Observations on the economic manufacture quantity model with learning and forgetting

The economic order (manufacture) quantity model with learning and forgetting has attracted the attention of researchers since the 1960s. All the models developed have limitations, of which two will be addressed in this article. First, the models found in the literature do not address the problem of when the learning exponent b approaches or exceeds the value 1, where these models are mathematically invalid for the special cases of b=1 and 2, and not investigated for the cases 1<b<2 and b>2. Second, the models found in the literature assume that the holding cost per unit is fixed even though the unit production cost is decreasing because of learning. This limitation would suggest producing in smaller lot‐sizes than their optimal values. Mathematical models are developed, and existing learning models are revised to overcome these limitations. Numerical examples are presented with results discussed.     

Competences-based performance model of multi-skilled workers with learning and forgetting

The relationship between performance and experience is non-linear, thus planning models that seek to manage workforce development through task assignment are difficult to solve. This gets even more complicated when taking into account multi-skilled workers that are capable of performing a variety of tasks. In this paper we develop a competences-based analytical model of the performance of multi-skilled workers undertaking repetitive tasks, taking into account learning and forgetting. A learning curve can be used to estimate improvement when repeating the same operation. Inverse phenomenon is forgetting, which can occur due to interruption in the production process. The Performance Evaluation Algorithm (PEA) was developed for two cases: fixed shift duration and fixed production output. The aim was to build a tool that better describes the capabilities of workers to perform repetitive tasks by binding together hierarchical competences modeled as a weighted digraph together with a learning and forgetting curve model (LFCM) to express individual learning rates.     

A multi-stage production-inventory model with learning and forgetting effects,rework and scrap

This paper studies a serial production line where a proportion of defective items is produced at each stage. Defective units enter a rework process, which is imperfect as well. Twice defective items are scrapped. This paper also considers learning and forgetting in production and rework processes and studies how the number of shipments of a lot from a production stage to the next influences the overall performance of the system. A model for a multi-stage production-inventory system is developed and optimized against an aggregate performance measure of four partial measures that are based on production time, process yield, in-process inventory and shipment frequency. Each of these partial performance measures is weighed by the system’s decision maker in accordance to importance. The numerical results show how the values of learning rates, weights assigned to the partial performance measures and the number of production stages influence the overall performance of the system.     

Multi-server retrial model with variable number of active servers

This paper deals with a multi-server retrial queueing model in which the number of active servers depends on the number of customers in the system. To this end, the servers are switched on and off according to a multi-threshold strategy. For a fixed choice of the threshold levels, the stationary distribution and various performance measures of the system are calculated. In the case of equidistant connection levels, the optimum threshold level is numerically computed.     

A multiple-vendor single-buyer integrated inventory model with a variable number of vendors

Supply chain management is concerned with the coordination of material and information flows in multi-stage production systems. A closer look at the literature reveals that previous research on the coordination of multi-stage production systems has predominantly focused on the sales side of the supply chain, whereas problems that arise on the supply side have often been neglected. This article closes this gap by studying the coordination of a supplier network in an integrated inventory model. Specifically, we consider a buyer sourcing a product from heterogeneous suppliers and tackle both the supplier selection and lot size decision with the objective to minimise total system costs. First, we provide mathematical formulations for the problem under study, and then suggest a two-stage solution procedure to derive a solution. Numerical studies indicate that our solution procedure reduces the total number of supplier combinations that have to be tested for optimality, and that it may support initiatives which aim on increasing the efficiency of the supply chain as a heuristic planning tool.     

Cost allocation with learning and forgetting considerations in a monopolistically competitive market

The objective of this study is to investigate the optimal cost-allocation rate for a new product in order to minimise the incumbent firm's cost under a monopolistically competitive market. From the incumbent's perspective, within a given length of the production run in the introduction or growth stage of the product life cycle, the impacts of the competitors’ entry and the learning and forgetting effects are taken into account in estimating the incumbent's costs. Furthermore, a Bayesian decision model is proposed to determine the optimal cost-allocation rate by considering both expert opinions and available information. Such a rate may assist the managers in evaluating a favourable percentage of the production cost borne by the incumbent firm. A case illustration demonstrates the application of the proposed model. The sensitivity analyses indicate that a higher increasing rate of competition, or a smaller degree of dispersion of the competitors’ entry scale in the introduction or growth stage would incur a higher optimal cost-allocation rate with a higher incumbent's expected total cost. In addition, the optimal cost-allocation rate and the incumbent's expected total cost would be positively correlated with the learning and forgetting rates, regardless of being under setup or production. Finally, it is suggested that managers should pay more attention to the learning and forgetting effects at the production stage than those at the setup stage.     

Determining the number of Kanbans for unbalanced serial production systems

This paper deals with the problem to determine the number of Kanbans for unbalanced serial production systems under the stochastic conditions. The simulation experiments for the constructed model of Kanban system derive the fundamental information about the problem, and an algorithm to determine the optimal number of Kanbans is proposed.     

FOPS: A new framework for the optimization with variable number of dimensions

A single‐ and multi‐objective optimization package is presented and described in detail. It contains an ensemble of local and global optimization routines. Procedures controlling variable number of dimensions are implemented as well, which is a rare feature among optimization oriented packages. The package is provided as a MATLAB toolbox. It excels in versatility and extensibility, which is demonstrated on a series of examples covering classical electromagnetism and antenna design. It is taken for granted that defining parameters of the optimization method can be set prior to the simulation run. However, its effective performance can be changed during the optimization run thanks to the full control feature. Moreover, it opens new possibilities in merging various algorithms into hybrids, performing complex dynamic programming tasks, or exploiting third party software. These advantages render the package as a perfect tool to deal with nowadays challenging engineering tasks.     

The effect of worker learning and forgetting on storage reassignment decisions in order picking systems

Order picking is a time-intensive and costly logistics activity as it involves a high amount of manual work. Prior research has mostly neglected the influence of human factors on the efficiency of order picking systems. This paper develops a mathematical model that investigates the impact of learning and forgetting of a heterogeneous workforce on order picking time and, consequently, on storage assignment decisions. In particular, the paper investigates when to change a storage assignment and when to keep it if learning and forgetting occur among the members of an order picking workforce. The results show that learning and forgetting should be considered in order to achieve a proper planning of storage assignment strategies.     

Monotonic convergence of iterative learning control systems with variable pass length

A growing number of researchers consider iterative learning control (ILC) a promising tool for numerous control problems in biomedical application systems. We will briefly discuss why classical ILC theory is technically too restrictive for some of these applications. Subsequently, we will extend the classical ILC design in the lifted systems framework to the class of repetitive trajectory tracking tasks with variable pass length. We will analyse the closed-loop dynamics for two standard learning laws, and we will discuss in which sense the tracking error can be reduced by which controller design strategies. Necessary and sufficient conditions for monotonic convergence will be derived. We then summarise all results in a set of practical controller design guidelines. Finally, a simulation study is presented, which demonstrates the usefulness of these guidelines and illustrates the special dynamics that occur in variable pass length learning.     

Determining the interval number of a triangle-free graph

The interval numberi (G) of a graphG withn vertices is the lowest integerm such thatG is the intersection graph of some family of setsI ₁, ...,I _n with everyI _i being the union of at mostm real intervals. In this article, an idea is presented for the algorithmic determination ofi (G), ifG is triangle-free. An example for the application of these considerations is given.     

Convergence and stability properties of an adaptive regulator with variable forgetting factor

A modified version of Fortescue's adaptive regulator is described, based on a minimum-variance estimator with variable forgetting factor and a d-step ahead control law. As in the Fortescue algorithm, the forgetting factor is chosen at each step to keep a measure of the information content constant, but the formula obtained is slightly different and avoids the need for an arbitrary lower bound. It also makes possible a proof of convergence for a deterministic linear system, without additional assumptions. A similar analysis is given for an incremental version of the regulator.     

The role of forgetting in the evolution and learning of language

Lewis signalling games illustrate how language might evolve from random behaviour. The probability of evolving an optimal signalling language is, in part, a function of what learning strategy the agents use. Here we investigate three learning strategies, each of which allows agents to forget old experience. In each case, we find that forgetting increases the probability of evolving an optimal language. It does this by making it less likely that past partial success will continue to reinforce suboptimal practice. The learning strategies considered here show how forgetting past experience can promote learning in the context of games with suboptimal equilibria.     

考虑学习/遗忘特性的软件项目调度多目标优化方法

人员作为软件项目调度过程中的核心资源,其学习遗忘特性是无法忽视的.借鉴已有学习和遗忘模型,构建学习/遗忘效应与人员技能水平之间的动态关联模型,进而给出考虑人员学习/遗忘效应的软件项目调度多目标优化模型.针对该模型,采用新型调度方案编码方式和不可行解修复方法,给出基于改进NSGA-II的软件项目调度多目标优化方法.面向具有不同项目规模的算例仿真实验表明,考虑人员的学习能力有利于改善调度方案性能,而遗忘效应则会使调度方案的项目总工期和成本增加.因此,在软件项目调度问题中,考虑人员的学习和遗忘效应是十分必要的.     

Asymptotic stability of model reference systems with variable structure control

The application of theory of variable structure systems (VSS) in the design of controllers for single input-single output model reference systems is considered. It is shown that the resulting controller has similar structure as those obtained using the second method of Lyapunov except that the states of the model are also used. The error trajectories move towards the switching surface for all values of the error and continues on it as sliding motions. The present approach clarifies the relationship between stability and nonminimum phase zeros of the plant.     

A new variable modified Chaplygin gas model interacting with a scalar field

We present a new form of the well-known Chaplygin gas model by introducing inhomogeneity in the equation of state. This model explains ω = −1 crossing. We also give a graphic representation of the model using the {r, s} parameters. We considered an interaction of this model with a scalar field by introducing a phenomenological coupling function and show that the potential decays with time.     

Determining the number of internal stability of a graph

The number of internal stability or independence number of an undirected graph has many important applications. Computationally it belongs to the class of intractable problems known as NP-Hard. In this paper we develop a tree search algorithm to determine the ndependence number of an undirected graph. Extensive computational experience on 2400 randomly generated graphs ranging from 20% to 90% densities and from 50 to 200 vertice has shown that the proposed algorithm is very effective.     

Construction of a quality model for machine learning systems

Software Quality Journal - Nowadays, systems containing components based on machine learning (ML) methods are becoming more widespread. In order to ensure the intended behavior of a software...     

Optimizing a multiserver queuing system with a variable number of servers

A multiserver Poisson queuing system with losses, with a variable number of servers, and an additive quality functional is investigated. All major characteristic of the system are obtained in an explicit form. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 92–101, July–August 2007.