Two-Stage Production Planning Under Stochastic Demand:Case Study of Fertilizer Manufacturing

Agriculture is a key facilitator of economic prosperity and nourishes the huge global population.To achieve sustainable agriculture,several factors should be considered,such as increasing nutrient and water efficiency and/or improving soil health and quality.Using fertilizer is one of the fastest and easiest ways to improve the quality of nutrients inland and increase the effectiveness of crop yields.Fertilizer supplies most of the necessary nutrients for plants,and it is estimated that at least 30%-50%of crop yields is attributable to commercial fertilizer nutrient inputs.Fertilizer is always a major concern in achieving sustainable and efficient agriculture.Applying reasonable and customized fertilizerswill require a significant increase in the number of formulae,involving increasing costs and the accurate forecasting of the right time to apply the suitable formulae.An alternative solution is given by two-stage production planning under stochastic demand,which divides a planning schedule into two stages.The primary stage has non-existing demand information,the inputs of which are the proportion of raw materials needed for producing fertilizer products,the cost for purchasing materials,and the production cost.The total quantity of purchased material and produced products to be used in the blending process must be defined to meet as small as possible a paid cost.At the second stage,demand appears under multiple scenarios and their respective possibilities.This stage will provide a solution for each occurring scenario to achieve the best profit.The two-stage approach is presented in this paper,the mathematical model of which is based on linear integer programming.Considering the diversity of fertilizer types,themathematicalmodel can advise manufacturers about which products will generate as much as profit as possible.Specifically,two objectives are taken into account.First,the paper’s thesis focuses on minimizing overall system costs,e.g.,including inventory cost,purchasing cost,unit cost,and ordering cost at Stage 1.Second,the thesis pays attention tomaximizing total profit based on information from customer demand,as well as being informed regarding concerns about system cost at Stage 2.

Multiproduct and multistage integrated production planning model and algorithm based on an available production capacity network

This research attempts to devise a multistage and multiproduct short-term integrative production plan that can dynamically change based on the order priority and virtual occupancy for application in steel plants. Considering factors such as the delivery time, varietal compatibility between different products, production capacity of variety per hour, minimum or maximum batch size, and transfer time, we propose an available production capacity network with varietal compatibility and virtual occupancy for enhancing production plan implementation and quick adjustment in the case of dynamic production changes. Here available means the remaining production capacity after virtual occupancy.To quickly build an available production capacity network and increase the speed of algorithm solving, constraint selection and cutting methods with order priority were used for model solving. Finally, the genetic algorithm improved with local search was used to optimize the proposed production plan and significantly reduce the order delay rate. The validity of the proposed model and algorithm was numerically verified by simulating actual production practices. The simulation results demonstrate that the model and improved algorithm result in an effective production plan.

Production Planning of a Failure-Prone Manufacturing/Remanufacturing System with Production-Dependent Failure Rates

This paper deals with the production-dependent failure rates for a hybrid manufacturing/remanufacturing system subject to random failures and repairs. The failure rate of the manufacturing machine depends on its production rate, while the failure rate of the remanufacturing machine is constant. In the proposed model, the manufacturing machine is characterized by a higher production rate. The machines produce one type of final product and unmet demand is backlogged. At the expected end of their usage, products are collected from the market and kept in recoverable inventory for future remanufacturing, or disposed of. The objective of the system is to find the production rates of the manufacturing and the remanufacturing machines that would minimize a discounted overall cost consisting of serviceable inventory cost, backlog cost and holding cost for returns. A computational algorithm, based on numerical methods, is used for solving the optimality conditions obtained from the application of the stochastic dynamic programming approach. Finally, a numerical example and sensitivity analyses are presented to illustrate the usefulness of the proposed approach. Our results clearly show that the optimal control policy of the system is obtained when the failure rates of the machine depend on its production rate.

HEURISTIC MODELING FOR A DYNAMIC AND GOAL PROGRAMMING IN PRODUCTION PLANNING OF CONTINUOUS MANUFACTURING SYSTEMS

At the first sight it seems that advanced operation research is not used enough in continuous production systems as comparison with mass production, batch production and job shop systems, but really in a comprehensive evaluation the advanced operation research techniques can be used in continuous production systems in developing countries very widely, because of initial inadequate plant layout, stage by stage development of production lines, the purchase of second hand machineries from various countries, plurality of customers. A case of production system planning is proposed for a chemical company in which the above mentioned conditions are almost presented. The goals and constraints in this issue are as follows： （1） Minimizing deviation of customer＇s requirements. （2） Maximizing the profit. （3） Minimizing the frequencies of changes in formula production. （4） Minimizing the inventory of final products. （5） Balancing the production sections with regard to rate in production. （6） Limitation in inventory of raw material. The present situation is in such a way that various techniques such as goal programming, linear programming and dynamic programming can be used. But dynamic production programming issues are divided into two categories, at first one with limitation in production capacity and another with unlimited production capacity. For the first category, a systematic and acceptable solution has not been presented yet. Therefore an innovative method is used to convert the dynamic situation to a zero- one model. At last this issue is changed to a goal programming model with non-linear limitations with the use of GRG algorithm and that＇s how it is solved.

A Hybrid Programming Model for Optimal Production Planning under Demand Uncertainty in Refinery

生产在不确定性下面计划在植物宽的优化被看作最重要的问题之一。首先，在这篇文章，有一致分发假设的一个随机的编程模型为精炼厂生产在需求不确定性，然后与随机的编程合并线性编程模型的一个混合编程模型下面计划被开发由一个重量因素的被建议。随后，片明智的线性近似功能被导出并且适用在一致分发假设下面解决混合编程模型。当时，案例研究证明线性近似算法是有效的解决混合编程模型，与错误≤ 0 .5% 一起偏差 / 平均数≤ 2 0% 。模拟结果显示有一个适当重量因素(0.1-0.2 ) 的混合编程模型能有效地在需求不确定性下面改进最佳的运作的策略，完成比线性编程模型和随机的编程的更高的利润有大约 1.5% 和 0.4% 改进的分别地。

A Novel Close-loop Strategy for Integrating Process Operations of Fluidized Catalytic Cracking Unit with Production Planning Optimization

普通当模特儿的系统产生的生产计划模型不为进程操作包含限制，并且一个解决方案由这些模型优化被称为一个伪最佳的计划。伪最佳的计划不能为没有相应操作条件某时在实践被执行。以便决定一个实际上可行的最佳的计划和联合起来的使流体化的催化裂开的相应操作条件(FCCU ) ，新奇靠近环的综合策略包括一个伪最佳的计划的决心，操作 FCCU 的条件和计划模型的生产的修订寻找，在这篇文章被建议。在策略，一个概括基因算法(GA ) 结合了 FCCU 的一个顺序的过程模拟器被使用寻找实现 FCCU 的伪最佳的计划的操作条件并且作为一个最后的基因个人在 GA 搜索输出最佳的个人。当没有相应操作条件被发现时，最后的基因个人基于修正(FGIC ) 方法被介绍修订计划模型的生产，然后一个新伪最佳的生产计划是坚定的。上述步被重复直到一个实际上可行的最佳的计划和 FCCU 的相应操作条件被获得。靠近环的综合策略被二个盒子验证，并且策略在决定一个实际上执行的最佳的计划和 FCCU 的相应操作条件是有效的，这被显示。

Infeasibility Diagnosis on the Linear Programming Model of Production Planning in Refinery

In order to effectively diagnose the infeasible linear programming (LP) model of production planning in refinery, the article proposed three stages strategy based on constraints’ classification and infeasibility analysis. Generally, infeasibility sources involve structural inconsistencies and data errors, and the data errors are further classified intoⅠ, Ⅱ and Ⅲ. The three stages strategy are: (1) Check data when they are inputted to detect data error Ⅰ and repair them; (2) Inspect data whether they are accorded with material balance before solving the LP model to identify data error Ⅱ and repair them; (3) Find irreducible inconsistent system of infeasible LP model and give diagnosis information priority-ranked to recognize data error Ⅲ and structural inconsistencies. These stages could be automatically executed by computer, and the approach has been applied to diagnose the infeasible model well in our graphic I/O petro-chemical industry modeling system.

Genetic Algorithm Based Production Planning for Alternative Process Production

Production planning under flexible job shop environment is studied.A mathematic model is formulated to help improve alternative process production.This model,in which genetic algorithm is used,is expected to result in better production planning,hence towards the aim of minimizing production cost under the constraints of delivery time and other scheduling conditions.By means of this algorithm,all planning schemes which could meet all requirements of the constraints within the whole solution space are exhaustively searched so as to find the optimal one.Also,a case study is given in the end to support and validate this model.Our results show that genetic algorithm is capable of locating feasible process routes to reduce production cost for certain tasks.

Stochastic Programming For Order Allocation And Production Planning

Stochastic demand is an important factor that heavily affects production planning.It influences activities such as purchasing,manufacturing,and selling,and quick adaption is required.In production planning,for reasons such as reducing costs and obtaining supplier discounts,many decisions must be made in the initial stage when demand has not been realized.The effects of non-optimal decisions will propagate to later stages,which can lead to losses due to overstocks or out-of-stocks.To find the optimal solutions for the initial and later stage regarding demand realization,this study proposes a stochastic two-stage linear program-ming model for a multi-supplier,multi-material,and multi-product purchasing and production planning process.The objective function is the expected total cost after two stages,and the results include detailed plans for purchasing and production in each demand scenario.Small-scale problems are solved through a deterministic equivalent transformation technique.To solve the problems in the large scale,an algorithm combining metaheuristic and sample average approximation is suggested.This algorithm can be implemented in parallel to utilize the power of the solver.The algorithm based on the observation that if the remaining quantity of materials and number of units of products at the end of the initial stage are given,then the problems of the first and second stages can be decomposed.

Integration of real options into short-term mine planning and production scheduling

Commodity prices have fallen sharply due to the global financial crisis. This has adversely affected the viability of some mining projects, including leading to the possibility of bankruptcy for some companies. These price falls reflect uncertainties and risks associated with mining projects. In recent years, much work has been published related to the application of real options pricing theory to value life-of-mine plans in response to long term financial uncertainty and risk. However, there are uncertainties and risks associated with medium/short-term mining operations. Real options theory can also be applied to tactical decisions involving uncertainties and risks. This paper will investigate the application of real options in the mining industry and present a methodology developed at University of Queensland, Australia, for integrating real options into medium/short-term mine planning and production scheduling. A case study will demonstrate the validity and usefulness of the methodology and techniques developed.

Multi-Objective Production Planning Using Lexicographic Procedure

This paper presents a multi-objective production planning model for a factory operating under a multi-product, and multi-period environment using the lexicographic (pre-emptive) procedure. The model objectives are to maximize the profit, minimize the total cost, and maximize the Overall Service Level (OSL) of the customers. The system consists of three potential suppliers that serve the factory to serve three customers/distributors. The performance of the developed model is illustrated using a verification example. Discussion of the results proved the efficacy of the model. Also, the effect of the deviation percentages on the different objectives is discussed.

Optimized algorithm in mine production planning, mined material destination, and ultimate pit limit

在采矿工程经济中,矿山生产计划、开采材料目的地和最终开采极限(UPL)之间存在着整体的联系,而实际信息及其在采矿经济中产生的效应会加强这种联系,因此,建立优化算法来减少经济计算的误差是非常重要的。本文提出一种考虑重要设计参数和经济性的逻辑数学算法,该算法在不同的设计成分之间建立了一个优化的重复过程,并使其将矿山经济参数最大化,产生最大的矿石量和最高的安全度。该模型在截止品位、矿井设计和矿山规划之间建立了新的关系,并通过计算目标提供了最大的效益。结果表明:与以往的生产设计和生产方法相比,矿山生产的净现值提高了3%。

AGILITY INDEXES AND APPLICATION OF PRODUCTION PLANNING

The agility of production planning is defined as two characters： synchronization and flexibility. Measurement indexes for evaluating agility are then divided into two dimensions separately. Synchronization includes two horizontal indexes： order lead time ratio and demand fulfilling rate; Two vertical indexes： instruction-reaction cycle time and resource matching rate. Flexibility includes five indexes： scope flexibility, delivery flexibility, variety flexibility, capacity buffer, inventory buffer and modification flexibility. Quantitative formulas for each measurement index are constructed. One application is discussed to illustrate the feasibility and reasonability of the indexes.

Stability of Production Planning Problem with Fuzzy Parameters

The traditional production planning model based upon the famous linear programming formulation has been well known in the literature. The consideration of uncertainty in manufacturing systems supposes a great advance. Models for production planning which do not recognize the uncertainty can be expected to generate inferior planning decisions as compared to models that explicitly account the uncertainty. This paper deals with production planning problem with fuzzy parameters in both of the objective function and constraints. We have a planning problem to maximize revenues net of the production inventory and lost sales cost. The existing results concerning the qualitative and quantitative analysis of basic notions in parametric production planning problem with fuzzy parameters. These notions are the set of feasible parameters, the solvability set and the stability set of the first kind.

A Review of Quantitative Analysis (QA) in Production Planning Decisions Using the Linear Programming Model

The purpose of this paper was to examine the role of quantitative analysis in production planning decisions. This draws from the observed imperatives of quantitative analysis in business decisions and its capacity for predictability and enhanced decision making given the increasingly complex nature of the business environment. The paper therefore addressed the historical evolution of quantitative technique as an efficient and effective decision-making tool. The content of the paper addressed commonly applied quantitative technique in manufacturing firms today which is, linear programming and its subsequent impact on production planning decisions. The results based on a congruence of views revealed that the “best-fit” application of quantitative analysis models and tools can untangle the complexities of production and planning decision making process in order to achieve the organizational goal. This is, as literature also showed that there is obviously no consensus or integrated model that is capable of solving all managerial problem, different models such as the linear programming model have however been developed to cater for different problems as they arise. The workability or suitability of quantitative analysis is actually premised on its appropriate application. The paper recommends the application of quantitative analysis using linear programming in solving various resource allocation related issues in the primary production planning function of manufacturing firms.

Production Planning and Control of the Pipeline Assembly Enterprise under SCM

It is vital for pipeline assembly enterprise to respond to changing market needs quickly and keep its cost advantage. A production planning and control （PPC） model under supply chain management combining with operation characteristics of pipeline assembly enterprise was proposed. The present model can realize synchroni- zation in real-time response in production by establishing a win-win corporate model, classified regulation be- tween strategic parts and non-strategic parts, postponing the production of special modules and guaranteeing pro- duction at the bottleneck.

Production Planning Based on BOM Optimization

According to a prototype enterprise, a rulebased Bill of Materials （BOM） structure is designed in order to get optimal design and management of product BOM. The constraint rules and optional objects for product data structure optimization are considered by associating customer demands with product BOM. Furthermore, the functional model of production planning system for assembling enterprise is given based on customization and BOM optimization.

Studies on Production Planning of Dispersion Type U3Si2-Al Fuel in Plate-Type Fuel Elements for Nuclear Research Reactors

Several fuel plants that supply nuclear research reactors need to increase their production capacity in order to meet the growing demand for this kind of nuclear fuel. After the enlargement of the production capacity of such plants, there will be the need of managing the new production level. That level is usually the industrial one, which poses challenges to the managerial staff. Such challenges come from the fact that several of those plants operate today on a laboratorial basis and do not carry inventory. The change to the industrial production pace asks for new actions regarding planning and control. The production process based on the hydrolysis of UF6 is not a frequent production route for nuclear fuel. Production planning and control of the industrial level of fuel production on that production route is a new field of studies. The approach of the paper consists in the creation of a mathematical linear model for minimization of costs. We also carried out a sensitivity analysis of the model. The results help in minimizing costs in different production schemes and show the need of inventory. The mathematical model is dynamic, so that it issues better results if performed monthly. The management team will therefore have a clearer view of the costs and of the new, necessary production and inventory levels.

Liaohe Planning to Build One Million Tonsof Super-Heavy Oil Production Base

WiththepriceincreaseofPetroleumProductsintheinternationalmarketandthematurity'oftechnologyfortheproductionofsuper-heavyoil,LiaohehasestablishedaframeworkplanfortheconstructionofproductioncapacityforBlockDu-32.AproduchonbasewadanannualoutputofImillion...

Collaborative production planning between supply chain partners by Lagrangian relaxation

A collaborative planning framework based on the Lagrangian Relaxation was developed to coordinate and optimize the production planning of independent partners in multiple tier supply chains. Linking constraints and dependent demand constraints were added to the monolithic Multi-Level, multi-item Capacitated Lot Sizing Problem (MLCLSP). MLCLSP was Lagrangian relaxed and decomposed into facility-separable subproblems. Surrogate gradient algorithm was used to update Lagrangian multipliers, which coordinate decentralized decisions of the facilities. Production planning of independent partners could be appropriately coordinated and optimized by this framework without intruding their decisionities and private information. Experimental results show that the proposed coordination mechanism and procedure come close to optimal results as obtained by central coordination.