A two-stage stochastic program for scheduling and allocating cross-trained workers

A two-stage stochastic program is developed for scheduling and allocating cross-trained workers in a multi-department service environment with random demands. The first stage corresponds to scheduling days-off over a time horizon such as a week or month. The second stage is the recourse action that deals with allocating available workers at the beginning of a day to accommodate realized demands. After the general two-stage model is formulated, a special case is introduced for computational testing. The testing helps quantify the value of cross-training as a function of problem characteristics. Results show that cross-training can be more valuable than perfect information, especially when demand uncertainty is high

Factors Affecting the Development of Workforce Versatility

Among all strategies supporting the firms' flexibility and agility, the development of human resources versatility holds a promising place. This article presents an investigation of the factors affecting the development of this flexibility lever, related to the problem of planning and scheduling industrial activities, taking into account two dimensions of flexibility: the modulation of working time, which provides the company with fluctuating work capacities, and the versatility of operators: for all the multi-skilled workers, we adopt a dynamic vision of their competences. Therefore, this model takes into account the evolution of their skills over time, depending on how much they were put in practice in previous periods. The model was solved by using an approach relying on genetic algorithm that used an indirect encoding to build the chromosome genotype, and then a serial scheduling scheme is adopted to build the solution

Workforce planning and facility utilization using a two-stage stochastic recourse approach

Hi-tech manufacturing uses sophisticated and capital intensive processes that require a highly skilled workforce. Fluctuating demand leads to either a shortage of skilled workers that causes unmet demand or an excess of skilled labor that causes worker idleness. This mismatch in the available and required skillsets is a source of potential loss for the organization. This thesis formulates an industry-motivated workforce planning and facility utilization problem as a two-stage stochastic recourse program that considers fluctuating demand over a long planning horizon and includes business and labor rules, e.g., hiring, firing, overtime, cross-training, and shift swapping, that govern the structure of the workforce. Solutions to this problem are computed using a scenario-based approach and indicate that the cost of workforce formation can be significantly reduced by using the recourse problem

Implementation of Cross-training for Multi-shift Worker Allocation

In workforce allocation, gaps between workers available and workers needed at various operations result in production delays and a loss of profitability for the manufacturer. These gaps can be reduced by overtime assignments of workers from other shifts. However, for a multiple shift planning horizon, a mix of cross-training of workers over different tasks along with overtime assignments may be a good strategy. This work develops an industry-motivated cross-training framework that identifies workers and operations for normal, overtime, and training assignments. A mixed integer programming model that integrates all three assignment tasks is formulated and solved. The production scenario consists of skill level based qualifications for workers that need to be assigned to operations in every shift. Factory floor conditions such as limits on worker levels at specific operations, scheduling restrictions and worker training protocols are also considered. The data taken into account includes parameters such as man-machine ratio, tool count, and limits on skill qualifications for workers. The output of the model provides a cross-training schedule and an assignment schedule that can be used by floor managers on a shift-by-shift basis. The MIP model is implemented in C# using the .NET framework and the IBM ILOG CPLEX Optimizer

Enabling flexibility through strategic management of complex engineering systems

”Flexibility is a highly desired attribute of many systems operating in changing or uncertain conditions. It is a common theme in complex systems to identify where flexibility is generated within a system and how to model the processes needed to maintain and sustain flexibility. The key research question that is addressed is: how do we create a new definition of workforce flexibility within a human-technology-artificial intelligence environment? Workforce flexibility is the management of organizational labor capacities and capabilities in operational environments using a broad and diffuse set of tools and approaches to mitigate system imbalances caused by uncertainties or changes. We establish a baseline reference for managers to use in choosing flexibility methods for specific applications and we determine the scope and effectiveness of these traditional flexibility methods. The unique contributions of this research are: a) a new definition of workforce flexibility for a human-technology work environment versus traditional definitions; b) using a system of systems (SoS) approach to create and sustain that flexibility; and c) applying a coordinating strategy for optimal workforce flexibility within the human- technology framework. This dissertation research fills the gap of how we can model flexibility using SoS engineering to show where flexibility emerges and what strategies a manager can use to manage flexibility within this technology construct”--Abstract, page iii

Optimising Training for Service Delivery

We study the problem of training a roster of engineers, who are scheduled to respond to service calls that require a set of skills, and where engineers and calls have different locations. Both training an engineer in a skill and sending an engineer to respond a non-local service call incur a cost. Alternatively, a local contractor can be hired. The problem consists in training engineers in skills so that the quality of service (i.e. response time) is maximised and costs are minimised. The problem is hard to solve in practice partly because (1) the value of training an engineer in one skill depends on other training decisions, (2) evaluating training decisions means evaluating the schedules that are now made possible by the new skills, and (3) these schedules must be computed over a long time horizon, otherwise training may not pay off. We show that a monolithic approach to this problem is not practical. Instead, we decompose it into three subproblems, modelled with MiniZinc. This allows us to pick the approach that works best for each subproblem (MIP or CP) and provide good solutions to the problem. Data is provided by a multinational company

Cross-trained workforce planning models

Cross-training has emerged as an effective method for increasing workforce flexibility in the face of uncertain demand. Despite recently receiving substantial attention in workforce planning literature, a number of challenges towards making the best use of cross-training remain. Most notably, approaches to automating the allocation of workers to their skills are typically not scalable to industrial sized problems. Secondly, insights into the nature of valuable cross-training actions are restricted to a small set of predefined structures. This thesis develops a multi-period cross-trained workforce planning model with temporal demand flexibility. Temporal demand flexibility enables the flow of incomplete work (or carryover ) across the planning horizon to be modelled, as well as an the option to utilise spare capacity by completing some work early. Set in a proposed Aggregate Planning stage, the model permits the planning of large and complex workforces over a horizon of many months and provides a bridge between the traditional Tactical and Operational stages of workforce planning. The performance of the different levels of planning flexibility the model offers is evaluated in an industry motivated case study. An extensive numerical study, under various supply and demand characteristics, leads to an evaluation of the value of cross-training as a supply strategy in this domain. The problem of effectively staffing a pre-fixed training structure (such as the modified chain or block) is an aspect of cross-training which has been extensively studied in the literature. In this thesis, we attempt to address the more frequently faced problem of ‘how should we train our existing workforce to improve demand coverage?’. We propose a two-stage stochastic programming model which extends existing literature by allowing the structure of cross-training to vary freely. The benefit of the resulting targeted training solutions are shown in application using a case study provided by BT. A wider numerical study highlights ‘rules-of-thumb’ for effective training solutions under a variety of characteristics for uncertain demand

Human-Machine Collaborative Optimization via Apprenticeship Scheduling

Coordinating agents to complete a set of tasks with intercoupled temporal and resource constraints is computationally challenging, yet human domain experts can solve these difficult scheduling problems using paradigms learned through years of apprenticeship. A process for manually codifying this domain knowledge within a computational framework is necessary to scale beyond the ``single-expert, single-trainee" apprenticeship model. However, human domain experts often have difficulty describing their decision-making processes, causing the codification of this knowledge to become laborious. We propose a new approach for capturing domain-expert heuristics through a pairwise ranking formulation. Our approach is model-free and does not require enumerating or iterating through a large state space. We empirically demonstrate that this approach accurately learns multifaceted heuristics on a synthetic data set incorporating job-shop scheduling and vehicle routing problems, as well as on two real-world data sets consisting of demonstrations of experts solving a weapon-to-target assignment problem and a hospital resource allocation problem. We also demonstrate that policies learned from human scheduling demonstration via apprenticeship learning can substantially improve the efficiency of a branch-and-bound search for an optimal schedule. We employ this human-machine collaborative optimization technique on a variant of the weapon-to-target assignment problem. We demonstrate that this technique generates solutions substantially superior to those produced by human domain experts at a rate up to 9.5 times faster than an optimization approach and can be applied to optimally solve problems twice as complex as those solved by a human demonstrator.Comment: Portions of this paper were published in the Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI) in 2016 and in the Proceedings of Robotics: Science and Systems (RSS) in 2016. The paper consists of 50 pages with 11 figures and 4 table

A Model for Contingent Manpower Planning: Insights from a High Clock Speed Industry

Intense competitive pressures have led to compressed product life cycles and frequent introduction of new products. This creates demand volatility and a consequent pressure on manufacturing to meet this variable demand. In this paper we model the manpower planning issues for a computer manufacturer during the product introduction phase when a quick ramp-up of production to meet rapidly increasing demand is a key requirement. A mix of permanent and contingent workers with different skill sets is considered. Some important issues addressed in this research are (a) how to assign workers with different skills to maximize production (b) what is the induction rate of contingent workers to achieve the desired ramp-up and (c) what are the key decision factors that impact manufacturing performance An LP model is proposed to minimize overall costs subject to complex scheduling, skills, and learning rate requirements. Our analysis indicates that cost of induction of contingent workers, overtime cost premium, and the amount of overtime have significant impact on performance. The findings of the study will be useful to managers in planning and allocation of workers of different skills to various manufacturing processes and to determine the optimal number of contingent workers to induct.Singapore-MIT Alliance (SMA

Mathematical Models and Solution Approach for Staff Scheduling with Cross-Training at Call Centers

Call centers face demand that varies throughout the week across multiple service categories and typically employ non-standard workforce schedules to meet this demand. In call centers, cross-training provides a buffer against fluctuation of demand between categories and is widely used. Full cross-training, however, is financially impractical in most cases, which has created a challenging problem in how to optimize a cross-trained workforce, i.e., a) what categories should be cross-trained, b) what portion of the workforce should be cross-trained, and c) how to schedule their weekly assignments. This problem is motivated by the need of a Fortune 50 company\u27s technology support center to schedule its workforce with multiple service categories. To solve this problem to its fullest extent, a mixed integer programming model that addresses staff assignment composition, shift scheduling, days off assignment, and break assignment across multi-skilled agents is proposed. The model is gigantic in size with thousands of general integer variables and is hard to solve. To improve computational efficiency, a two-phase sequential optimization approach is developed. The first phase is to find the optimal composition of the workforce to decide what categories should be cross-trained and when they should be deployed; the second phase is a staff scheduling model to find the size of the workforce with their skill sets and their shifts and weekly tours. The two-phase approach is an order of magnitude faster than the original model and is able to obtain better solutions orders of magnitude faster. Experimental results with real data from the company clearly demonstrate the significance of cross-training; even partial limited cross-training, where 30% - 40% of the workforce is cross-trained with limited (two out of nine) skills per agent, results in considerable performance improvements. The model, when tested in the strategic analysis of the staff composition, suggested an estimated savings of 4% - 9% on staffing cost with an improved service level. Compared with other flexibility options such as part-time shifts, experiment results seem to suggest that cross-training could be a more effective approach to hedge against demand fluctuations when multiple service categories are involved