An exact algorithm for a workforce allocation problem with application to an analysis of cross-training policies

The evaluation of workforce staffing and scheduling policies is of paramount importance for meeting the challenge of simultaneously providing good customer service and low operational costs. Policy studies are particularly critical in workforce environments plagued by staffing shortages. The cross-utilization of employees among different departments or work centers is a well-recognized staffing policy for coping with shortages. We revisit a non-linear assignment problem for allocating cross-trained workers so as to maximize overall utility, which is measured using a quadratic function of labor shortages. We develop a branch-and-bound algorithm that efficiently provides optimal solutions for problems of practical size. This algorithm is then used to conduct a computational investigation of cross-training policies. Among the most critical factors affecting utility improvement are the coefficient of variation for demand, worker absenteeism, the percentage of cross-trained workers and cross-training breadth. Several important interactions among these and other factors are also identified.     

A comparison of cross-training policies in different job shops

This research compares a set of cross-training policies represented by different numbers of cross-trained workers, additional skills per cross-trained worker, and additional machines. The policies are evaluated in job shops, represented by different efficiency losses, labour utilization, variability in processing times, and worker absenteeism. Our results show that adding one machine in each department and cross-training one or two workers from each department with one additional skill is generally sufficient to realize most of the benefits of cross-training. Cross-training is thus beneficial in most job shops, unless the cost of the minimal training and spare machines is high. Our results also show that the value of cross-training and adding machines depends very much on the environment, and it is better to spread cross-training over more workers than to train a few workers with more skills.     

Hierarchical cross-training in work-in-process-constrained systems

We study Work-In-Process (WIP)-constrained flowlines staffed by partially cross-trained workers with hierarchical skill sets. We characterize the optimal worker-to-task assignment policy for CONWIP systems with two workers and general stochastic processing times. This leads us to the “fixed-before-shared” principle, which states that a flexible worker should process a task he/she is uniquely qualified for before helping other workers with shared tasks. To provide insights on the performance opportunity of hierarchical cross-training in systems with limited WIP, we provide a complete characterization of the optimal policy and closed-form expressions of the resulting throughput for the case of exponential processing times. We extend our results to the more general case of floater workers, and illustrate their applicability to various real-world systems. Our analysis shows that hierarchical cross-training can provide significant benefits, but should be implemented with care in WIP-constrained environments such as those making use of pull systems.     

Chained cross-training of workers for robust performance

Training workers to perform multiple tasks can improve workforce agility for dealing with variations in workload. However, cross-training can be costly, time consuming to implement, is limited by worker learning capacity, and can lead to ambiguity about work responsibilities. Therefore, it is important to implement cross-training in the most efficient way and especially, due to the training time required, in a way that is robust to system changes. We use queueing and simulation analysis to investigate cross-training in the context of maintenance in a manufacturing plant. The tasks are independent and can be represented as a set of parallel queues that are served by dedicated and cross-trained workers. We propose a cross-training strategy called chaining, in which a few workers are strategically cross-trained, and show that it yields most of the benefits of cross-training all workers, with much less effort. Most importantly, we demonstrate that cross-training workers to form a “complete chain” is extremely robust in the following ways: (i) it is insensitive to the variety of ways a complete chain can be formed; (ii) it performs well even if there are major changes to or uncertainty in system parameters (such as mean task arrival rates); and (iii) performance is insensitive to control decisions that, without complete chaining, can significantly harm performance.     

Task assignment considering cross-training goals and due dates

When a worker performs a task at which he is not fully experienced, he is increasing his future performance in doing this task. Thus, task assignment can consider objectives regarding task accomplishment and objectives regarding cross-training. The contribution of this paper lies in presenting and modelling the assignment of a set of tasks to a set of workers considering cross-training goals and that some of the tasks have to be completed at given due dates. The influence of the experience of one task on the performance on other tasks is taken into account. The model allows (1) testing the feasibility of a given combination of cross-training goals and due dates; (2) obtaining the task assignment that maximises the total work done – considering the tasks that have a due date and the tasks that do not; and (3) calculating the change on the total quantity of work performed because of the establishment of cross-training goals or due dates. A computational experiment is carried out by using MILP optimisation software.     

Agile workforce evaluation: a framework for cross-training and coordination

This paper outlines approaches for assessing and classifying manufacturing and service operations in terms of their suitability for use of cross-trained (flexible) workers. We refer to our overall framework as agile workforce evaluation. The primary contributions of this paper are: (i) a strategic assessment framework that structures the key mechanisms by which cross-training can support organizational strategy; (ii) a tactical framework that identifies key factors to guide the selection of an architecture and worker coordination policy for implementing workforce agility; (iii) a classification of workforce agility architectures; (iv) a survey of a broad range of archetypical classes of worker coordination policies; (v) a survey of the literature with an operational perspective on workforce agility; and (vi) identification of opportunities for research and development of architectures for specific production environments.     

Cross-training workers in Dual Resource Constrained systems with heterogeneous processing times

In this paper, we explore the effect of cross-training workers in Dual Resource Constrained (DRC) systems with machines having different mean processing times. By means of queuing and simulation analysis, we show that the detrimental effects of pooling (cross-training) previously found in single resource constrained (SRC) heterogeneous systems are also apparent in DRC heterogeneous systems. Fully cross-training workers in DRC heterogeneous systems is only beneficial if the differences between mean processing times are not too large, otherwise cross-training should be pursued within homogeneous subgroups of machines. Due to the limited machine availability, DRC systems are unable to use some of the potential assignment flexibility from cross-trained workers (pooled queues) that can be used in SRC systems. However, it appears that this restriction in the DRC system may even improve the system mean flow (waiting) time performance compared to the SRC system for relatively large differences in processing time. Finally, in fully flexible multiple server queuing systems, restricting the assignment flexibility by applying a decentral when-rule (i.e. a commonly used labour assignment rule in practice and research) instead of a central when-rule also seems to improve the mean flow time performance under processing time differences.     

Labour flexibility and staffing levels in a dual-resource constrained job shop

In many manufacturing organizations, increasing process flexibility is becoming more important while the reliance on product cost to measure manufacturing performance is being lessened. As a result, companies are placing more emphasis on developing a cross-trained workforce in an effort to improve the flexibility of their operations. Having a cross-trained workforce allows managers to move workers around to adjust to temporary overloads in the shop. Another approach to increasing process flexibility is through the addition of labour to create a capacity buffer. Adding more labour improves flexibility since it reduces the average utilization in the shop thereby reducing the possibility of any overload occurring in the first place. This paper compares the benefits realized by the development of a multi-skilled workforce with the benefits realized by additional workforce staffing. Both strategies exhibit improvement in the simulation of a hypothetical dual resource constrained hybrid job-shop. Results suggest that developing a multi-skilled workforce is a more conservative approach to manufacturing improvement than simply increasing levels of staffing. However, the use of additional labour results in a much more pronounced improvement than cross-training. A combination of the two strategies appears to be the best choice     

Cross-training policies and team performance

Labour flexibility is an important issue in the design and development of teams. By means of an analytical study this paper investigates the impact of cross-training on team performance. Four cross-training policies are distinguished and compared according to their effects on important performance measures, such as the load of the bottleneck worker and the number of newly used qualifications seen in various situations. These measures indicate a team's effectiveness and efficiency. Furthermore, they are related to psychological, social and organizational aspects of team functioning. A task assignment heuristic serves as a tool for comparing the cross-training policies. This is applied in an experimental study in which the team situation varies with respect to the cross-training policy, the level of absenteeism, and the variation in the mix of orders. It is shown that a worker-oriented cross-training policy, which attempts to spread multi-functionality evenly among employees, performs well. This policy offers the opportunity to shift work among employees to keep the load of the bottleneck worker low. The required coordination effort for allocating workers to tasks is also relatively low. In line with previous research, this study shows a diminishing positive effect of expanding the level of labour flexibility. The coordination effort required to apply additional flexibility appears to increase linearly with the amount of additional cross-training. The diminishing positive effect and the linearly increasing coordination effort suggest that managers should critically consider the level of labour flexibility in worker teams.     

Worker allocation in lean U-shaped production lines

U-shaped lines are widely used in lean systems. In U-shaped production lines, each worker handles one or more machines on the line: the worker allocation problem is to establish which machines are handled by which worker. This differs from the widely-investigated U-line assembly line balancing problem in that the assignment of tasks to line locations is fixed. This paper address the worker allocation problem for lean U-shaped production lines where the objectives are to minimize the quantity of workers and maximize full work: such allocations provide the opportunity to eliminate the least-utilized worker by improving processes accordingly. A mathematical model is developed: the model allows for any allocation of machines to workers so long as workers do not cross paths. Walking times are considered, where workers follow circular paths and walk around other worker(s) on the line if necessary. A heuristic algorithm for tackling the problem is developed, along with a procedure representing the ‘traditional’ approach of constructing standard operations routines. Computational experiments considering three line sizes (up to 20 machines) and three takt time levels are performed. The results show that the proposed algorithm both improves upon the traditional approach and is more likely to provide optimal solutions.     

The impact of the amount of work in process on the use of cross-training

Cross-training is becoming increasingly important to firms in order to cope with the more stringent performance requirements they are faced with in today's market. However, many firms put considerable effort into cross-training their workers only to find out that their workers favour the familiar tasks and hardly use and maintain the newly acquired skills. In this paper we explore the hypothesis that reducing the amount of work in process in a constant work in process (CONWIP) controlled job shop with worker preferences forces workers to make a more balanced use of the skills they possess. We test this hypothesis by means of a simulation study with the level of cross-training as moderating variable. Based on this study, it can be concluded that the control and limitation of the amount of work in process breaks the pattern of workers remaining at their preferred machines and constrains the workers to use and maintain their other skills more.     

Chained cross-training of assembly line workers

To function properly, assembly lines require the presence of every worker. When a worker is absent, management must scramble quickly to find a replacement. Cross-training workers to perform multiple tasks mitigates this difficulty. However, since cross-training is costly and limited by learning capacity and can confound the search for quality problems, it should be used judiciously. The present paper proposes a training strategy called chaining in which workers are trained to perform a second task, and the assignments of task types to workers are linked in a chain. It is shown that chaining is a practical and effective strategy for prioritizing cross-training to compensate for absenteeism on assembly lines.     

Worker assignment in cellular manufacturing considering technical and human skills

This paper considers the problem of assigning workers to manufacturing cells in order to maximize the effectiveness of the organization. Organization effectiveness is assumed to be a function of the productivity, output quality, and training costs associated with a particular worker assignment. Traditionally, these worker assignments have been based only on the technical skills of the workers. The proposed model also includes human skills and permits the ability to change the skill levels of workers by providing them with additional training. The problem is formulated as a mixed integer programming problem. A total of 32 test problems were developed and varied with regard to the total training time, the available training time for each worker, the training costs, the productivity coefficients and the quality level coefficients. Results indicate that this model provides better worker assignments than one that only considers technical skills.     

Cross-training effectiveness and profitability

We performed a cost-benefit analysis of the employee cross-training process on a mixed-model assembly line. We first simulated the manufacturing process to demonstrate the savings which result from cross-training. We then presented a linear integer program designed to make cost-effective cross-training assignments for a specified number of assembly jobs and workers. Next, we examined the profitability of these assignments for several work stations over various time horizons. In addition, we derived insights into the cross-training assignment process from these results and we explain how the integer program can be used to improve efficiency in production planning.     

Forming effective worker teams for cellular manufacturing

Cellular manufacturing has been extensively adopted as a measure to reduce cycle time, increase productivity, and improve product quality. The past research in cellular manufacturing has focused on the methodology for identification of machine groups, part families, and determination of processing routes. The relocation of existing workers into cells and their training for a team-oriented, cellular manufacturing environment have largely been ignored. In this research, a mixed integer, goal programming model is formulated for guiding the worker assignment and training process to create worker teams with high team synergy and individual job fitness meeting cell requirements for technical and administrative skills. The model integrates psychological, organizational, and technical factors. Several solution methods including greedy heuristic, filtered beam search, and simulated annealing techniques are developed and tested. It appears that heuristics such as beam search are capable of obtaining good solutions with reasonable computational effort.     

Rule mining for scheduling cross training with a heterogeneous workforce

This paper presents an association rule mining based framework for workforce scheduling to assist managers with robust real-time assignment decisions. We assume heterogeneous individual learning and forgetting behaviours, in which worker productivity changes dynamically. We explore a parallel production system that meets a specified production requirement over a fixed time horizon with the minimum workforce resources based on the number of worker-periods assigned. Three managerial policies are considered including: setting a maximum allowable individual cross-training level, balancing workload among workers and an unconstrained policy. We propose the use of several schedule attributes to quantify key aspects of optimised schedules that may, in turn, aid in determining robust assignment rules and the development of better cross-training policies. Current results indicate that the proposed approach is effective at identifying important rules, many of which add to our knowledge of useful workforce scheduling strategies.     

Multi-objective cell formation and production planning in dynamic virtual cellular manufacturing systems

This article presents a fuzzy goal programming-based approach for solving a multi-objective mathematical model of cell formation problem and production planning in a dynamic virtual cellular manufacturing system. In a dynamic environment, the product mix and part demand change over a planning horizon decomposed into several time periods. Thus, the cell formation done for one period may be no longer efficient for subsequent periods and hence reconfiguration of cells is required. Due to the variation of demand and necessity of reconfiguration of cells, the virtual cellular manufacturing (VCM) concept has been proposed by researchers to utilise the benefits of cellular manufacturing without reconfiguration charges. In a VCM system, machines, parts and workers are temporarily grouped for one period during which machines and workers of a group dedicatedly serve the parts of that group. The only difference of VCM with a real CM is that machines of the same group are not necessarily brought to a physical proximity in VCM. The virtual cells are created periodically depending on changes in demand volumes and mix, as new parts accumulate during a planning horizon. The major advantage of the proposed model is the consideration of demand and part mix variation over a multi-period planning horizon with worker flexibility. The aim is to minimise holding cost, backorder cost and exceptional elements in a cubic space of machine–part–worker incidence matrix. To illustrate the applicability of the proposed model, an example has been solved and computational results are presented.     

Modelling and integration of customer flexibility in the order commitment process for high mix low volume production

With increasing product variety and dynamic demand fluctuation, manufacturing industry is moving towards a high product mix and low order volume production environment. Consequently, the order commitment process is becoming one of the most important processes for manufacturing firms to meet individual customer's needs with limited resources. However, demands for shortened delivery lead time, diverse customer requirements and more frequent customer orders have made the order commitment task more challenging. This paper attempts to tackle these new challenges by incorporating not only manufacturing flexibility but also flexibility from the demand side. Customer flexibility is characterised by customer indifference to certain product attributes and/or delivery schedules. Intuitively, with the consideration of customer flexibility, both manufacturers’ and customers’ interests can be better served since the solution space of matching demand and supply can be extended beyond the traditional domain purely from a manufacturing perspective. To this end, a systematic approach is developed to characterise and model customer flexibility. A mixed-integer-programming model is formulated to provide optimal order commitment decisions.     

Minimising total cost for training and assigning multiskilled workers in seru production systems

This paper investigates the multiskilled worker training and assignment (MWT&A) problem of the seru production system (SPS), which is a new type of assembly line configured as multiple assembly cells, or so-called serus. The configuration of the SPS emphasises production efficiency and flexibility, achieved by multiskilled workers (MWs) able to cope with the demand of high-variety and low-volume manufacturing. Well-arranged and trained MWs are viewed as a critical factor when it comes to enhancing the performance of SPSs. This paper studies the MWT&A problem in the SPS with the aim of minimising the total cost, specifically, the workers’ training cost and the balance cost of processing times of the MWs in serus. This study provides an applicable mathematical programming model and designs a two-phase heuristic, named the SAIG algorithm, to effectively and efficiently solve this problem. The performance of the proposed algorithm is demonstrated by a comparison with the state-of-the-art heuristic through a series of computational experiments.