A just-in-time three-level integrated manufacturing system for linearly time-varying demand process

This paper considers a just-in-time (JIT) manufacturing system in which a single manufacturer procures raw materials from a single supplier, process them to produce finished products, and then deliver the products to a single-buyer. The customer demand rate is assumed to be linearly decreasing time-varying. In the JIT system, in order to minimize the suppliers as well as the buyers holding costs, the supply of raw materials and the delivery of finished products are made in small quantities. In this case, both the supply and the delivery may require multiple installments for a single production lot. We develop a mathematical model for this problem, propose a simple methodology for solving the model, and illustrate the effectiveness of the method with numerical examples.     

Multi-vendor integrated procurement-production system under shared transportation and just-in-time delivery system

Just-in-time (JIT) procurement is one of the important elements of lean production system. Successful implementation of JIT needs vendor-manufacturer cooperation on small lot size delivery and inbound logistics cost reduction. Unlike the most recent literature focusing on single-vendor and single-buyer integrated inventory systems, this paper studies a multi-vendor integrated procurement-production inventory system that incorporates delivery and shared transportation costs. A multi-vendor optimal model is developed here for deciding the batch size of vendor's production, and delivery frequencies of different vendors to the manufacturer. Solution procedures for two special cases—uncapacitated and capacitated models are developed; especially, a new approximate method for capacitated model is devised. Numerical examples demonstrate the solution mechanism for the model. The results highlight cooperation between vendors and manufacturers on JIT procurement practices.     

An inventory model with partial backordering and unit backorder cost linearly increasing with the waiting time

As the implementation of JIT practice becomes increasingly popular, each echelon in a supply chain tends to carry fewer inventories, and thus the whole supply chain is made more vulnerable to lost sales and/or backorders. The purpose of this paper is to recast the inventory model to be more relevant to current situations, where the penalty cost for a shortage occurrence at a downstream stage in a supply chain is continually transmitted to the upstream stages. The supplier, in this case, at the upstream of the supply chain is responsible for all the downstream shortages due to the chain reaction of its backlog. The current paper proposes a model in which the backorder cost per unit time is a linearly increasing function of shortage time, and it claims that the optimal policy for the supplier is setting the optimal shortage time per inventory cycle to minimize its total relevant cost in a JIT environment.     

Earliness–tardiness production planning for just-in-time manufacturing: A unifying approach by goal programming

With popularity of the just-in-time (JIT) philosophy, researchers have started to seek the integration of Manufacturing Resource Planning (MRP-II) and JIT methodologies. This paper deals with the master production planning problem for a mass manufacturing system in the JIT environment, an earliness–tardiness production planning (ETPP) problem. The objective is to determine the optimum production rate for each product so that the total penalties imposed on the early and tardy production for all production periods be minimized. A goal programming (GP) approach is proposed to formulate the ETPP problem in a more generalized form, which includes several existing models in one unifying model. Moreover, the proposed GP algorithm ensures a global optimum solution, while the existing ones did not. In addition, it also possesses the advantages over others, such as easier to comprehend, easier to solve, and easier to extend it to the problem of multiple goals.     

Suppliers selection in the presence of both cardinal and ordinal data

Traditionally, supplier selection models are based on cardinal data with less emphasis on ordinal data. However, with the widespread use of manufacturing philosophies such as just-in-time (JIT), emphasis has shifted to the simultaneous consideration of cardinal and ordinal data in supplier selection process. To select the best suppliers in the presence of both cardinal and ordinal data, this paper proposes an innovative method, which is based on imprecise data envelopment analysis (IDEA). A numerical example demonstrates the application of the proposed method.     

A review of credibilistic portfolio selection

This paper reviews the credibilistic portfolio selection approaches which deal with fuzzy portfolio selection problem based on credibility measure. The reason for choosing credibility measure is given. Several mathematical definitions of risk of an investment in the portfolio are introduced. Some credibilistic portfolio selection models are presented, including mean-risk model, mean-variance model, mean-semivariance model, credibility maximization model, α-return maximization model, entropy optimization model and game models. A hybrid intelligent algorithm for solving the optimization models is documented. In addition, as extensions of credibilistic portfolio selection approaches, the paper also gives a brief review of some hybrid portfolio selection models.     

设备空间磁场预测的传感器布阵优化

本文研究了铁磁性设备周围空间传感器布阵的问题。我们建立了关于传感器位置和数量优化的数学模型,并通过遗传算法对模型进行求解。首先,本文选用对传感器数量和距离要求较少的旋转椭球体作为磁场远场换算的模型。在旋转椭球体模型中,传感器分布位置不当会导致磁场计算系数矩阵的条件数过大,模型将出现病态,因而计算得到的远场磁场结果不可靠。所以,本文以旋转椭球体模型中的系数矩阵条件数为优化目标,建立数学模型优化单个设备上方传感器的数量与位置分布,并利用遗传算法对模型求解。其次,通过实验验证了本模型对于单个设备的传感器位置和数量优化是有效的,且所用传感器数量少,计算结果可靠。最后,将单个设备传感器位置和数量的优化模型推广到多个设备,以两个设备为代表用同时优化和分别优化两种方法计算传感器位置,根据实验计算这两种方法都具有较高的远场磁场计算精度,但分开优化的方法在实际计算更加简便、容易操作。     

Decision architectures for production planning in multi-stage multi-product manufacturing systems

Recent trends in automated manufacturing call for hierarchical decision architectures for production planning, suitable for integration with part flow controls. Different design approaches are currently adopted for implementing production planning architectures, depending either on the objective of defining a centralized production plan for the whole manufacturing system (as in the case of MRP and OPT), or on the desire of coordinating local plans for the component work cells (as for JIT). The paper analyzes such approaches by use of a unifying mathematical formulation of the production plan optimization problem, to recognize the main features of the existing planning approaches, and compare their usefulness in different manufacturing processes.     

Just-in-time replenishment decisions for assembly manufacturing with investor-supplied finance

While JIT ideas have been enthusiastically embraced by manufacturing practitioners, the small replenishment batch sizes advocated are difficult to reconcile with the standard management science cost trade-off approach. The difficulty is diagnosed as being due to the standard assumption that capital for inventory is borrowed and hence boundless. We present a new analysis of inventory reduction decisions, such as adopting JIT replenishment or component substitution, using a deterministic batch sizing model which assumes that inventory is financed by the investors in the company and is thus finite. As a consequence, the investment level is treated as an additional variable of the decision analysis. Using the well established technique of constrained optimisation it is shown that for investor-financed operations the effective value of money invested in inventory is the marginal return on investment of the company, and increases with the degree of constraint. Thus, JIT policy options are especially favourable when low levels of inventory investment are sought, even without setup cost reduction, because the capital formerly invested in stock holdings of the JIT components can be reinvested in the inventory of other components to make their replenishment more efficient using larger batch sizes. The analysis is illustrated using an actual case study of a small manufacturing enterprise seeking to reduce inventory and increase return on investment. The analysis has interesting practical implications for inventory managers including a proposed simple method for identifying candidate components for JIT replenishment.     

An optimal batch size for integrated production–inventory policy in a supply chain

This study presents a new integrated production–inventory policy under a finite planning horizon and a linear trend in demand. We assume that the vendor makes a single product and supplies it to a buyer with a non-periodic and just-in-time (JIT) replenishment policy in a supply chain environment. The objective is to minimize the joint total costs incurred by the vendor and the buyer. In this study, first, we develop a mathematical model and prove that it has the optimal solution. Then, we describe an explicit solution procedure for obtaining the optimal solution. Finally, we provide two numerical examples to illustrate both increasing and decreasing demands in our proposed model, and we show that the performance of the integrated consideration is better than the performance of any independent decision from either the buyer or the vendor.     

基于GA-SA的混合U型装配线平衡

在JIT生产系统中，混合U型装配线是一种能够满足市场多样化需求的柔性系统，章综合考虑作业元素的分配和产品的投产排序两个因素，建立了混合U型装配线的平衡模型，给出了人工智能算法的平衡方法，从全局优化的角度研究了混合U型装配线的平衡问题。     

铁磁性设备补偿磁场的数学模型及其应用

研究用永磁体对铁磁性设备进行磁场补偿的问题,建立了补偿磁场的数学模型.将设备划分成若干个小长方体后,基于磁矩量法建立了数学模型,并对补偿磁场进行拟合.在计算模型中的耦合系数矩阵时,用多个点的平均值作为耦合系数的有效值,提高了计算结果的可靠性和稳定性.并且,针对永磁体距离设备很近时,设备呈现出的非线性磁化特性,通过优化方法求解各个单元的等效磁化率,这种方法不需要知道铁磁材料的磁化曲线和设备结构,便于计算和实际应用.最后,通过实验设计与数值计算,得到了永磁体对设备进行补偿的磁场分布,模型计算结果与实际测量数据误差11%以内,这说明该模型能够满足工业要求,具有实际应用价值.     

基于模糊需求的多产品供应商选择的多目标规划模型

由决策于环境的不确定性,供应商选择问题存在大量的模糊信息,传统的确定性规划模型已经不能够很好地处理此类问题。本文基于模糊需求量信息,对于多产品供应商问题建立了模糊多目标规划模型。同时考虑到各目标及约束的重要性程度不同的影响,通过引进适当的权重对多目标规划模型进行求解。文中结合实际算例验证模型的可行性和有效性。     

Modelling and stability analysis in human population genetics with selection and mutation

Population genetics is a scientific discipline that has extensively benefitted from mathematical modelling; since the Hardy‐Weinberg law (1908) to date, many mathematical models have been designed to describe the genotype frequencies evolution in a population. Existing models differ in adopted hypothesis on evolutionary forces (such as, for example, mutation, selection, and migration) acting in the population. Mathematical analysis of population genetics models help to understand if the genetic population admits an equilibrium, ie, genotype frequencies that will not change over time. Nevertheless, the existence of an equilibrium is only an aspect of a more complex issue concerning the conditions that would allow or prevent populations to reach the equilibrium. This latter matter, much more complex, has been only partially investigated in population genetics studies. We here propose a new mathematical model to analyse the genotype frequencies distribution in a population over time and under two major evolutionary forces, namely, mutation and selection; the model allows for both infinite and finite populations. In this paper, we present our model and we analyse its convergence properties to the equilibrium genotype frequency; we also derive conditions allowing convergence. Moreover, we show that our model is a generalisation of the Hardy‐Weinberg law and of subsequent models that allow for selection or mutation. Some examples of applications are reported at the end of the paper, and the code that simulates our model is available online at https://www.ding.unisannio.it/persone/docenti/del-vecchio for free use and testing.     

Representing and Learning Distributions with the Aid of a Neural Network

This paper describes a method by which a neural network learns to fit a distribution to sample data. The neural network may be used to replace the input distributions required in a simulation or mathematical model and it allows random variates to be generated for subsequent use in the model. Results are given for several data sets which indicate the method is robust and can represent different families of continuous distributions. The neural network is a three-layer feed-forward network of size (1-3-3-1). This paper suggests that the method is an alternative approach to the problem of selection of suitable continuous distributions and random variate generation techniques for use in simulation and mathematical models.     

“Optimization of aircraft maintenance/support infrastructure using genetic algorithms—level of repair analysis”

Level of repair analysis (LORA) is an approach used during the design stage of complex equipment for analysis of the cost effectiveness of competing maintenance strategies. LORA is carried as a part of the life cycle cost and cost of ownership analysis and plays a significant role in minimizing the life cycle cost and cost of ownership of the capital equipment. Since many purchasing decisions of complex equipment are based on cost of ownership, it has become essential to carry out LORA to compete in the market. In this paper, we develop a mathematical model for LORA and propose a solution methodology based on genetic algorithms. The concept is illustrated using a hypothetical aircraft engine.     

Optimum Redundancy with Equipment that Operates and Idles

Despite their widespread exclusion from the literature on reliability and replacement, many items of equipment are subject to failures to idle as well as failures to operate. For such equipment a new optimisation problem arises at the stage of systems design in terms of the optimal use of redundancy to maximise expected systems life. The models hitherto used as the basis for the solution of this optimization problem ignore the dependence that should exist for the solutions upon the operating and idling requirements to which the system is to be exposed. In this paper a simple model for equipment subject to such opposite failure modes is constructed which takes explicit account of the proportion of time the equipment is in use. The implications of this new model for the selection of an optimum redundancy configuration are illustrated for the case where four identical items of equipment are available.     

The performance evaluation of a multi-stage JIT production system with stochastic demand and production capacities

This paper discusses a single-item, multi-stage, serial Just-in-Time (JIT) production system with stochastic demand and production capacities. The JIT production system is modeled as a discrete-time, M/G/1-type Markov chain. A necessary and sufficient condition, or a stability condition, under which the system has a steady-state distribution is derived. A performance evaluation algorithm is then developed using the matrix analytic methods. In numerical examples, the optimal numbers of kanbans are determined by the proposed algorithm. The optimal numbers of kanbans are robust for the variations in production capacity distribution and demand distribution.     

Capacitated plant selection in a decentralized manufacturing environment: A bilevel optimization approach

Most facility selection and production planning approaches assume centralized decision making using monolithic models. In this paper, we address a capacitated plant selection problem in a decentralized manufacturing environment where the principal firm and the auxiliary plants operate independently in an organizational hierarchy. A non-monolithic model is developed for plant selection in the decentralized decision making process. The developed model considers the independence relationship between the principal firm and the selected plants. It also takes into account the opportunity costs of over-setting production capacities in the opened plants. The developed mathematical programming model is a two-level nonlinear programming model with integer and continuous decision variables. It was transformed into an equivalent single level model, linearized and solved by available optimization software. Computational examples are presented.     

Asset portfolio optimization using support vector machines and real-coded genetic algorithm

This paper presents an integrated approach for portfolio selection in a multicriteria decision making framework. Firstly, we use Support Vector Machines for classifying financial assets in three pre-defined classes, based on their performance on some key financial criteria. Next, we employ Real-Coded Genetic Algorithm to solve a mathematical model of the multicriteria portfolio selection problem in the respective classes incorporating investor-preferences.