems of reasonable size.     

活动长度有限制的多工序批量加工生产计划研究

当前的化工制造中,有很多工厂使用柔性制造设备,并采用批生产模式来组织生产.由于对设备进行准备和清理的成本比较大,加工的排序一般采用多批次加工同一种产品的活动（campaign）模式.在实际的生产中,由于需要保证产品质量和减少库存,应该考虑限制活动的最大长度.本文针对活动长度有限制的多工序批量加工问题进行研究,利用状态-任务-网络概念和层级模型方法,提出了修正的活动计划模型.该模型是基于混合整数线性规划模型,并且以供应网络内总生产成本和物流成本最小化作为目标函数.最后用一个算例来说明所构建模型的有效性.     

Uncertainty and Investment in Electricity Generation with an Application to the Case of Hydro-Québec

The electricity industry is undergoing a substantial process of restructuring, with an emphasis on the introduction of competition in the generation sector. Traditional planning methods are not necessarily appropriate for this new environment. This paper extends a previously developed linear programming model to the problem of optimal expansion planning in the face of uncertainty. The model explicitly accounts for equipment availability and load duration curves in selecting optimal investment. The use of the model is illustrated with a simple 2-region problem calibrated with data from Hydro-Québec and the northeastern United States that suggests how the LP model can help decision makers.     

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.     

Goal Programming and Agricultural Planning

Goal Programming is similar in structure to linear programming, but offers a more flexible approach to planning problems by allowing a number of goals which are not necessarily compatible to be taken into account, simultaneously. The use of linear programming in farm planning is reviewed briefly. Consideration is given to published evidence of the goals of farmers, and ways in which these goals can be represented. A goal programming model of a 600 acre mixed farm is described and evaluated. Advantages and shortcomings of goal programming in relation to linear programming are considered. It is found that goal programming can be used as a means of generating a range of possible solutions to the planning problem.     

A stochastic linear programming approach to hierarchical production planning

This paper examines production planning decisions. The process is formulated as a hierarchical production planning (HPP) model under uncertain demand. A review of HPP articles indicates that while current models do consider uncertainty as a part of their solution methods, a deficiency persists since these models fail to incorporate the uncertain demand explicitly in the formulation of the problem. A stochastic linear programming model (SLP) is proposed to better reflect reality and to provide a superior solution. The model remains computationally tractable despite the precise incorporation of uncertainty and the imposition of penalties when constraints are violated. A problem is introduced which illustrates the superiority of the proposed model over those currently being applied.     

An interval approach based on expectation optimization for fuzzy random bilevel linear programming problems

This paper considers a class of bilevel linear programming problems in which the coefficients of both objective functions are fuzzy random variables. The main idea of this paper is to introduce the Pareto optimal solution in a multi-objective bilevel programming problem as a solution for a fuzzy random bilevel programming problem. To this end, a stochastic interval bilevel linear programming problem is first introduced in terms of α-cuts of fuzzy random variables. On the basis of an order relation of interval numbers and the expectation optimization model, the stochastic interval bilevel linear programming problem can be transformed into a multi-objective bilevel programming problem which is solved by means of weighted linear combination technique. In order to compare different optimal solutions depending on different cuts, two criterions are given to provide the preferable optimal solutions for the upper and lower level decision makers respectively. Finally, a production planning problem is given to demonstrate the feasibility of the proposed approach.     

An Application of Branch and Cut to Open Pit Mine Scheduling

The economic viability of the modern day mine is highly dependent upon careful planning and management. Declining trends in average ore grades, increasing mining costs and environmental considerations will ensure that this situation will remain in the foreseeable future. The operation and management of a large open pit mine having a life of several years is an enormous and complex task. Though a number of optimization techniques have been successfully applied to resolve some important problems, the problem of determining an optimal production schedule over the life of the deposit is still very much unresolved. In this paper we will critically examine the techniques that are being used in the mining industry for production scheduling indicating their limitations. In addition, we present a mixed integer linear programming model for the scheduling problems along with a Branch and Cut solution strategy. Computational results for practical sized problems are discussed.     

Scheduling of brand production and shipping within a sugar supply chain

The Australian sugar industry exports about 90% of its five million tonne annual sugar production on the open market to customers in several countries, who request various brands of raw sugar. In planning at this interface of the sugar supply chain, an objective is to schedule the brands of sugar each mill produces throughout the annual harvest season, along with the ports that each ship loads at, to minimize total costs of sugar production and shipping. The complexity of such planning for the sugar industry has been overcome through the development and solution of a mixed-integer programming model to perform the task. The model is used as an annual planning tool to obtain a base schedule, as well as a rescheduling tool to revise the plan during the year as mill production rates and shipments change. Using the Australian sugar industry as a case study, this paper focuses on the mathematical model and solution using two known meta-heuristics based on local search. Using the 2002/2003 and 2003/2004 financial years, a comparison is made between the schedules produced in practice using manual methods and those using the model, which show a total potential cost savings of up to AU$4.0?M for the 2 years.     

An integrated optimization model for managing the global value chain of a chemical commodities manufacturer

The realization of supply chain management concepts goes along with the introduction of comprehensive software systems for supporting decisions at the strategic, tactical, and operational planning level. Moreover, in industry the focus has shifted from a pure logistics-oriented view towards the integration of pricing and revenue issues into cross-functional value chain planning models. This paper presents a practical decision support tool for global value chain planning in the production of chemical commodities. The proposed linear optimization model consists of various modules that reflect sales, distribution, production, and procurement activities within a company-internal value chain. The objective of the model is to maximize profit by coordinating all activities within the supply chain. The model formulation is related to a real industry case. It is shown how the model can be used to support decision making from sales to procurement by volume and value.     

Stochastic multi-site supply chain planning in textile and apparel industry under demand and price uncertainties with risk aversion

A multi-product, multi-period, multi-site supply chain production and transportation planning problem, in the textile and apparel industry, under demand and price uncertainties is considered in this paper. The problem is formulated using a two-stage stochastic programming model taking into account the production amount, the inventory and backorder levels as well as the amounts of products to be transported between the different plants and customers in each period. Risk management is addressed by incorporating a risk measure into the stochastic programming model as a second objective function, which leads to a multi-objective optimization model. The objectives aim to simultaneously maximize the expected net profit and minimize the financial risk measured. Two risk measures are compared: the conditional-value-at-risk and the downside risk. As the considered objective functions conflict with each other’s, the problem solution is a front of Pareto optimal robust alternatives, which represents the trade-off among the different objective functions. A case study using real data from textile and apparel industry in Tunisia is presented to illustrate the effectiveness of the proposed model and the robustness of the obtained solutions.     

Development of a new approach for deterministic supply chain network design

This paper proposes a mixed integer linear programming model and solution algorithm for solving supply chain network design problems in deterministic, multi-commodity, single-period contexts. The strategic level of supply chain planning and tactical level planning of supply chain are aggregated to propose an integrated model. The model integrates location and capacity choices for suppliers, plants and warehouses selection, product range assignment and production flows. The open-or-close decisions for the facilities are binary decision variables and the production and transportation flow decisions are continuous decision variables. Consequently, this problem is a binary mixed integer linear programming problem. In this paper, a modified version of Benders’ decomposition is proposed to solve the model. The most difficulty associated with the Benders’ decomposition is the solution of master problem, as in many real-life problems the model will be NP-hard and very time consuming. In the proposed procedure, the master problem will be developed using the surrogate constraints. We show that the main constraints of the master problem can be replaced by the strongest surrogate constraint. The generated problem with the strongest surrogate constraint is a valid relaxation of the main problem. Furthermore, a near-optimal initial solution is generated for a reduction in the number of iterations.