Workload Smoothing Research Articles

The fuzzy human-robot collaboration assembly line balancing problem

Consideration is given to the assembly line balancing problem (ALBP) in production lines employed collaborative robots. Human–robot collaboration promises high advantages in manufacturing regarding automation, productivity, accuracy as well as flexibility in production. This technology is really challenging but requires redesigning of assembly lines to effectively involve the available human- and robot-resources. As robots can collaborate with humans sharing the assembly tasks in the same workstation, production managers experience an increasingly complex ALBP setting. Moreover, a crucial issue raised within this context is the variance and uncertainty in processing times for manual (human) work. Processing times for human work are subject to the nature and skills of the human worker. We explore the heuristic solution of this NP-hard problem using a problem-specific metaheuristic. Our aim is to investigate the effects of utilizing collaborate robots in manual assembly lines with respect to both production rate and workload smoothing. Simulation experiments on a real-life case study borrowed from the literature show how to tackle the problem under uncertainty (fuzziness) in task processing times.

Modelling and application of joint maintenance grouping and workload smoothing for an automotive plant

In the maintenance optimisation framework, grouping maintenance is a promising solution for maintenance planning of multi-component systems, in which maintenance activities are performed together to reduce maintenance costs. One of the most widely identified challenges in real applications of grouping maintenance is that it may disturb the maintenance workload balance (smoothness), causing many difficulties in production and/or labour scheduling and inventory management. In this study, we propose a joint optimisation approach for maintenance grouping and workload balancing to address the above challenge. First, a mathematical model of the joint optimisation problem was derived. A multi-objective grouping optimisation approach based on the Weighted Sum model and Genetic Algorithm was implemented to determine the Pareto-optimal grouping solution. The proposed approach was applied to a real case study of an automotive plant comprising 40 production lines with 1090 components. The results highlighted the advantages, effectiveness, and flexibility of the proposed maintenance approach in real-world applications.

R-SALSA: A branch, bound, and remember algorithm for the workload smoothing problem on simple assembly lines

We consider a simple assembly line balancing problem with given cycle time and number of stations. A quadratic objective function based on a so-called smoothness index SX levels the workloads of the stations. For this problem, called SALBP-SX, only a few solution procedures have been proposed in literature so far. In this paper, we extend and improve the branch-and-bound procedure SALSA (Simple Assembly Line Smoothing Algorithm) of Walter et al. (2021) to a bidirectional branch, bound, and remember algorithm called R-SALSA (R for remember). Like SALSA, it is based on a dynamic programming scheme which pre-determines potential workloads of the stations and provides a construction plan for possible station loads. This scheme is extended by the new concept of supporters and preventers which significantly enhances branching, bounding, and logical tests. Furthermore, a tailored heuristic that searches for improved initial solutions, a bidirectional branching scheme and additional dominance rules are integrated. In extensive computational experiments, we find out that our new procedure clearly outperforms all former exact solution procedures on benchmark data sets with up to 1000 tasks.

Straight assembly line balancing by workload smoothing: new results

Abstract Assembly line balancing by workload smoothing is very common; it aims to appropriately assign tasks to the stations of an assembly line, to ensure as similar as possible workloads for the stations. A shortcoming of the mathematical models developed in the literature is the optimization of workload smoothing when only all potential stations are considered. Therefore, the obtained solution may not be the global optimal solution and also may not be effective for real world cases. To overcome this shortcoming, some new workload smoothing criteria and their related mixed integer linear mathematical models are developed for three different settings: (1) workload smoothing optimization, when all potential stations are considered, (2) workload smoothing and minimization of the number of stations are optimized simultaneously, (3) global workload smoothing optimization regardless of the number of considered stations. The proposed formulations are associated with fewer variables and constraints compared with models previously presented in the literature and lead to better results according to an extensive numerical study. The proposed models can be applied in practice for designing the assembly lines of, inter alia, automobile and electronic equipment production systems.

On the performance of task-oriented branch-and-bound algorithms for workload smoothing in simple assembly line balancing

Smoothing the workloads among the stations of an already installed assembly line is one of the major objectives in assembly line (re-)balancing. In order to find a feasible task-station assignment that distributes the total workload as equal as possible, two exact task-oriented branch-and-bound algorithms have recently been proposed. In this paper, we systematically analyse their effectiveness in solving the workload smoothing problem on simple assembly lines. In our experiments, we also examine the performance of a state-of-the-art mathematical programming solver and a ‘combined’ exact branch-and-bound procedure that integrates components of the two algorithms from the literature. In terms of theory, we show the equivalence of two recently developed local lower bounding arguments and suggest a slight improvement of the bound. We also propose an enhanced feasibility test.

Exact solution approaches for the workload smoothing in assembly lines

In this paper, the problem of minimizing the smoothness index for an assembly line given a fixed cycle time and the number of workstations is studied. This problem which is known as the workload smoothing line balancing problem (WSLBP) is a mixed-integer quadratic programming problem. Until recently, this problem has only been tackled using heuristic approaches. Recently, there have been some attempts to solve this problem exactly using mixed-integer linear programming (MILP). The MILP formulations, however, are not usually capable of solving large size problem instances. In this paper, the aim is to solve the WSLBP using mathematical programming formulations by using off-the-shelf solvers. Differently from the literature some non-MILP formulations are also considered for the problem. For this purpose, three MILP formulations, one from the literature, and two non-MILP formulations are compared. The two non-MILP formulations include a mixed-integer second order cone programming formulation and a constraint programming model. The superiority of the non-MILP formulations over the considered MILP formulations is experimentally shown.

SALSA: Combining branch-and-bound with dynamic programming to smoothen workloads in simple assembly line balancing

We consider a version of the well-known simple assembly line balancing problem (called SALBP-SX) where, given the cycle time and the number of stations, the workloads of the stations are to be leveled according to an adequately defined smoothness index SX. Our index SX involves for each station the quadratic deviation of its workload from the average (or ideal) workload and is therefore closely related to the variance, which is a common measure of dispersion in statistics. Contrary to the existing literature on workload smoothing in ALB, which often treats the optimization of a prespecified smoothness index as a secondary objective, we consider our SX-objective as the single one in order to account for the practical relevance of fair workload distributions and avoiding overloaded bottleneck stations.To optimally solve SALBP-SX, we develop a tailored branch-and-bound procedure. It contains a new station-oriented branching scheme, new lower bound arguments, logical tests and, in particular, a dynamic programming scheme for the pre-calculation of potential workloads, which accelerates the procedure greatly. In comprehensive computational experiments, we show that our method clearly outperforms a class of recently developed task-oriented branch-and-bound procedures and also the mathematical programming solver Gurobi.

An efficient branch and bound algorithm for smoothing the workloads on simple assembly lines

In this study, we develop a branch and bound solution algorithm to solve the workload smoothing problem. Our algorithm incorporates new formulas for dynamically computing a lower bound on the optimal value of the objective function and for determining the earliest workstations for tasks. It also uses a fast heuristic for computing a good initial upper bound. A comprehensive experimental analysis is conducted in this study. The analysis demonstrates the outstanding performance of the algorithm and its efficiency in solving medium-sized workload smoothing problems.

A fast and effective heuristic for smoothing workloads on assembly lines: algorithm design and experimental analysis

Workload smoothing on assembly lines, which aims to evenly assign tasks to stations, supports workforce planning and resource optimization. In this paper, we study smoothing assembly lines and develop a problem-specific heuristic to efficiently solve large-sized instances. To build solutions, the algorithm uses a number of well-known priority rules for task assignment in conjunction with a probabilistic decision-making procedure for closing workstations. We conduct an experimental design for selecting the best performing priority rules and for tuning the probabilistic decision-making procedure. The efficiency of our algorithm is tested and demonstrated through an extensive experimental study.

A note on “Workload smoothing in simple assembly line balancing”

Workload smoothing is a variant of the well-known simple assembly line balancing problem. Given the number of (work) stations and the cycle time, the objective is to minimize the sum of squared workloads. Recently, Azizoğlu and İmat [Computers & Operations Research 89 (2018) 51–57] have proposed an exact branch-and-bound algorithm to solve this problem. However, we reveal that one of the lower bounding procedures used within their algorithm is incorrect. By means of an example, we demonstrate that the wrong bound can prevent their branch-and-bound algorithm from finding optimal solutions. We correct the bounding argument and also provide a tighter formulation.

Integrating workload smoothing and inventory reduction in three intermodal logistics platforms of a European car manufacturer

We consider the optimization of container loading at three intermodal logistics platforms (ILP) of a large European car manufacturer (ECM). The decisions focus both on the loading day of each container and on its filling with the products in inventory, which are gradually received over the week from inland suppliers. The objective is either to reduce the largest inventory level needed in the ILP, or to smooth the weekly workload. We develop a solution methodology that allows the handling of complex loading constraints related to dimensions and weight of the products. We model the problem as a mixed integer linear program and we develop a decomposition heuristic to solve it. We perform extensive computation tests on real instances provided by ECM. Compared with current industrial practices, our solutions yield an average improvement of 46.8% for the inventory reduction and of 25.8% for the smoothing of the workload. Our results highlight the benefit of jointly optimizing container loading and operations scheduling.

How Does Workload Affect Test Ordering Behavior of Physicians? An Empirical Investigation

We investigate the relationship between workload and the test ordering behavior of physicians, in an operational context where test ordering may act as a substitute for service process time. We define workload in two forms: the unfinished workload, that is, the number of patients waiting to be examined, and the finished workload, that is, the cumulative number of patients examined before a given patient in a work day. We hypothesize that physicians order more diagnostic tests at higher unfinished workload levels to speed-up, increase patient satisfaction and due to increased stress, and order fewer diagnostic tests at higher finished workload levels due to fatigue. Empirical analysis of data from a public training and research hospital provides strong evidence supporting both hypotheses: As the number of patients waiting increases from 0 to 28 patients, 2.3 more tests are ordered per patient on average, indicating a 22% increase. By contrast, as the finished load increases from 1 to 48 patients, 2.3 fewer tests are ordered per patient, corresponding to a 18% decrease. Our results suggest that workload smoothing mechanisms such as appointment systems alone may have significant cost saving implications. We also report the results of several robustness tests which confirm our results.

A Problem Specific Heuristic for Smoothing the Workload in Simple Assembly Lines

Workload smoothing techniques have been used to establish a balance among stations in assembly lines by assigning the tasks evenly to stations. Smoothing facilitates planning the workforce and optimizing the resource allocation problems. Considering these advantages, we address smoothing simple assembly line in this research and develop a problem specific heuristic algorithm to solve the large instances effectively. We test the effectiveness of the algorithm with experimental study.

Outside the Box Warehousing: When Thinking of Inputs as Outputs Makes Sense

AbstractAs the supply chain revolution continues, small and medium‐sized enterprises and smaller facilities of large companies experience an increased pressure from their adjacent supply chain partners and their own senior management to improve their performance. This places higher demands on the accuracy of their performance measurement, particularly labor productivity in warehouses. Smaller facilities cannot afford to implement engineered labor standards (ELS) and rely on traditional metrics of output, such as piece count, which do not provide the reliable level of accuracy demanded today. Changing the traditional view of the inputs‐outputs paradigm, this study suggests a unique labor productivity metric for non‐ELS facilities based on warehouse lift‐truck utilization data. Empirical tests using a longitudinal data set from an automotive parts distribution center provide evidence that the new metric is more accurate than the traditional output metrics because it is not affected by the assignment contribution error due to workload smoothing. The new metric offers managers an opportunity to fine‐tune labor productivity measurement in warehouses and other environments with extensive lift‐truck utilization without investing in ELS projects.

Workload smoothing in two-sided assembly lines

PurposeThe purpose of this paper is to define new criteria for measuring workload smoothness of two-sided assembly lines and propose an algorithm to solve a two-sided assembly line balancing problem focusing on distributing the idle time and the workload as evenly as possible among the workstations.Design/methodology/approachThis paper points out that the mean absolute deviation (MAD) and the smoothness index (SI) used to measure the workload smoothing in one-sided assembly lines are both inappropriate to evaluate the workload balance among workstations in two-sided assembly lines, as the idle time occur at the beginning and in the middle of a cycle within workstations. Then, the finish-time-based SI and MAD (FSI and FMAD) are defined, and a heuristic procedure based on the core mechanism of Moodie and Young method is proposed to smooth the assembly workload in two-sided assembly lines.FindingsThe computational results indicate that the proposed heuristic algorithm combined with the FMAD is effective in distributing the idle time and the workload among workstations as evenly as possible in two-sided assembly lines.Practical implicationsThe two-sided assembly line balancing problem with the objective of the line efficiency can be effectively solved by the proposed approach.Originality/valueThe FMAD is proposed to effectively improve the workload smoothing in two-sided assembly lines.

Workload smoothing in simple assembly line balancing

This paper considers a simple assembly line balancing problem with fixed number of workstations and prespecified cycle time. Our objective is to minimize the sum of the squared deviations of the workstation loads around the cycle time, hence maintain workload smoothing. We develop several optimality properties and bounding mechanisms, and use them in our branch and bound algorithm. The results of our computational study reveal that our branch and bound algorithm is capable of solving medium sized problem instances in reasonable times.

Surge Capacity Deployment in Hospitals: Effectiveness of Response and Mitigation Strategies

Major hospitals frequently lack adequate space to accommodate emergency patients. Managers can take actions to create surge capacity, an immediate additional supply of medical services to accommodate increased demand. We study operational strategies that improve surge capacity, and we identify how they can be deployed most effectively based on the characteristics of individual hospitals.Recent government regulations in the United States have increased pressure on hospitals to improve emergency preparedness. Specifically, hospitals must be able to show that they have taken adequate measures to manage surge capacity. We formulate an optimization model of early disposition actions that can be used to create surge capacity in a hospital. We analyze the model to understand its structural properties and compare two strategies to improve surge capacity: coordinated early discharge, which occurs during the response, and inpatient workload smoothing, which can help mitigate the need for response actions. We show analytically that without coordination, hospitals always act too conservatively in discharging patients to accommodate surge arrivals, and that smoothing the elective inpatient workload reduces the expected cost of surge response. In the numerical study, we find a utilization sweet spot in which smoothing is best at increasing surge capacity, and we show coordination increases the number of surges and number of early discharges, while smoothing mitigates these effects, making surges less frequent and less costly. Coordination is effective at increasing surge capacity for all types of hospitals, but when considering the holistic impact to the hospital, coordination and workload smoothing are often complementary strategies for improving surge response. Moreover, hospitals with sufficiently many electives and moderately high utilization should prioritize mitigation efforts when planning for emergencies.

The type E simple assembly line balancing problem: A mixed integer linear programming formulation

Although the simple assembly line balancing problem (SALBP) is the topic of many studies, typically they either consider minimizing the number of stations for a given cycle time (called type one), or minimizing the cycle time for a given number of stations (called type two). Rarely, type E of the problem has been considered. In the type E, cycle time and number of stations are both decision variables, and the objective is to maximize the line efficiency. This paper presents a mixed integer linear programming formulation for the type E simple assembly line balancing problem. Moreover, to further strengthen the presented formulation, two enhancement techniques in the form of valid inequalities and auxiliary variables are proposed. As the secondary objectives of the problem, minimization of the number of stations, the cycle time, and the smoothness index are studied as well. In the case of workload smoothing, three different linearization methods are employed and compared for minimizing the smoothness index. The results of computational study on the benchmark data set demonstrate the efficacy of the improved formulation

Aircraft Final Assembly Line Balancing and Workload Smoothing: A Methodological Analysis

Assembly Line Balancing (ALB) comprises ordering of tasks among workstations to satisfy precedence constraints and objective functions. Due to the specific features of an aircraft, such approach is not fully suitable for the case of an aircraft Final Assembly Line (FAL). Where, the number of workstations relates to technological criteria rather than to a calculation aiming to minimize a specific parameter. Workload smoothing is addressed once the FAL configuration is defined. To improve current practices, a methodological approach was taken to address the conceptual modeling of an aircraft assembly line.

Estimating and Enhancing Real-Time Data Service Delays: Control-Theoretic Approaches

It is essential to process real-time data service requests such as stock quotes and trade transactions in a timely manner using fresh data, which represent the current real-world phenomena such as the stock market status. Users may simply leave when the database service delay is excessive. Also, temporally inconsistent data may give an outdated view of the real-world status. However, supporting the desired timeliness and freshness is challenging due to dynamic workloads. To address the problem, we present new approaches for 1) database backlog estimation, 2) fine-grained closed-loop admission control based on the backlog model, and 3) incoming load smoothing. Our backlog estimation and control-theoretic approaches aim to support the desired service delay bound without degrading the data freshness, critical for real-time data services. Specifically, we design, implement, and evaluate two feedback controllers based on linear control theory and fuzzy logic control theory, to meet the desired service delay. Workload smoothing, under overload, helps the database admit and process more transactions in a timely fashion by probabilistically reducing the burstiness of incoming data service requests. In terms of the data service delay and throughput, our closed-loop admission control and probabilistic load smoothing schemes considerably outperform several baselines in the experiments undertaken in a stock trading database testbed.