Incorporating human fatigue and recovery into the learning–forgetting process

The available learning and forgetting models do not consider the physical loading that performing a task requires. In some situations, physical loading results in workers’ fatigue on the job that is followed by rest breaks to alleviate it. The aim of this paper is to present the “learning–forgetting–fatigue–recovery model” (LFFRM) that addresses possible issues relating to workers’ capabilities and restrictions in manufacturing environments. Numerical examples are solved to address some research questions regarding the model optimization and its constraints. The main results show that incorporating learning into a production process decreases fatigue and improves the performance of the system. Worker fatigue, on the other hand, increases production time and decreases production output. A recovery break must be of enough length to alleviate some of the accumulated fatigue. However, longer recovery times extend the lead time and deteriorate the production performance due to forgetting.     

Single-machine scheduling with learning and forgetting effects

Scheduling with learning effects has been widely studied in the past decade. With the increasingly moving toward shorter product cycle times in many production lines, workers in this changeable environment must constantly learn new skill and technology. As a result, the forgetting effect might occur in these situations. In this paper, we propose a model with the consideration of both the learning and forgetting effects. We show some single-machine problems remain polynomially solvable under the proposed model.     

Batch sizing under learning and forgetting: Steady state characteristics for the constant demand case

We analyze steady-state characteristics of batch production time for a constant-demand lot sizing problem with learning and forgetting in production time. We report a new type of convergence, the alternating convergence, in which the batch production time alternates between two different values.     

Assigning cross-trained workers to departments: A two-stage optimization model to maximize utility and skill improvement

We develop a general framework that is applicable in both manufacturing and service settings for assigning cross-trained workers across departments. The framework consists of a two-stage optimization model where two objective functions, departmental utility and skill improvement, are considered sequentially. Departmental utility is a function of departmental labor shortage and the first-stage optimization model maximizes total departmental utility subject to typical assignment constraints. The second stage model seeks to maximize total skill improvement, which is quantified by a hyperbolic learning curve, while trying not to deviate from the utility level obtained during the first stage optimization. Our computational experiments suggest that incorporating the skill improvement function explicitly in the model results in significant improvement in the total skill level of the workforce and thus leads to more effective worker assignments.     

具有学习-遗忘效应的半导体批调度问题研究

半导体生产制造系统具有大规模、工艺繁杂、随机性大、可重入等显著特点。以半导体最终测试阶段批处理调度为基础,把学习-遗忘效应应用到典型半导体批调度问题中,构建基于学习-遗忘效应的批调度模型。分别结合调度问题和调度模型对双层算法(粒子群算法&萤火虫算法)进行设计,通过仿真实验检验了双层算法在求解具有学习遗忘效应的批调度模型方面的可行性和有效性,并对比分析以最大完工时间为优化目标的实验结果,探讨学习遗忘效应对半导体批调度问题的影响程度,对实际半导体生产具有重要指导意义。     

Examination of flexibility acquisition policies in dual resource constrained job shops with simultaneous worker learning and forgetting effects

This study investigates worker training related issues in dual resource constrained (DRC)job shop environments with the simultaneous presence of learning, forgetting (which causes relearning) and worker attrition effects. Learning and forgetting occurs as workers are trained in different departments on the shop floor. A recent survey of job shops based in the US indicates that firms are concerned about the relearning losses that accompany worker transfers, and are using a variety of strategies to reduce the effects of relearning. This study uses the learn-forget-learn (LFL) model to capture different learning and forgetting environments in order to understand whether up-front training can be used to reduce relearning and realize the benefits of worker flexibility. Results show that the existing forgetting rate has a significant impact on inventory and customer service performance. Extensive up-front training helps reduce relearning, however, it does not always help improve performance.     

Learning effects and the phenomenon of moving bottlenecks in a two-stage production system

This paper studies the effects of learning and forgetting on a two-stage production system and the position of a potential bottleneck in the system. We start with developing a model for a two-stage serial production system where semi-finished items are fed by the first stage to the second stage, which, in turn, processes the items to their final state. The finished items are transferred either to a subsequent stage or to customers. The paper assumes that both stages of the production system considered are subject to learning and forgetting effects. Learning quickens the production rate as more experience is gained (i.e., when the number of repetitions increases), while forgetting has the opposite effect when production is intermittent (i.e., experience is lost over production breaks). The paper studies how different values of the learning and forgetting parameters influence the ratio of the production rates of both stages and the flow of material in the system. The results of the paper indicate that learning may cause a bottleneck to shift its position in a production system. This happens when an initially slower stage overtakes a previously faster stage over time due to a higher learning rate. The paper thus contributes to the literature on moving bottlenecks and provides practitioners with a model that helps predicting where bottlenecks may arise in the production system, and which enables the system to flexibly react to moving bottlenecks.     

Cournot competition with hyperbolic learning and myopic firms: A note

In this note, we provide a Cournot oligopoly model of learning-by-doing that incorporates both learning spillovers and organizational forgetting, relaxing the commonly made assumption of linear learning by considering a hyperbolic learning curve that depends on both own and rivals’ experience. The analysis is conducted under the assumption of myopic firms. We show that conditions exist under which more competition, captured by an increase in the number of firms, worsens both productive and allocative efficiency at the steady-state equilibrium.     

Learning and forgetting-based worker selection for tasks of varying complexity

This paper presents an approach for selecting workers for tasks of varying complexity based on individual learning and forgetting characteristics in order to improve system productivity. The performance of a learning and forgetting-based selection (LFBS) policy is examined using simulation and compared to a baseline policy representing criteria used in practice. The effects of factors including worker redundancy and task-tenure on productivity are also examined in the environment of continuously staffed independent tasks. Results demonstrate that the LFBs policy significantly improves productivity relative to common practice and suggests that lower levels of redundancy and shorter task-tenures tend to mitigate some of the negative effects of forgetting.     

Finite difference reaction-diffusion systems with coupled boundary conditions and time delays

This paper is concerned with finite difference solutions of a coupled system of reaction-diffusion equations with nonlinear boundary conditions and time delays. The system is coupled through the reaction functions as well as the boundary conditions, and the time delays may appear in both the reaction functions and the boundary functions. The reaction-diffusion system is discretized by the finite difference method, and the investigation is devoted to the finite difference equations for both the time-dependent problem and its corresponding steady-state problem. This investigation includes the existence and uniqueness of a finite difference solution for nonquasimonotone functions, monotone convergence of the time-dependent solution to a maximal or a minimal steady-state solution for quasimonotone functions, and local and global attractors of the time-dependent system, including the convergence of the time-dependent solution to a unique steady-state solution. Also discussed are some computational algorithms for numerical solutions of the steady-state problem when the reaction function and the boundary function are quasimonotone. All the results for the coupled reaction-diffusion equations are directly applicable to systems of parabolic-ordinary equations and to reaction-diffusion systems without time delays.     

Forgetting the initial distribution for Hidden Markov Models

The forgetting of the initial distribution for discrete Hidden Markov Models (HMM) is addressed: a new set of conditions is proposed, to establish the forgetting property of the filter, at a polynomial and geometric rate. Both a pathwise-type convergence of the total variation distance of the filter started from two different initial distributions, and a convergence in expectation are considered. The results are illustrated using different HMM of interest: the dynamic tobit model, the nonlinear state space model and the stochastic volatility model.     

Worker deployment in dual resource constrained systems with a task-type factor

This paper investigates worker learning and forgetting phenomenon in a dual resource constrained system (DRC) setting. Worker learning and forgetting in two and three stage DRC systems are modeled according to the dual-phase learning and forgetting model (DPLFM), which is based on the theory that a task has separate cognitive and motor requirements. Results show that the task-type (with respect to its learning rate and proportion of cognitive and motor requirements) affects the performance of training and deployment policies in DRC systems, and as such it should be included in future DRC research.     

Optimal dynamic advertising policies for hereditary processes

In this paper, the Nerlove-Arrow model of optimal dynamic advertising policies is generalized by assuming a general probability distribution of the forgetting time, rather than the exponential one. A control problem with integrodifferential equations of motion is defined for which the transitory and steady-state properties of the optimal advertising policy are examined. The effects of assumptions like IHR-distributions and DHR-distributions, the existence of an upper bound for the forgetting time, etc., are explained. It is shown that there are two (in the case of an exponential distribution even three) different current-value adjoint functions associated with the problem, and relations between the two (three) are established. Also provided is a sensitivity analysis.Thanks are due to G. Feichtinger and S. Jorgensen for useful discussions.     

Large deviations behavior of counting processes and their inverses

We show, under regularity conditions, that a counting process satisfies a large deviations principle in or the Gärtner-Ellis condition (convergence of the normalized logarithmic moment generating functions) if and only if its inverse process does. We show, again under regularity conditions, that embedded regenerative structure is sufficient for the counting process or its inverse process to have exponential asymptotics, and thus satisfy the Gärtner-Ellis condition. These results help characterize the small-tail asymptotic behavior of steady-state distributions in queueing models, e.g., the waiting time, workload and queue length.     

A genetic algorithm for cellular manufacturing design and layout

Cellular manufacturing (CM) is an approach that can be used to enhance both flexibility and efficiency in today’s small-to-medium lot production environment. The design of a CM system (CMS) often involves three major decisions: cell formation, group layout, and group schedule. Ideally, these decisions should be addressed simultaneously in order to obtain the best results. However, due to the complexity and NP-complete nature of each decision and the limitations of traditional approaches, most researchers have only addressed these decisions sequentially or independently. In this study, a hierarchical genetic algorithm is developed to simultaneously form manufacturing cells and determine the group layout of a CMS. The intrinsic features of our proposed algorithm include a hierarchical chromosome structure to encode two important cell design decisions, a new selection scheme to dynamically consider two correlated fitness functions, and a group mutation operator to increase the probability of mutation. From the computational analyses, these proposed structure and operators are found to be effective in improving solution quality as well as accelerating convergence.     

Online regularized learning with pairwise loss functions

Recently, there has been considerable work on analyzing learning algorithms with pairwise loss functions in the batch setting. There is relatively little theoretical work on analyzing their online algorithms, despite of their popularity in practice due to the scalability to big data. In this paper, we consider online learning algorithms with pairwise loss functions based on regularization schemes in reproducing kernel Hilbert spaces. In particular, we establish the convergence of the last iterate of the online algorithm under a very weak assumption on the step sizes and derive satisfactory convergence rates for polynomially decaying step sizes. Our technique uses Rademacher complexities which handle function classes associated with pairwise loss functions. Since pairwise learning involves pairs of examples, which are no longer i.i.d., standard techniques do not directly apply to such pairwise learning algorithms. Hence, our results are a non-trivial extension of those in the setting of univariate loss functions to the pairwise setting.     

Optimization of manufacturing systems using a neural network metamodel with a new training approach

In this study, two manufacturing systems, a kanban-controlled system and a multi-stage, multi-server production line in a diamond tool production system, are optimized utilizing neural network metamodels (tst_NNM) trained via tabu search (TS) which was developed previously by the authors. The most widely used training algorithm for neural networks has been back propagation which is based on a gradient technique that requires significant computational effort. To deal with the major shortcomings of back propagation (BP) such as the tendency to converge to a local optimal and a slow convergence rate, the TS metaheuristic method is used for the training of artificial neural networks to improve the performance of the metamodelling approach. The metamodels are analysed based on their ability to predict simulation results versus traditional neural network metamodels that have been trained by BP algorithm (bp_NNM). Computational results show that tst_NNM is superior to bp_NNM for both of the manufacturing systems.     

A detailed workforce planning model including non-linear dependence of capacity on the size of the staff and cash management

This paper introduces an original planning model which integrates production, human resources and cash management decisions, taking into account the consequences that decisions in one area may have on other areas and allowing all these areas to be coordinated. The most relevant characteristics of the planning problem are: (1) production capacity is a non-linear function of the size of the staff; (2) firing costs may depend on the worker who is fired; (3) working time is managed under a working time account (WTA) scheme, so positive balances must be paid to workers who leave the company; (4) there is a learning period for hired workers; and (5) cash management is included. A mixed integer linear program is designed to solve the problem. Despite the size and complexity of the model, it can be solved in a reasonable time. A numerical example, the main results of a computational experiment and a sensibility analysis illustrate the performance and benefits of the model.     

An Online Actor–Critic Algorithm with Function Approximation for Constrained Markov Decision Processes

We develop an online actor–critic reinforcement learning algorithm with function approximation for a problem of control under inequality constraints. We consider the long-run average cost Markov decision process (MDP) framework in which both the objective and the constraint functions are suitable policy-dependent long-run averages of certain sample path functions. The Lagrange multiplier method is used to handle the inequality constraints. We prove the asymptotic almost sure convergence of our algorithm to a locally optimal solution. We also provide the results of numerical experiments on a problem of routing in a multi-stage queueing network with constraints on long-run average queue lengths. We observe that our algorithm exhibits good performance on this setting and converges to a feasible point.     

Incorporating ergonomic risks into assembly line balancing

In manufacturing, control of ergonomic risks at manual workplaces is a necessity commanded by legislation, care for health of workers and economic considerations. Methods for estimating ergonomic risks of workplaces are integrated into production routines at most firms that use the assembly-type of production. Assembly line re-balancing, i.e., re-assignment of tasks to workers, is an effective and, in case that no additional workstations are required, inexpensive method to reduce ergonomic risks. In our article, we show that even though most ergonomic risk estimation methods involve nonlinear functions, they can be integrated into assembly line balancing techniques at low additional computational cost. Our computational experiments indicate that re-balancing often leads to a substantial mitigation of ergonomic risks.