Production, Manufacturing and Logistics
Calibrating cross-training to meet demand mix variation and employee absence

https://doi.org/10.1016/j.ejor.2015.07.036Get rights and content

Highlights

  • We study the cross-training that a work team needs in order to cope with demand mix variation.

  • Demand mix variation is defined in a straightforward, business sense manner.

  • A certain level of absences is also considered.

  • To numerically solve the problem a constraint-based selection procedure is developed.

Abstract

We address the problem of determining the cross-training that a work team needs in order to cope with demand mix variation and absences. We consider the case in which all workers can be trained on all tasks, the workforce is a resource that determines the capacity and a complete forecasting of demand is not available. The demand mix variation that the organization wants to be able to cope with is fixed by establishing a maximum time to devote to each product. We contend that this approach is straightforward, has managerial practicality and can be applied to a broad range of practical scenarios. It is required that the demand mix variation be met, even if there are a certain level of absences. To numerically solve the mathematical problem, a constraint-based selection procedure is developed, which we term CODEMI. We provide illustrated examples demonstrating solution quality for the approximation, and we report on an illustrative set of computational cases.

Introduction

Demand-mix flexibility, also called product flexibility and process flexibility, consists of the capacity of a production process to produce a variety of products to meet demand mix variability. The benefits of this flexibility have been demonstrated by Jordan and Graves (1995). Cross-training workers can increase production flexibility, thereby helping it to efficiently deliver a broader range of products by increasing overall workforce skills, so that they can cope with a wider range of possible demands (Hopp & VanOyen, 2004). Thus, cross-training workers are potentially an effective source of demand mix flexibility.

The question of ‘who should be trained on which tasks?’ is an important one for many organizations, some of whom adopt cross-training policies not as a response to direct skill requirements, but rather for employee job enrichment, to reduce boredom, or to create greater agility globally. To obtain some of these benefits, the specification of particular levels of cross-training may not be necessary. More often, cross-training is necessary for gaining flexibility in order to cope with demand variations, and redundancy, as a compensation for employee absences. In this case, the effectiveness of cross-training depends in largely upon how cross-training is carried out. When acquiring ability in new tasks requires significant durations and concomitant training cost, establishing the appropriate cross-training goals becomes critical.

The literature distinguishes between cases in which various specific patterns of flexibility are considered, and when full flexibility is assumed or allowed. Furthermore, situations in which the workforce is the only essential resource must be distinguished from those in which other resources are involved (see Section 2.1). The problem addressed here corresponds to full flexibility, with the workforce as the critical resource, as is common in practice. This situation can be found in call centers (Batta, Berman, & Wang, 2007), maintenance service operations (Brusco & Johns, 1998), nurse staffing (Bard & Purnomo, 2005) and retail services (Berman & Larson, 2004), among others. In fact, labor is often the limiting resource in practice (Slomp & Molleman, 2002).

Some literature addresses demand mix variation by considering a set of future demands along with the corresponding probabilities of occurrence (see Section 2.2). In this paper, the demand scenarios to be covered will be defined by establishing the degree of variability that the organization wants to be able to meet. This approach had not been previously dealt with in the literature and has practical applicability, as we will support below.

When addressing cross-training and demand coverage, different complementary characteristics can be considered. The skills involved can be either categorical or hierarchical. Categorical skills are binary in nature, and as such are either possessed or not possessed at all (De Bruecker, Van den Bergh, & Demeulemeester, 2014). When skills are hierarchical, they can be performed at different levels, as it has been assumed by some previous research (Azizi and Liang, 2013, Pinker et al., 2009). Similarly, the literature has considered homogenous or heterogeneous workers from the point of view of learning capacity (Shafer, Nembhard, & Uzumeri, 2001).

In addition, cross-training in a single department or between departments can be considered (Van den Bergh, Beliën, De Bruecker, Demeulemeester, & De Boeck, 2013), the possibility of overtime can be included (Wright & Mahar, 2013) and, for each worker, primary and secondary skills can be distinguished (De Matta and Peters, 2009, Guerry et al., 2013). In this paper, several straightforward assumptions regarding these options have been adopted: categorical skills, homogeneity of workers regarding learning, one single department, with no overtime considered. Primary and secondary skills are not differentiated when defining cross-training objectives.

The objective of this paper is to develop a method for determining cross-training goals for a work team in order to meet a certain level of demand mix variation, which is established by using the time devoted to each product. It is assumed that there is some level of worker absenteeism and that all workers can be trained to perform each task. Previous cross-training is taken into account to consider cases wherein there may be preexisting teams and cross trained skills. The problem is analyzed and solved via the development and use of a constraints-based selection procedure, which we term CODEMI. We will examine this novel approach using several computational cases. A primary contribution of the paper is the development of this novel and practical approach for addressing the cross-training problem.

In the remainder of this paper we discuss the relevant literature review in Section 2, followed by definitions and description of the problem, along with definitions of the relevant variables for our modeling approach in Section 3, the model itself and discussion on scope and disaggregation. Section 4 presents a novel procedure for generating solutions, illustrative examples, an evaluation of the solution approximation obtained, and computational performance. We report our conclusions in Section 5.

Section snippets

Flexibility and cross-training

The operations management literature on flexibility can be classified into two main streams (Chou, Chua, Teo, & Zheng, 2010): (1) work that describes and examines the value of different patterns of flexibility and (2) work assuming potential full flexibility, in which any resource, such as machines or workers, can eventually perform any task. The first group of work focuses on schemes that, with limited resource flexibility, provide outcome flexibility that is not far from optimal. This result

Solution procedure algorithm

We propose a procedural algorithm (COnstraints for DEmand MIxes, CODEMI) for solving the general problem posited that applies the concept of constraint selection, which is based on the idea that only a few constraints bind the optimal solution. Various general algorithms have been developed for solving a range of linear problems (Arsham, 2007, Myers, 1992). The idea of adding constraints based on partial results obtained follows the classical work of Dantzig, Fulkerson, and Johnson (1954). We

Conclusions

We addressed the problem of determining a cross-training skill matrix that a work team must have in place in order to meet a level of demand mix variation and workplace absences. Demand mix variations are defined in a straightforward manner in order to relate well to common business practices, thereby allowing for practical use and future improvements of the proposed approach. This paper contributes to the literature on determining appropriate cross training levels and skill matrices for groups

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