Hybrid genetic algorithms and line search method for industrial production planning with non-linear fitness function

Many engineering, science, information technology and management optimization problems can be considered as non-linear programming real-world problems where all or some of the parameters and variables involved are uncertain in nature. These can only be quantified using intelligent computational techniques such as evolutionary computation and fuzzy logic. The main objective of this research paper is to solve non-linear fuzzy optimization problem where the technological coefficient in the constraints involved are fuzzy numbers, which was represented by logistic membership functions using the hybrid evolutionary optimization approach. To explore the applicability of the present study, a numerical example is considered to determine the production planning for the decision variables and profit of the company.     

A production inventory model with fuzzy random demand and with flexibility and reliability considerations

The classical inventory control models assume that items are produced by perfectly reliable production process with a fixed set-up cost. While the reliability of the production process cannot be increased without a price, its set-up cost can be reduced with investment in flexibility improvement. In this paper, a production inventory model with flexibility and reliability (of production process) consideration is developed in an imprecise and uncertain mixed environment. The aim of this paper is to introduce demand as a fuzzy random variable in an imperfect production process. Here, the set-up cost and the reliability of the production process along with the production period are the decision variables. Due to fuzzy-randomness of the demand, expected average profit of the model is a fuzzy quantity and its graded mean integration value (GMIV) is optimized using unconstraint signomial geometric programming to determine optimal decision for the decision maker (DM). A numerical example has been considered to illustrate the model.     

带有专家信度的无人机任务分配最小风险问题

战场环境中不确定因素的存在往往导致确定条件下获得的无人机任务分配方案不可行或者非最优,而传统期望值模型通常适应于长期规划,难以考虑不确定变量波动对某次决策的影响.针对目标价值不确定的无人机任务分配问题,首先,基于不确定理论建立以信度函数为目标的最小风险模型;然后,通过引入不确定向量的两种假设,将上述模型转化为带有分式目标函数的优化问题;最后,定义以比率为特征的辅助函数,并推导其单调性等性质,提出求解最小风险解的比率一维搜索直接算法.实验结果表明,与期望值模型相比,所提出的最小风险模型及其算法能规避不确定变量标准差较大的侦察目标点,并可通过调整预设收益获得多种不同信度水平的供选择方案.     

Robust capacitated facility location model for acquisitions under uncertainty

We study a new robust formulation for strategic location and capacity planning considering potential company acquisitions under uncertainty. Long-term logistics network planning is among the most difficult decisions for supply-chain managers. While costs, demands, etc. may be known or estimated well for the short-term, their future development is uncertain and difficult to predict.A new model formulation for the robust capacitated facility location problem is presented to cope with uncertainty in planning. Minimizing the expectation of the relative regrets across scenarios over multiple periods is the objective. It is achieved by dynamically assigning multi-level production allocations, locations and capacity adjustments for uncertain parameter development over time. Considering acquisitions for profit maximization and its supply-chain impact is new as well as the simultaneous decision of capacity adjustment and facility location over time. The solution of the novel robust formulation provides a single setup where good results can be achieved for any realized scenario. Hence, the solution may not be optimal for one particular scenario but may be good, i.e. the highest expected profit to gain, for any highly probable future realization. We show that robust mixed-integer linear programming model achieves superior results to the deterministic configurations in exhaustive computational tests. This dynamic robust formulation allows the supply-chain to favorably adapt to acquisitions and uncertain developments of revenue, demand and costs and hence reduces the potential negative impacts of uncertainty on supply-chain operations.     

在供应链决策中的多阶生产规划支持模式研究

以液晶显示器(TFT-LCD)制造业为例，对供应链中多阶生产规划问题进行了研究。运用混合整数线性规划，以企业整体获利最大为目标，考虑材料成本随时间的变化以及库存对资金的占用和市场需求量、需求价格的变动，对工厂生产做出安排，给出不同时段的库存状态，由此开发TFT-LCD产业多阶生产规划决策支持系统，为生产安排提供决策依据。通过在TFT-LCD厂的应用，证明了该系统的实 用性。     

Solution of fuzzy integrated production and marketing planning based on extension principle

The integration of production and marketing planning is crucial in practice for increasing a firm’s profit. However, the conventional inventory models determine the selling price and demand quantity for a retailer’s maximal profit with exactly known parameters. When the demand quantity, unit cost, and production rate are represented as fuzzy numbers, the profit calculated from the model should be fuzzy as well. Unlike previous studies, this paper develops a solution method to find the fuzzy profit of the integrated production and marketing planning problem when the demand quantity, unit cost, and production rate are represented as fuzzy numbers. Based on Zadeh’s extension principle, we transform the problem into a pair of two-level mathematical programming models to calculate the lower bound and upper bound of the fuzzy profit. According to the duality theorem of geometric programming technique, the two-level mathematical program is transformed into the one-level conventional geometric program to solve. At a specific α-level, we can derive the global optimum solutions for the lower and upper bounds of the fuzzy profit by applying well-developed theories of geometric programming. Examples are given to illustrate the whole idea proposed in this paper.     

Solution of fuzzy integrated production and marketing planning based on extension principle

The integration of production and marketing planning is crucial in practice for increasing a firm’s profit. However, the conventional inventory models determine the selling price and demand quantity for a retailer’s maximal profit with exactly known parameters. When the demand quantity, unit cost, and production rate are represented as fuzzy numbers, the profit calculated from the model should be fuzzy as well. Unlike previous studies, this paper develops a solution method to find the fuzzy profit of the integrated production and marketing planning problem when the demand quantity, unit cost, and production rate are represented as fuzzy numbers. Based on Zadeh’s extension principle, we transform the problem into a pair of two-level mathematical programming models to calculate the lower bound and upper bound of the fuzzy profit. According to the duality theorem of geometric programming technique, the two-level mathematical program is transformed into the one-level conventional geometric program to solve. At a specific α-level, we can derive the global optimum solutions for the lower and upper bounds of the fuzzy profit by applying well-developed theories of geometric programming. Examples are given to illustrate the whole idea proposed in this paper.     

Pricing and production lot-size/scheduling with finite capacity for a deteriorating item over a finite horizon

Although the lately evolved manufacturing technologies such as enterprise resource planning (ERP) provide a unified platform for managing and integrating core business processes within a firm, the decision-making between marketing and production planning still remains rather disjoint. It is due in large parts to the inherent weaknesses of ERP such as the fixed and static parameter settings and uncapacitated assumption. To rectify these drawbacks, we propose a decision model that solves optimally the production lot-size/scheduling problem taking into account the dynamic aspects of customer's demand as well as the restriction of finite capacity in a plant. More specifically, we consider a single product that is subject to continuous decay, faces a price-dependent and time-varying demand, and time-varying deteriorating rate, production rate, and variable production cost, with the objective of maximizing the profit stream over multi-period planning horizon. We propose both coordinated and decentralized decision-making policies that drive the solution of the multivariate maximization problem. Both policies are formulated as dynamic programming models and solved by numerical search techniques. In our numerical experiments, the solution procedure is demonstrated, comparative study is conducted, and sensitivity analysis is carried out with respect to major parameters. The numerical result shows that the solution generated by the coordinated policy outperforms that by the decentralized policy in maximizing net profit and many other quantifiable measures such as minimizing inventory investment and storage capacity.Scope and purposeWe consider a manufacturing firm who produces and sells a single product that is subjected to continuous decay over a lifetime, faces a price-dependent and time-varying demand function, shortages are allowed and a completely backlogged, and has the objective of determining price and production lot-size/scheduling so as to maximize the total profit stream over multi-period planning horizon. We develop a tactical-level decision model that solves the production scheduling problem taking into account the dynamic nature of customer's demand which is partially controllable through pricing schemes. As analogous to the sales and operations planning, the proposed scheme can be used as a coordination center of the APS system within a generic enterprise resource planning framework which integrates and coordinates distinct functions within a firm.This paper differs from the existing works in several ways. First, we propose a dynamic version of the joint pricing and lot-size/scheduling problem taking into account the capacitated constraint. Second, several key factors being considered in the model, such as the demand rate, deteriorating rate, production rate, and variable production cost are assumed time-varying that reflect the dynamic nature of the market and the learning effect of the production system. A third difference between the past research and ours is that the price can be adjusted upward or downward in our model, making the proposed pricing policy more responsive to the structural change in demand or supply.     

服务水平约束下基于可调节鲁棒优化的固定比例生产与库存计划模型

在不确定需求环境下,研究由原材料供应商、制造商和客户组成的三级供应链中,具有固定比例生产系统的制造商多周期生产与库存计划问题.采用区间不确定集描述市场需求不确定性,并利用联合机会约束刻画制造商的服务水平要求,在线性决策规则下建立带有联合机会约束的固定比例生产系统生产与库存仿射可调节鲁棒优化模型.进一步,将所建模型等价转换为易于求解的线性规划问题.考虑到不确定扰动系数在模型鲁棒性与解的保守性之间的调节作用,给出能够有效提高具有固定比例生产系统的制造商利润并同时满足预设服务水平的不确定扰动系数优化算法.数值算例表明,基于所提出模型获得的运作方案能够有效应对供需平衡程度的变化,并且能以较高利润满足预设服务水平要求.     

Fuzzy Production Planning and its Application to Decision Making

This paper presents new methods for solving a production-planning problem. First the modified s-curve membership function as a methodology is constructed. Then fuzzy production planning problems with vagueness parameters alpha and fuzzy objective coefficients, fuzzy technical coefficients and fuzzy resource variables are outlined. The objective of this paper is to find a satisfactory solution for optimal profit in which vagueness is playing major factor in selecting the solution. Finally a practical application of decision-making in production planning is illustrated.     

Uncertain project scheduling problem with resource constraints

Project scheduling problem is to make a schedule for allocating the loans to a project such that the total cost and the completion time of the project are balanced under some constraints. This paper presents an uncertain project scheduling problem, of which both the duration times and the resources allocation times are uncertain variables. An uncertain programming model with multiple objectives is obtained, whose first objective is to minimize the total cost, and second objective is to minimize the overtime. Genetic algorithm is employed to solve the proposed uncertain project scheduling model, and its efficiency is illustrated by a numerical experiment.     

Minimum risk criterion for uncertain production planning problems

This paper considers a new class of multi-product source and multi-period fuzzy random production planning problems with minimum risk and service levels where both the demands and the production costs are assumed to be uncertain and characterized as fuzzy random variables with known distributions. The proposed problems are formulated as a fuzzy random production planning (FRPP) model by maximizing the mean chance of the total costs less than a given allowable investment level. Because the exact value of the objective function for a given decision variable cannot be easily obtained, we adopt an approximation approach (AA) to evaluate the objective value and then discuss the convergence of the AA, including the convergence of the objective value, the convergence of the optimal solutions and the convergence of the optimal value. Since the approximating multi-product source multi-period FRPP model is neither linear nor convex, an approximation-based hybrid monkey algorithm (MA) which combines the AA, stochastic simulation (SS), neural network (NN) and MA is designed to solve the proposed model. Finally, numerical examples are provided to illustrate the effectiveness of the hybrid monkey algorithm.     

Robust supply chain design under uncertain demand in agile manufacturing

This paper considers a supply chain design problem for a new market opportunity with uncertain demand in an agile manufacturing setting. We consider the integrated optimization of logistics and production costs associated with the supply chain members. These problems routinely occur in a wide variety of industries including semiconductor manufacturing, multi-tier automotive supply chains, and consumer appliances to name a few. There are two types of decision variables: binary variables for selection of companies to form the supply chain and continuous variables associated with production planning. A scenario approach is used to handle the uncertainty of demand. The formulation is a robust optimization model with three components in the objective function: expected total costs, cost variability due to demand uncertainty, and expected penalty for demand unmet at the end of the planning horizon. The increase of computational time with the numbers of echelons and members per echelon necessitates a heuristic. A heuristic based on a k-shortest path algorithm is developed by using a surrogate distance to denote the effectiveness of each member in the supply chain. The heuristic can find an optimal solution very quickly in some small- and medium-size cases. For large problems, a “good” solution with a small gap relative to our lower bound is obtained in a short computational time.     

An operational optimization procedure for production scheduling

The methodology takes a sufficiently long time horizon and breaks the problem into two subproblems. The first subproblem is the long range planning model and the second the short run production scheduling model. The long range model is essentially a resource constrained model and has a linear programming formulation with a profit maximization objective function. The long range plan fixes the discretionary marketing variables, such as the selection of product line, and the timing and extent of promotional sales. It estimates manpower requirements and establishes the raw material procurement plans. Lagrange multipliers obtained in the long range model are then used in the short run production scheduling model. The scheduling algorithm, having a Lagrangian function for an objective, is the solution to an unconstrained maximization problem. This then reduces to one of sequential allocation of production facilities to products. The algorithm is being applied on a problem with five production lines, 126 products, 26 time periods and 32 raw material constraints.     

A goal programming model for aggregate production planning with resource utilization constraint

This paper addresses the aggregate production planning problem with different operational constraints, including production capacity, workforce level, factory locations, machine utilization, storage space and other resource limitations. Three production plants in North America and one in China are considered simultaneously. A pre-emptive goal programming model is developed to maximize profit, minimize repairing cost and maximize machine utilization of the Chinese production plant hierarchically. A set of data from a surface and materials science company is used to test the effectiveness and the efficiency of the proposed model. Results illustrate the flexibility and the robustness of the proposed model by adjusting goal priorities with respect to importance of each objective and the aspiration level with respect to desired target values.     

Fuzzy-genetic approach to aggregate production-distribution planning in supply chain management

Aggregate production-distribution planning (APDP) is one of the most important activities in supply chain management (SCM). When solving the problem of APDP, we are usually faced with uncertain market demands and capacities in production environment, imprecise process times, and other factors introducing inherent uncertainty to the solution. Using deterministic and stochastic models in such conditions may not lead to fully satisfactory results. Using fuzzy models allows us to remove this drawback. It also facilitates the inclusion of expert knowledge. However, the majority of existing fuzzy models deal only with separate aggregate production planning without taking into account the interrelated nature of production and distribution systems. This limited approach often leads to inadequate results. An integration of the two interconnected processes within a single production-distribution model would allow better planning and management. Due to the need for a joint general strategic plan for production and distribution and vague planning data, in this paper we develop a fuzzy integrated multi-period and multi-product production and distribution model in supply chain. The model is formulated in terms of fuzzy programming and the solution is provided by genetic optimization (genetic algorithm). The use of the interactive aggregate production-distribution planning procedure developed on the basis of the proposed fuzzy integrated model with fuzzy objective function and soft constraints allows sound trade-off between the maximization of profit and fillrate. The experimental results demonstrate high efficiency of the proposed method.     

A multi-plant production planning model considering non- repeated setup and aperiodic shipment

A new model for multi-plant production planning is developed. As the important actual features of some manufacturers, non-repeated setup and aperiodic shipment are appropriately introduced into the multi-plant production planning model and the corresponding constraints are accurately linearized. The new model is also applicable in the case of periodic shipment or backorder prohibition. Its effectiveness is examined by an instance which simulates many real characteristics. The experimental results indicate that the new model achieves the optimal profit. The sensitivity of unit setup cost and unit shipment cost is analyzed. The significance of backorder and the limitation of shipment at a time are discussed in detail.     

A decision support system for strategic planning in large-scale marketing channels: An example in the tile industry

This paper presents a decision support system for strategic planning in marketing channels. A dynamic model of the marketing channel is employed which comprises manufacturer and retailer levels. Decision making is achieved through a game theoretical inference mechanism in which each player (manufacturer/retailer) optimises for a long-term profit maximisation objective. Both historical data and managerial expertise are used for the parameterisation of the system's knowledge base. The decision support system provides a forecast of profit and sales and computes pricing and shelf space allocation strategies that maximise long-term profit. It offers facilities such as the study of coalitions, long-term decision-making in all phases of a product's life cycle, the impact of pricing, allocation strategies, production expansion, cost regulation, and others. The operationality of the system is illustrated in decision-making situations in the tile industry.     

A multi-objective optimization approach for integrated production planning under interval uncertainties in the steel industry

This paper investigates one of the key decision-making problems referring to the integrated production planning (IPP) for the steelmaking continuous casting-hot rolling (SCC-HR) process in the steel industry. The complexities of the practical IPP problem are mainly reflected in three aspects: large-scale decision variables; multiple objectives and interval-valued uncertain parameters. To deal with the difficulty of large-scale decision variables, we introduce a new concept named “order-set” for modeling. In addition, considering the multiple objectives and uncertainties of the given IPP problem, we construct a multi-objective optimization model with interval-valued objective functions to optimize the throughput of each process, the hot charge ratio of slabs, the utilization rate of tundishes and the additional cost of technical operations. Furthermore, we propose a novel approach based on a modified interval multi-objective optimization evolutionary algorithm (MI-MOEA) to solve the problem. The proposed model and algorithm were tested with daily production data from an iron and steel company in China. Computational experiments demonstrate that the proposed method generates quite effective and practical solutions within a short time. Based on the IPP model and MI-MOEA, an IPP system has been developed and implemented in the company.     

Production scheduling and vehicle routing with time windows for perishable food products

We propose a nonlinear mathematical model to consider production scheduling and vehicle routing with time windows for perishable food products in the same framework. The demands at retailers are assumed stochastic and perishable goods will deteriorate once they were produced. Thus the revenue of the supplier is uncertain and depends on the value and the transaction quantity of perishable products when they are carried to retailers. The objective of this model is to maximize the expected total profit of the supplier. The optimal production quantities, the time to start producing and the vehicle routes can be determined in the model simultaneously. Furthermore, we elaborate a solution algorithm composed of the constrained Nelder–Mead method and a heuristic for the vehicle routing with time windows to solve the complex problem. Computational results indicate our algorithm is effective and efficient.