A new stochastic planning model for make-to-order companies
with non-homogenous workforce problems.
Master thesis
By:
Rudi Torensma
Newcastle University University of Groningen Faculty of Economics and Business
DD MSc TOM April, 2019
r.p.torensma@student.rug.nl
Student numbers: S2567938 and B7066567 Thesis Supervisor:
S. Fazi Second Supervisor:
A new stochastic planning model for make-to-order companies
with non-homogenous workforce problems.
Abstract
In the last decade, workforce for production environments has become more flexible and less homogenous, due to demand diversity and increasing competition. This makes the planning of the workforce difficult. This paper focuses on the problem of planning the workforce capacity for make-to-order industries. The production flowlines have uncertain demand and some workstations need specific skills. This research provides a new model to improve the workforce planning for these production flowlines and will be using a two-stage stochastic recourse model to find the optimal permanent and temporary workforce. The model will be validated and tested with a case study of a medium sized make-to-order manufacturer. The results indicate that the proposed approach can be effectively used to plan permanent and temporary workers in make-to-order manufacturers with production flowlines.
Acknowledgement
Table of contents
1. Introduction 6
2. Literature background 7
2.1 Non-homogenous workforce 7
2.2 Uncertainties in workforce planning models 9
2.3 Research relevance and questions 10
3. Problem description and methodology 12
3.1 Problem description 12 3.2 Methodology 14 3.3 Model development 14 3.4 Notations 15 3.5 Model 17 4. Case study 19 4.1 Case description 19 4.2 Case data 20 5. Results 22 5.1 Case results 22
5.2 Verification and validation 23
5.3 Demand parameters 24
5.4 Allowable ratio of permanent workers 27
5.4 Cost of temporary workers 28
5.6 Summary of results 31
6. Discussion 32
7. Conclusion 33
6
1. Introduction
Today, several manufacturing industries are challenged by increasing competition, increasing product variety and decreasing product life cycles. As a result, the demand of industrial manufacturers has become more dynamic and they are more and more leaning towards a make-to-order (MTO) type of production (Sillekens et al., 2011), since reducing waste has become vital, both to be cost efficient and sustainable. However, this in turn requires prompter responses to the demand and higher flexibility both in the production process and the workforce (Chen et al., 2009).
Many industrial MTO companies need a flexible workforce, which means having the freedom to change the number of workers or changing the skillset of workers, based on production needs (Attia et al., 2014). Of course, this requires an available market of workers that could be hired temporarily (Bard et al., 2007). In this regard, it is crucial to plan the workforce both based on quantity and skill mix. With concern to the former, the crucial aspects are both to reduce the large costs of temporarily hired workers, which might, in the long term, justify hiring permanently instead, and also ensure enough production capacity. With concern to the latter, the workers should have the required skills and velocity to perform the relevant tasks (Lee, 2004). The complexity of this planning task is also given by the variability of the demand, which may lead to inaccurate workforce planning (Sadjadi et al., 2011).
Previous studies on workforce planning mainly formulate a simplified problem which neglects several real-life implications. The review paper of De Bruecker et al. (2015) about non-homogenous workforce planning, argues that in literature there are three major pitfalls while developing a workforce planning model. First, there are five effects of a non-homogenous workforce and many researchers neglects some of these effects. Second, many models fail to represent a realistic scenario, for example by not considering uncertainties. Third, the number of research papers with a workforce planning model which is tested on real-life cases is very limited. For instance the model of Techawiboonwong et al. (2006), assigns permanent and temporary workers to workstations based on a deterministic demand and does not consider the non-homogeneous skills of permanent workers. Other papers, such as Bard et al. (2007) and Sadjadi et al. (2011), include the uncertainties of the forecasted demand in their models, but use only one type of workforce. In general, literature lacks of a comprehensive model that considers both stochastic and non-homogeneous workforce.
7
with permanent and temporary workers. In particular, we extend the MPS-T model of Techawiboonwong et al. (2006) with stochasticity in which the above issues are considered. We start from an initial uncertain demand, and based on certain probability distribution we first decide upon permanent workforce. Next, workers are assigned to specific skilled or unskilled workstations and when needed temporary workers are hired. The goal is to minimize the workforce cost and to assign the right workers to the right tasks. We model this particular problem with a two-stage recourse model (Bard et al., 2007). As support of this study, the model is tested by analysing the case of an MTO company and is solved via an industrial solver. The numerical experiments show that a stochastic workforce planning model is cost beneficial compared to a deterministic planning model, especially when the demand variabilities are high. The structure of this paper will be as follows. In the second chapter, literature on workforce planning models is discussed. In the third chapter, the problem is explained in detail and the new model is developed. In the fourth chapter, a description of the case study is given. In the fifth chapter, the validity of the new model will be tested based on the results of the case study. In the sixth chapter, a discussion of the results is given. In the seventh chapter, the main conclusions are drawn and avenues for future research are proposed.
2. Literature background
In this section, an overview of the existing literature about workforce planning models will be given. The first subsection describes the effects of a non-homogenous workforce and how models consider these effects. The second subsection shows the importance of stochasticity and how researchers are considering stochasticity in their model. The third subsection gives the relevance of this research and the research question.
2.1 Non-homogenous workforce
8
non-homogenous workforce could be on the quality of the process, as long as some workers produce products with different quality than others.
One of the first workforce planning model which considers a non-homogenous workforce is developed by Li and Li (2000). In their paper, the workforce exists of professional workers and normal workers; Where, normal workers could only perform unskilled tasks and professional workers could perform every task and where normal workers are less expensive than professional workers. Therefore, a more professional workforce is more flexible against demand fluctuations, but also more expensive. This model is developed to help companies answering two questions, namely whether there are enough professional workers and whether the workforce is flexible enough to meet demand fluctuations. The model used six goals to plan the workforce and is solved by a discrete simulation event.
Most companies have more than two types of workers, for example Norman et al. (2002) consider that every worker could have one or more skills. Also every skill may be characterized by a particular skill level, which entails that workers with a higher skill level make the products faster and better. Training is needed to receive a higher skill level, therefore the wage of a worker remains the same. The objective of this model is meet the demand with the lowest costs. The costs of the model are training costs and scrap costs, which occurs when the quality of the product is not high enough. The objective of minimizing the costs is solved by using a mixed integer linear program.
9
2.2 Uncertainties in workforce planning models
Most workforce planning models made their decisions based on a forecasted demand, however the demand is hardly ever known (De Bruecker et al., 2015). Therefore, a stochastic model should be used to take these uncertainties into account, especially when these uncertainties become bigger.
Bard et al. (2007) is one of the first workforce planning paper which uses a stochastic model to plan the workforce, namely a two-stage recourse model. In this recourse model, the permanent workforce existing of full-time and part-time workers is determined in the first stage and the workers are assigned to specific shifts in the second stage. The model is developed for the planning problem that arises at United States Postal Service. In their problem, they have different shifts which need enough workforce to meet the fluctuated demand. However, every worker has the same working speed and the same skillset, therefore they do not have features in their model associated with a non-homogenous workforce. After the first stage, the company could not hire or fire workers, therefore the workforce is only made flexible against demand variabilities by using overtime hours. The goal of this model is to determine an optimal permanent workforce in the first stage, this workforce should fit every demand scenario in the second stage. The objective is created and solved by a mixed integer linear program.
A year later, Song and Huang (2008) developed also a two-stage recourse model. In their first decision stage, they determine the workforce per department and in the second stage workers could be transferred between departments. Therefore, the big difference between this model and the model of Bard et al. (2007) is that Song and Huang determine the workforce per shift or department instead for the whole company. To objective of this model is to meet the demand with minimizing the workforce costs including the transferring costs of workers between departments. The objective is solved by a discrete event simulation of the demand.
10
2.3 Research relevance and questions
Although many papers developed a workforce planning model with the focus of a non-homogenous workforce, De Bruecker et al. (2015) argue for further research to focus on uncertainties in a non-homogenous workforce planning model. The scope of this research is focussed on the workforce planning for MTO companies with uncertain demand. Current literature regarding this subject is focussed on developing a stochastic model to plan the homogenous workforce and lacks the effects of a non-homogenous workforce. Because, considering the effects of a non-homogenous workforce is essential for a good workforce planning model, further research is required. According to table 1, no specific paper has developed a stochastic model which considers the uncertainties in demand and the effects of a non-homogenous workforce. Such a model could support MTO companies to plan their workforce efficiently. Therefore, the research question of this paper will be as followed.
“How to plan the non-homogenous workforce for make-to-order companies with demand variability?”
In order to answer this main research question, supporting research questions are formulated. First, the effects of a non-homogenous workforce should be explored to plan the workforce for MTO companies. Second, the effects of uncertainties in demand should be considered and therefore stochasticity should be explored. For these reasons the sub questions for this research are:
Sub question 1: What are the effects of a non-homogenous workforce on the workforce planning for make-to-order companies?
11
TABLE 1.OVERVIEW OF RELATED ARTICLES
Article Non-homogenous workforce Making the workforce flexible against demand variabilities
Stochastic Solution technique
Li and Li task restriction, cost Non-homogenous workforce, overtime hours
No Goal programming/ simulation
Norman task efficiency, quality Non-homogenous workforce No Mixed integer linear programming
Techawiboonwong task restriction, cost Temporary workers, overtime No Mixed integer linear programming
Song and Huang - Transferring workers Yes simulation
Bard - Overtime hours Yes Mixed integer linear programming
Sadjadi - - Yes Mixed integer linear programming
Current paper Yes, task efficiency, task restriction, cost, quality
Non-homogenous workforce, Temporary workers, overtime
12
3. Problem description and methodology
The aim of this study is to explore the effects of a non-homogenous workforce and stochastic demand on the workforce planning of MTO companies. After exploring the effects, a new workforce planning model is developed that supports these MTO companies with their workforce problems. First, the problems of a non-homogenous workforce and uncertain demand on the workforce planning of MTO companies will be described. Second, the methodology will be given on solving these problems. Third, the model will be developed to plan the workforce efficiently for MTO companies with a non-homogenous workforce and demand variabilities.
3.1 Problem description
We consider the problem of planning the workforce for a limited period of time n, divided in subperiods. For each subperiod, demand is not deterministic. Furthermore, we consider a set of workstations and some of these workstations need a specific skill. Therefore, the workforce should be non-homogenous to assign the right skilled worker to the right workstation.
There is a starting non-homogenous workforce available, where each worker has a specific working capacity and skillset. There are also temporary workers available to meet the demand variabilities when needed. However, these temporary workers should also have the specific skill to work at a skilled workstation. Therefore the effects of a non-homogenous workforce should be considered for the starting workforce but also for the temporary workforce. The first effect is task restriction, because some workstations need a specific skilled worker and therefore workers need a particular skill to work at these workstations. The second effect is task efficiency, since every type of worker has his own working speed. The third effect is cost, because some type of workers has a higher wage than others. In most cases the cost difference between skilled and unskilled type of workers are high. The fourth effect is quality, because workers have different quality levels at workstations, which means that workers with a higher quality level produce a qualitative higher product.
13
backorder costs and a maximum backorder level should be taken into account. For that reason, it is necessary to meet at least partially the peaks in the demand. Thus, the workforce should be made flexible against these demand variabilities. Due the fact that most MTO companies have union contracts with their permanent workers, it is not possible to change their permanent workforce every time. Therefore, the workforce for MTO companies could be made flexible against demand variabilities in three ways, namely by having a more skilled permanent workforce, using overtime hours and hiring temporary workers.
In order to plan the optimal workforce for MTO Companies, a stochastic model should be developed where the uncertainty of demand, the effects of a non-homogenous workforce and backorders are considered. An example of a production line of a MTO company with a non-homogenous workforce is given in figure 1. This production line has four workstations, where workstation 1,2 and 4 need a specific skill. The company has seven type of workers, which all have a different skillset, working speed, wage and quality level.
Workstation 4 Skill 3 Workstation 1 Skill 1 Workstation 2 Skill 2 Workstation 3 Unskilled
Worker Type 1 Worker type 2 Worker type 3 Worker type 4 Worker type 5 Worker type 6
Skills: 1,2 1,3 2,3 1 2 3 unskilled Production capacity type: high high high medium medium medium low Wage type: high high high medium medium medium low Quality level high high high medium medium medium low
Worker type 7
14
3.2 Methodology
There are several ways to make a model stochastic, for example the recourse model. In a recourse model, some decisions must be made before there is relevant information available about the uncertainty (Higle, 2005). A recourse model could be characterized by its scenario tree, where each scenario problem has its own probability. For example, a manufacturer could have three scenario problems. One with high demand, one with low demand and a scenario with normal demand each with a certain probability. These three scenarios should all be accounted for to solve the recourse model.
A two-stage stochastic model is an example of a recourse model. In a two-stage recourse model, two decisions should be made based on the data available at the time (Shapiro and Philpott, 2007). The first-stage decision, which is also called the “here and now” decision should be made before any information is obtained about the uncertainty. This decision should not respond to any probability function. However, the second-stage decision should respond with the observations of the probability function or data. The goal of this model is to determine a first-stage solution that will leave the second-stage decision in a position to accomplish profitable outcomes for every scenario (Higle, 2005). This research uses a two-stage recourse model to determine in the first stage the optimal permanent workforce and in the second stage the right workers are assigned to the right task and if necessary the manufacturer could hire temporary workers and use overtime hours.
3.3 Model development
15
have traditionally been modelled as linear programs. Seeing that this model has integer and non-integer variables, a mixed integer linear program is modelled with the following notations.
3.4 Notations
3.3.1 Indices
t = time periods in the planning horizon, where t = 1, 2, …. ,T i = type of permanent worker, where i = 1, 2, …. , I
j = workstation, where j= 1, 2, .... , J
m = number of skills, where m= 1, 2, …. , M
l = skill level of temporary worker, where l= 1,2, …, L
3.3.2 Model parameters 𝑆𝑖𝑚 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑘𝑖𝑙𝑙𝑠 𝑚 𝑝𝑜𝑠𝑠𝑒𝑠𝑒𝑑 𝑏𝑦 𝑝𝑒𝑟𝑚𝑎𝑛𝑒𝑛𝑒𝑛𝑡 𝑤𝑜𝑟𝑘𝑒𝑟 𝑡𝑦𝑝𝑒 𝑖 𝑁𝑗𝑚 = 𝑁𝑒𝑐𝑒𝑠𝑠𝑎𝑟𝑦 𝑠𝑘𝑖𝑙𝑙 𝑚 𝑛𝑒𝑒𝑑𝑒𝑑 𝑓𝑜𝑟 𝑤𝑜𝑟𝑘𝑠𝑡𝑎𝑡𝑖𝑜𝑛 𝑗 𝐺𝑖𝑗𝑤= 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑜𝑓 𝑝𝑒𝑟𝑚𝑎𝑛𝑒𝑛𝑡 𝑤𝑜𝑟𝑘𝑒𝑟 𝑡𝑦𝑝𝑒 𝑖 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟 𝑝𝑒𝑟 𝑤𝑜𝑟𝑘𝑠𝑡𝑎𝑡𝑖𝑜𝑛 𝑗 𝐺𝑗𝑙𝑇𝑠= 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑜𝑓 𝑠𝑘𝑖𝑙𝑙𝑒𝑑 𝑡𝑒𝑚𝑝𝑜𝑟𝑎𝑟𝑦 𝑤𝑜𝑟𝑘𝑒𝑟 𝑝𝑒𝑟 𝑠𝑘𝑖𝑙𝑙 𝑙𝑒𝑣𝑒𝑙 𝑙 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟 𝑝𝑒𝑟 𝑤𝑜𝑟𝑘𝑠𝑡𝑎𝑡𝑖𝑜𝑛 𝑗 𝐺𝑗𝑙𝑇𝑢= 𝑝𝑟𝑜𝑑𝑢𝑡𝑖𝑜𝑛 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑜𝑓 𝑢𝑛𝑠𝑘𝑖𝑙𝑙𝑒𝑑 𝑡𝑒𝑚𝑝𝑜𝑟𝑎𝑟𝑦 𝑤𝑜𝑟𝑘𝑒𝑟 𝑝𝑒𝑟 𝑠𝑘𝑖𝑙𝑙 𝑙𝑒𝑣𝑒𝑙 𝑙 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟 𝑝𝑒𝑟 𝑤𝑜𝑟𝑘𝑠𝑡𝑎𝑡𝑖𝑜𝑛 𝑗 𝑞𝑖𝑗𝑤= 𝑞𝑢𝑎𝑙𝑖𝑡𝑦 𝑙𝑒𝑣𝑒𝑙 𝑜𝑓 𝑝𝑒𝑟𝑚𝑎𝑛𝑒𝑛𝑡 𝑤𝑜𝑟𝑘𝑒𝑟 𝑡𝑦𝑝𝑒 𝑖 𝑝𝑒𝑟 𝑤𝑜𝑟𝑘𝑠𝑡𝑎𝑡𝑖𝑜𝑛 𝑗 𝑞𝑗𝑙𝑇𝑠 = 𝑞𝑢𝑎𝑙𝑖𝑡𝑦 𝑙𝑒𝑣𝑒𝑙 𝑜𝑓 𝑠𝑘𝑖𝑙𝑙𝑒𝑑 𝑡𝑒𝑚𝑝𝑜𝑟𝑎𝑟𝑦 𝑤𝑜𝑟𝑘𝑒𝑟 𝑝𝑒𝑟 𝑠𝑘𝑖𝑙𝑙 𝑙𝑒𝑣𝑒𝑙 𝑙 𝑝𝑒𝑟 𝑤𝑜𝑟𝑘𝑠𝑡𝑎𝑡𝑖𝑜𝑛 𝑗 𝑞𝑗𝑙𝑇𝑢 = 𝑞𝑢𝑎𝑙𝑖𝑡𝑦 𝑙𝑒𝑣𝑒𝑙 𝑜𝑓 𝑢𝑛𝑠𝑘𝑖𝑙𝑙𝑒𝑑 𝑡𝑒𝑚𝑝𝑜𝑟𝑎𝑟𝑦 𝑤𝑜𝑟𝑘𝑒𝑟 𝑝𝑒𝑟 𝑠𝑘𝑖𝑙𝑙 𝑙𝑒𝑣𝑒𝑙 𝑙 𝑝𝑒𝑟 𝑤𝑜𝑟𝑘𝑠𝑡𝑎𝑡𝑖𝑜𝑛 𝑗 𝜎𝑗 = 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 𝑝𝑒𝑟𝑚𝑎𝑛𝑒𝑛𝑡 𝑤𝑜𝑟𝑘𝑒𝑟 𝑟𝑒𝑠𝑜𝑢𝑟𝑐𝑒 𝑎𝑡 𝑤𝑜𝑟𝑘𝑠𝑡𝑎𝑡𝑖𝑜𝑛 𝑗 𝑄𝑗= 𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑞𝑢𝑎𝑙𝑖𝑡𝑦 𝑙𝑒𝑣𝑒𝑙 𝑝𝑒𝑟 𝑤𝑜𝑟𝑘𝑠𝑡𝑎𝑡𝑖𝑜𝑛 𝐻 = 𝑟𝑒𝑔𝑢𝑙𝑎𝑟 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 ℎ𝑜𝑢𝑟𝑠 𝑎 = 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑜𝑣𝑒𝑟𝑡𝑖𝑚𝑒 ℎ𝑜𝑢𝑟𝑠 𝑏𝑚𝑎𝑥= 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑎𝑙𝑙𝑜𝑤𝑒𝑑 𝑏𝑎𝑐𝑘𝑜𝑟𝑑𝑒𝑟 𝑙𝑒𝑣𝑒𝑙 3.3.3 Model cost parameters
𝐶𝑖 = 𝑐𝑜𝑠𝑡 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟 𝑜𝑓 𝑢𝑠𝑖𝑛𝑔 𝑤𝑜𝑟𝑘𝑒𝑟 𝑡𝑦𝑝𝑒 𝑖
𝛼𝑢= 𝑐𝑜𝑠𝑡 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟 𝑜𝑓 𝑢𝑠𝑖𝑛𝑔 𝑢𝑛𝑠𝑘𝑖𝑙𝑙𝑒𝑑 𝑡𝑒𝑚𝑝𝑜𝑟𝑎𝑟𝑦 𝑤𝑜𝑟𝑘𝑒𝑟 𝛼𝑠 = 𝑐𝑜𝑠𝑡 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟 𝑜𝑓 𝑢𝑠𝑖𝑛𝑔 𝑠𝑘𝑖𝑙𝑙𝑒𝑑 𝑡𝑒𝑚𝑝𝑜𝑟𝑎𝑟𝑦 𝑤𝑜𝑟𝑘𝑒𝑟
16 𝜃𝑠= 𝑓𝑖𝑟𝑖𝑛𝑔 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑎 𝑠𝑘𝑖𝑙𝑙𝑒𝑑 𝑡𝑒𝑚𝑝𝑜𝑟𝑎𝑟𝑦 𝑤𝑜𝑟𝑘𝑒𝑟 𝜃𝑠= 𝑓𝑖𝑟𝑖𝑛𝑔 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑎𝑛 𝑢𝑛𝑠𝑘𝑖𝑙𝑙𝑒𝑑 𝑡𝑒𝑚𝑝𝑜𝑟𝑎𝑟𝑦 𝑤𝑜𝑟𝑘𝑒𝑟 𝜌𝑖 = 𝑤𝑜𝑟𝑘𝑒𝑟𝑡𝑦𝑝𝑒 𝑖 ℎ𝑜𝑢𝑟𝑙𝑦 𝑜𝑣𝑒𝑟𝑡𝑖𝑚𝑒 𝑐𝑜𝑠𝑡 𝛽 = 𝑏𝑎𝑐𝑘𝑜𝑟𝑑𝑒𝑟 ℎ𝑜𝑙𝑑𝑖𝑛𝑔 𝑐𝑜𝑠𝑡 𝑝𝑒𝑟 𝑖𝑡𝑒𝑚 3.3.4 Random parameter 𝐷̃𝑡𝑗= 𝐷𝑒𝑚𝑎𝑛𝑑 𝑖𝑛 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡 𝑓𝑜𝑟 𝑤𝑜𝑟𝑘𝑠𝑡𝑎𝑡𝑖𝑜𝑛 𝑗
3.3.5 First stage decision variable
𝑊𝑖 = 𝑡𝑜𝑡𝑎𝑙 𝑝𝑒𝑟𝑚𝑎𝑛𝑒𝑛𝑡 𝑤𝑜𝑟𝑘𝑒𝑟𝑠 𝑜𝑓 𝑡𝑦𝑝𝑒 𝑖
3.3.6 Second stage decision variables
𝑅𝑡𝑠= 𝑠𝑘𝑖𝑙𝑙𝑒𝑑 𝑡𝑒𝑚𝑝𝑜𝑟𝑎𝑟𝑦 𝑤𝑜𝑟𝑘𝑒𝑟𝑠 ℎ𝑖𝑟𝑒𝑑 𝑎𝑡 𝑡ℎ𝑒 𝑏𝑒𝑔𝑖𝑛𝑛𝑛𝑖𝑛𝑔 𝑜𝑓 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡 𝑅𝑡𝑢 = 𝑢𝑛𝑠𝑘𝑖𝑙𝑙𝑒𝑑 𝑡𝑒𝑚𝑝𝑜𝑟𝑎𝑟𝑦 𝑤𝑜𝑟𝑘𝑒𝑟𝑠 ℎ𝑖𝑟𝑒𝑑 𝑎𝑡 𝑡ℎ𝑒 𝑏𝑒𝑔𝑖𝑛𝑛𝑛𝑖𝑛𝑔 𝑜𝑓 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡 𝐹𝑡𝑙𝑠 = 𝑠𝑘𝑖𝑙𝑙𝑒𝑑 𝑡𝑒𝑚𝑝𝑜𝑟𝑎𝑟𝑦 𝑤𝑜𝑟𝑘𝑒𝑟𝑠 𝑤𝑖𝑡ℎ 𝑠𝑘𝑖𝑙𝑙 𝑙𝑒𝑣𝑒𝑙 𝑙 𝑓𝑖𝑟𝑒𝑑 𝑎𝑡 𝑡ℎ𝑒 𝑏𝑒𝑔𝑖𝑛𝑛𝑛𝑖𝑛𝑔 𝑜𝑓 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡 𝐹𝑡𝑙𝑢= 𝑢𝑛𝑠𝑘𝑖𝑙𝑙𝑒𝑑 𝑡𝑒𝑚𝑝𝑜𝑟𝑎𝑟𝑦 𝑤𝑜𝑟𝑘𝑒𝑟𝑠 𝑤𝑖𝑡ℎ 𝑠𝑘𝑖𝑙𝑙 𝑙𝑒𝑣𝑒𝑙 𝑙𝑓𝑖𝑟𝑒𝑑 𝑎𝑡 𝑡ℎ𝑒 𝑏𝑒𝑔𝑖𝑛𝑛𝑛𝑖𝑛𝑔 𝑜𝑓 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡 𝑇𝑡𝑙𝑠 = 𝑡𝑜𝑡𝑎𝑙 𝑠𝑘𝑖𝑙𝑙𝑒𝑑 𝑡𝑒𝑚𝑝𝑜𝑟𝑎𝑟𝑦 𝑤𝑜𝑟𝑘𝑒𝑟𝑠 𝑤𝑖𝑡ℎ 𝑠𝑘𝑖𝑙𝑙 𝑙𝑒𝑣𝑒𝑙 𝑙 𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑑 𝑖𝑛 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡 𝑇𝑡𝑙𝑢= 𝑡𝑜𝑡𝑎𝑙 𝑢𝑛𝑠𝑘𝑖𝑙𝑙𝑒𝑑 𝑡𝑒𝑚𝑝𝑜𝑟𝑎𝑟𝑦 𝑤𝑜𝑟𝑘𝑒𝑟𝑠 𝑤𝑖𝑡ℎ 𝑠𝑘𝑖𝑙𝑙 𝑙𝑒𝑣𝑒𝑙 𝑙 𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑑 𝑖𝑛 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡 𝑋𝑖𝑗𝑡𝑝 = 𝑡𝑜𝑡𝑎𝑙 𝑎𝑠𝑠𝑖𝑔𝑛𝑒𝑑 𝑤𝑜𝑟𝑘𝑖𝑛𝑔 ℎ𝑜𝑢𝑟𝑠 𝑜𝑓 𝑤𝑜𝑟𝑘𝑒𝑟 𝑡𝑦𝑝𝑒 𝑖 𝑖𝑛 𝑤𝑜𝑟𝑘𝑠𝑡𝑎𝑡𝑖𝑜𝑛 𝑗 𝑖𝑛 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡 𝑋𝑡𝑗𝑙𝑠 = 𝑡𝑜𝑡𝑎𝑙 𝑎𝑠𝑠𝑖𝑔𝑛𝑒𝑑 𝑤𝑜𝑟𝑘𝑖𝑛𝑔 ℎ𝑜𝑢𝑟𝑠 𝑜𝑓 𝑠𝑘𝑖𝑙𝑙𝑒𝑑 𝑡𝑒𝑚𝑝𝑜𝑟𝑎𝑟𝑦 𝑤𝑜𝑟𝑘𝑒𝑟𝑠 𝑤𝑖𝑡ℎ 𝑠𝑘𝑖𝑙𝑙 𝑙𝑒𝑣𝑒𝑙 𝑙 𝑖𝑛 𝑤𝑜𝑟𝑘𝑠𝑡𝑎𝑡𝑖𝑜𝑛 𝑗 𝑖𝑛 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡 𝑋𝑡𝑗𝑙𝑢 = 𝑡𝑜𝑡𝑎𝑙 𝑎𝑠𝑠𝑖𝑔𝑛𝑒𝑑 𝑤𝑜𝑟𝑘𝑖𝑛𝑔 ℎ𝑜𝑢𝑟𝑠 𝑜𝑓 𝑢𝑛𝑠𝑘𝑖𝑙𝑙𝑒𝑑 𝑡𝑒𝑚𝑝𝑜𝑟𝑎𝑟𝑦 𝑤𝑜𝑟𝑘𝑒𝑟𝑠 𝑤𝑖𝑡ℎ 𝑠𝑘𝑖𝑙𝑙 𝑙𝑒𝑣𝑒𝑙 𝑙 𝑖𝑛 𝑤𝑜𝑟𝑘𝑠𝑡𝑎𝑡𝑖𝑜𝑛 𝑗 𝑖𝑛 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡 𝑂𝑖𝑗𝑡= 𝑎𝑠𝑠𝑖𝑔𝑛𝑒𝑑 𝑜𝑣𝑒𝑟𝑡𝑖𝑚𝑒 ℎ𝑜𝑢𝑟𝑠 𝑓𝑜𝑟 𝑝𝑒𝑟𝑚𝑎𝑛𝑒𝑛𝑡 𝑤𝑜𝑟𝑘𝑒𝑟 𝑡𝑦𝑝𝑒 1 𝑖𝑛 𝑤𝑜𝑟𝑘𝑠𝑡𝑎𝑡𝑖𝑜𝑛 𝑗 𝑖𝑛 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡 𝐵𝑡𝑗 = 𝑏𝑎𝑐𝑘𝑙𝑜𝑔 𝑖𝑛 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡 𝑓𝑜𝑟 𝑤𝑜𝑟𝑘𝑠𝑡𝑎𝑡𝑖𝑜𝑛 𝑗
17
3.5 Model
The objective of this model is to minimize the costs associated with the workforce and backorder holding costs. The first stage objective function (1a) minimize the total permanent workforce costs which include the expected second stage costs. The second stage objective function (2a) minimizes the variable costs associated with the cost of hiring, firing, using temporary workers, using overtime hours and backorders.
18 (1 − 𝜎𝑗) ∑𝐼𝑖=1(𝑋𝑖𝑗𝑡𝑝 + 𝑂𝑖𝑗𝑡)≥ 𝜎𝑗∑𝐿𝑙=1(𝑋𝑡𝑗𝑙𝑠 + 𝑋𝑡𝑗𝑙𝑢 ) ∀t,j (2g) ∑𝐿𝑙=1𝑇𝑡𝑙𝑠 = ∑𝐿𝑙=1(𝑇𝑡−1𝑙𝑠 + 𝑅𝑡𝑠− 𝐹𝑡𝑙𝑠) ∀t (2h) ∑𝐿𝑙=1𝑇𝑡𝑙𝑢 = ∑𝐿𝑙=1(𝑇𝑡−1𝑙𝑢 + 𝑅𝑡𝑢 − 𝐹𝑡𝑙𝑢) ∀t (2i) 𝑇𝑡𝑙𝑠 ≥ 1 𝐻∑ 𝑋𝑡𝑗𝑙 𝑠 𝐽 𝑗=1 ∀t,l (2j) 𝑇𝑡𝑙𝑢 ≥ 1 𝐻∑ 𝑋𝑡𝑗𝑙 𝑢 𝐽 𝑗=1 ∀t,l (2k) 𝑇𝑡𝑙+1𝑠 = 𝑇𝑡−1𝑙𝑠 − 𝐹𝑡𝑙𝑠 ∀t,l (2l) 𝑇𝑡𝑙+1𝑢 = 𝑇𝑡−1𝑙𝑢 − 𝐹𝑡𝑙𝑢 ∀t,l (2m) 𝑅𝑡𝑠 = 𝑇𝑡1𝑠 ∀t (2n) 𝑅𝑡𝑢 = 𝑇𝑡1𝑢 ∀t (2o) 𝑄𝑗 ≤ ∑ 1 𝐻𝑋𝑖𝑗𝑡 𝑝 𝑞𝑖𝑗𝑤 𝐼 𝑖=1 + ∑ 1 𝐻𝑋𝑡𝑗𝑙 𝑠 𝑞 𝑗𝑙𝑇𝑠 𝐽 𝑗=1 + ∑ 1 𝐻𝑋𝑡𝑗𝑙 𝑢 𝑞 𝑗𝑙𝑇𝑢 𝐽 𝑗=1 ∀t,j (2p)
19
which is set in constraints (2e) and 2(f). Some workstations need a higher percentage of permanent workers to perform the task efficiently. Therefore, every workstation has its own minimum percentage of permanent workers. Constraint (2g) ensures that this ratio will not be exceeded. Constraints (2h) and (2i) are so called workforce balance constraints, which keep track of the number of temporary workers are currently employed. The next two constraints (2j – 2k) are labour capacity constraints. These constraints ensure that current employed temporary workers do not work more than the regular production hours. Constraints (2l) and (2m) make sure that temporary workers who worked already in the previous period get a higher learning level. A higher learning level means that they have a higher production capacity. The two constraints (2n) and (2o) ensure that every hired temporary worker starts at learning level 1. The last constraint (2p) ensures that the workers at a workstation together have the right quality level to produce the products with the minimal quality.
4. Case study
Many researchers fail to test and validate their workforce planning model on case studies, hence this study test the developed workforce planning model on a MTO company. Therefore, the model will be tested on real-life workforce problems. In the first subsection, the case description is given and in the second subsection the data of the case study is provided.
4.1 Case description
20
working speed per workstation. Moreover, a beginning temporary worker has a different working capacity then a temporary worker who already worked in previous periods, because there is a learning curve for temporary workers. Cost is also an effect in this company, where some type of workers has a higher wage then other type of workers. Especially, the different wage between skilled and unskilled workers are big. Quality, the last effect is not present in this case study, because the company does not have a particular quality level for the cars. Therefore the quality levels will not be considered in this case study. Furthermore, the case company does not know how many cars there are arriving and flow through the production line. As a result, the workforce should be made flexible against these variabilities by using a more skilled permanent workforce, overtime hours and temporary workers.
FIGURE 2.THE NON-HOMOGENOUS WORKFORCE OF THE CASE COMPANY
4.2 Case data
During the case study qualitative data and quantitative data are obtained. Qualitative data such as cost parameters are obtained by meetings with the operation manager and financial director. Quantitative date are obtained by historical data to determine the distribution of the demand. The case study parameters are shown in table 2, which have been examined for validation by the director of the case company.
Workstation 4 Photo studio Workstation 1 Entry Workstation 2 Technical service Workstation 3 Washing
Skill 1 Skill 2 Unskilled Skill 3
Cars
Worker Type 1 Worker type 2 Worker type 3 Worker type 4 Skilled Unskilled Skills: 1 1,2 3 unskilled 1,2,3 unskilled Production capacity type: 1 2 3 4 5 6 Wage type: 1 2 3 4 5 6
21 Case study parameters
T = 6 periods (1 period is one month) I = 4 types of workers
J = 4 workstations M = 3 types of skills
L = 2 skill levels Sim = [[1, 0, 0], [1, 1, 0], [0, 0, 1], [0, 0, 0]] Njm =[[1, 0, 0],[0, 1, 0],[0, 0, 0],[0, 0, 1]] Gwij = [[4.25, 0, 9, 0],[4, 5, 0, 0],[0, 0, 0, 3.3],[0, 0, 10, 0]] Gtsjl =[[4, 4.5, 0, 3], [4.25, 5, 0, 3.3]] Gtujl = [[0, 0, 9, 0], [0, 0, 10, 0]] σj = [0.7, 0.8, 0.5, 0.8] h = 178 a = 18 bmax = 500 Ci =[11.57, 14.99, 14.99, 10.02] αu =15 αs =20 δu =0 δs =0 θu =5 θs =10 ρ =[17.36, 22.49, 22.49, 15.03] β = 8
Dj = 2000 with P = 0,5 for every workstation Dj = 3000 with P = 0,5 for every workstation
TABLE 2.CASE STUDY PARAMETERS
22
5. Results
The results of the case study and the validation of the model are described in this section. In the first subsection, the results of the case study are given. The second subsection includes the verification and validation process of the model. To validate the model, the behaviour of the model is studied under three different parameters. First the demand parameter will change, next the allowable ratio of permanent workers will change and last the cost of temporary workers changes. Finally, a summary is given on the behaviour of the model. The model is solved via an industrial solver called CPLEX, however the solution time of a model with integer variables could be very long. For this reason, the relative mix integer program gap tolerance is set at 1%, which means that the solution will be in a range of 1% of the optimal solution. This tolerance will decrease the solution time enormously.
5.1 Case results
We consider in this study a single instance and vary several parameters. These parameters gave the following results. The permanent workforce of the company should be 3 workers of type 1, 3 workers of type 2, 4 workers of type 3 and 1 worker of type 4. The total costs of the permanent workforce are divided by normal and overtime costs. Also, the total temporary costs are divided by two costs, namely the cost of unskilled and skilled temporary workers. The last cost factor in this model are backorder costs. However, the total costs of the backorders are in this case study €10,38 and therefore the backorder costs are negligible in this study. So, the total workforce costs are €194.453,36, which are shown in table 3.
23
of the case study. With a demand of 2500 the permanent workforce is 4 workers of type 1, 3 workers of type 2, 4 workers of type 3 and one worker of type 4. Now, the model is calculated with this fixed permanent workforce. This resulted in a total workforce cost of €195.240,93. Therefore, the VSS is in this case €787,57 per 6 periods, which means that the company only saves €131,- per period by using a stochastic model. Therefore, it could be argued that in this case a stochastic model is not necessary needed to plan the workforce.
5.2 Verification and validation
The results of the case study and the performance measures of the model are meaningless if the model is not a good representation of the real system. There are two steps of judging how good a model represent the real system (Hillston, 2003). First, the model should implement the assumptions correctly (verification). Second, the assumptions should been made reasonable with respect to the real system (validation). There are several ways to check the verification of a model, however in this study a continuity and degeneracy test is conducted to check the assumptions of the model. With a continuity test, the model is tested on its continuous. In other words, the output of a model should change a little when the input of the model (normal parameters) changes a bit (Hillston, 2003). In this case, the normal parameters of the hiring and firing costs and the maximum overtime hours are changed, which resulted in a stable output. A degeneracy test is the opposite of the continuity test. In this test the model should change a lot when extreme parameters are changed a bit (Hilston, 2003). In this case the production capacity of permanent workers are changed slightly which resulted in a big change of the output. According to these test, it is argued that the model implements the assumptions correctly.
Case study results
Total workforce costs 194.453,36
Total permanent workforce costs 165.318,69 Total temporary workforce costs 29.134,67
Normal costs 158.040,96 Unskilled temporary workforce costs 7.796,25
Overtime costs 7.277,73 Skilled temporary workforce costs 21.328,04
Backorder holding costs 10,38
Performance measure Total savings Savings per period Savings percentage
EVPI 16.230,33 2700,- 9%
VSS 787,57 131,- 0.4%
24
There are only three ways to check the validation of a model according to Hilston (2003), namely expert intuition, real system measurements and theoretical analysis. With expert intuition, the model should be examined by someone other than the modeller, who should have experiences in modelling and knowledge about the system. However, an expert is not found in this research. With real system measurements, the model is compared with a real system and is the most reliable way of validation. Yet, this is often not possible because the real system does not exist or it is too expensive to carry out the measurements. In this study, the real system does not exist and therefore the last way to validate a model should be undertaken. With theoretical analysis, the model should behave correctly based on theoretical laws. In this research, two theoretical laws are tested. First, the workforce costs are positive related to the demand, which means that the costs increase when the demand increases. Second, the use of temporary workers is negative related to the hour wages of temporary workers, which means that the model should use more permanent workers when the hour wage of temporary workers increases. Both theoretical laws are tested here below.
5.3 Tweaking demand parameters
25
FIGURE 3.WORKFORCE COSTS AS RELATED TO THE HIGHEST DEMAND PARAMETER
Figure 4 illustrates the performance measures of the stochastic model when the highest demand parameter changes. The EVPI rises linearly, because the total workforce costs of the stochastic model is also rising linear. The VSS is relatively high, as the fixed permanent workforce of the deterministic demand of the case study is too big for the first two demands. After the first two demands, the VSS becomes almost zero, because the fixed permanent workforce is almost optimal for this kind of demands. On the other hand, when the demand increases the permanent workforce is too low. Hence, more temporary workers must be hired to fulfil the demand until a certain point that the ratio of minimum permanent workers are exceeded. After this point, a company cannot use more temporary workers, which results in backorders. These backorders pile up and therefore cost increase significantly. Therefore, the VSS becomes really high.
FIGURE 4.PERFORMANCE MEASURES AS RELATED TO THE HIGHEST DEMAND PARAMETER
26
Second, the lowest demand parameter will be changed by steps of 10 percent starting from 60 to 140 percent. Figure 5 shows the results of this test. As shown the total costs of the workforce is changing a lot by changing the highest demand parameter, while it is slightly changing with the lowest demand parameter. Despite the lower demand, the costs will not change, as the case company still requires the same amount of workers for handling the highest demand parameter. The company must hire more permanent workers in cases where the permanent workforce cannot handle the lower demand. Hence, the permanent and total workforce costs are rising. It is shown, that costs of permanent and total workforce are rising after the baseline. Further, it is expected that the permanent workforce cost will decrease when the lowest demand parameter reach a point where the cost of using temporary workers is less expensive than having a larger permanent workforce. However, this point is not reached in figure 5, because the minimal allowable ratio of permanent workers will be exceeded, which will be explained more in the next section.
FIGURE 5.WORKFORCE COSTS AS RELATED TO THE LOWEST DEMAND PARAMETER
EVPI is decreasing linearly if the lowest demand parameter becomes higher (figure 6). Based on the two tests of the demand parameters, it is clear that the EVPI becomes higher, when the diversity of the demand increases and therefore is related to this diversity. The VSS is only changing when the lowest demand parameter becomes higher than the deterministic demand of 2500 in the case study. In this case, a higher permanent workforce is needed.
27
FIGURE 6.PERFORMANCE MEASURES AS RELATED TO THE LOWEST DEMAND PARAMETER
5.4 Tweaking the allowable ratio of permanent workers
The second test in this research is changing the allowable ratio of permanent workers per workstation with steps of 10 percent, where a lower ratio means that the manufacturer could use more temporary workers than with a higher ratio. The ratio will start and end at a minimum percentage of 40 till 90 percent at workstation 1, 50 till 100 percent at workstation 2, 20 till 70 percent of workstation 3 and 50 till 100 percent at workstation 4. The results of the costs are shown in figure 7.
FIGURE 7.WORKFORCE COSTS AS RELATED TO THE ALLOWABLE RATIO OF PERMANENT WORKERS PER WORKSTATION
0,00 5.000,00 10.000,00 15.000,00 20.000,00 25.000,00 30.000,00 35.000,00 40.000,00 45.000,00 50.000,00 CO ST S A V IN G S (€) LOWEST DEMAND EVPI VSS 0,00 50.000,00 100.000,00 150.000,00 200.000,00 250.000,00 0 , 4 0 , 5 0 , 2 0 , 5 0 , 5 0 , 6 , 0 , 4 0 , 6 0 , 6 0 , 7 0 , 4 0 , 7 0 , 7 0 , 8 0 , 5 0 , 8 0 , 8 0 , 9 0 , 6 0 , 9 0 , 9 1 0 , 7 1 W O R KF O R CE CO ST S (€)
MINIMUM LEVEL OF PERMANENT WORKERS PER WORKSTATION
28
In this test, the total workforce costs will rise when the ratio reach a particular point. At this (threshold) point the ratio becomes a constraint. In this case, a workstation needs more permanent workers than optimal. Looking at figure 7, it is stated that the ratio becomes a constraint after the percentage of 70 at workstation 1, 80 at workstation 2, 50 at workstation 3 and 80 at workstation 4. After this threshold point, the manufacturer needs to hire more permanent workers which result in increased total workforce costs.
FIGURE 8.PERFORMANCE MEASURES AS RELATED TO ALLOWABLE RATIO OF PERMANENT WORKERS PER WORKSTATION The EVPI and the VSS only change after the threshold point, where both measures increase after this point. In figure 8 it is shown that the VSS is increasing significantly after the threshold point. Thus, it could be said that a manufacturer should take stochasticity into account when a high ratio is established.
5.5 Cost of temporary workers
The last two tests performed in this research are changing the cost parameters of temporary workers (α) with and without the allowable ratio of permanent workers per workstation. Parameter α is changed by steps of 5 percent starting from 70 to 120 percent. The first results of the test with the ratio is shown in figure 9. Two effects occur when the hour wage of a temporary worker decreases. First, the total workforce costs will decrease in a straight line, which is normal when a cost factor decreases. The second effect happens, when the cost factor meets a point that using temporary workers saves more money than having one extra permanent
0,00 5.000,00 10.000,00 15.000,00 20.000,00 25.000,00 30.000,00 35.000,00 40.000,00 45.000,00 0 , 4 0 , 5 0 , 2 0 , 5 0 , 5 0 , 6 , 0 , 4 0 , 6 0 , 6 0 , 7 0 , 4 0 , 7 0 , 7 0 , 8 0 , 5 0 , 8 0 , 8 0 , 9 0 , 6 0 , 9 0 , 9 1 0 , 7 1 CO ST S A V IN G S (€)
MINIMUM RATIO OF PERMANENT WORKERS PER WORKSTATION,
29
worker. In the case this point is met, the manufacturer should fire a permanent worker and use more temporary workers. Consequently, the permanent workforce costs decrease and the temporary workforce costs increase. This effect happens at α=105 percent. In figure 7 it occurs only once, because the hour wage is still too high to meet the second point or the allowable ratio is too high. Hence, the last test without this ratio has followed and the result of this test are given by figure 10. According to these results, the allowable ratio withhold the manufacturer to use more temporary workers even if it is cheaper and it starts around 90 percent of the hour wage of a temporary worker.
FIGURE 9.WORKFORCE COSTS WITH THE ALLOWABLE RATIO AS RELATED TO HOUR WAGE OF TEMPORARY WORKERS
FIGURE 10.WORKFORCE COSTS WITHOUT THE ALLOWABLE RATIO AS RELATED TO HOUR WAGE OF TEMPORARY WORKERS
0,00 50.000,00 100.000,00 150.000,00 200.000,00 250.000,00 7 0 % 7 5 % 8 0 % 8 5 % 9 0 % 9 5 % 1 0 0 % 1 0 5 % 1 1 0 % 1 1 5 % 1 2 0 % W O R KF O R CE CO ST S (€)
HOUR WAGE OF TEMPORARY WORKERS
TC TPWC TTWC 0,00 50.000,00 100.000,00 150.000,00 200.000,00 250.000,00 7 0 % 7 5 % 8 0 % 8 5 % 9 0 % 9 5 % 1 0 0 % 1 0 5 % 1 1 0 % 1 1 5 % 1 2 0 % W O R KF O R CE CO ST S (€)
HOURWAGE OF TEMPORARY WORKERS
30
The performance measures of the last two tests are shown in figure 11 and 12. In cases where the case company maintains an allowable ratio, the VSS is increasing a little and the EPVI is decreasing when the cost parameter α is decreasing (figure 11). Therefore, it is argued that this model performs better when the cost of using a temporary worker is reduced. Especially, if there is no allowable ratio of permanent workers, where the VSS is increasing a lot and the EPVI is almost decreasing to zero (figure 12).
FIGURE 11.PERFORMANCE MEASURES WITH ALLOWABLE RATIO AS RELATED TO HOUR WAGE OF TEMPORARY WORKERS
FIGURE 12.PERFORMANCE MEASURES WITHOUT ALLOWABLE RATIO AS RELATED TO HOUR WAGE OF TEMPORARY WORKERS
0,00 5.000,00 10.000,00 15.000,00 20.000,00 25.000,00 7 0 % 7 5 % 8 0 % 8 5 % 9 0 % 9 5 % 1 0 0 % 1 0 5 % 1 1 0 % 1 1 5 % 1 2 0 % CO ST S A V IN G S (€)
HOURWAGE OF TEMPORARY WORKERS
EVPI VSS 0,00 5.000,00 10.000,00 15.000,00 20.000,00 25.000,00 7 0 % 7 5 % 8 0 % 8 5 % 9 0 % 9 5 % 1 0 0 % 1 0 5 % 1 1 0 % 1 1 5 % 1 2 0 % CO ST S A V IN G S (€)
HOURWAGE OF TEMPORARY WORKERS
31
5.6 Summary of the results
32
6. Discussion
The aim of this paper was to plan the workforce for manufacturers in the MTO industry which have a non-homogenous workforce, uncertain demand and backorders. This study provides a new model that supports manufacturers with these problems to plan their workforce. It has been found, that it is very important to determine the right permanent workforce and use a reasonable number of temporary workers. Furthermore, it is found that the amount of permanent workers is changing when the demand changes. Therefore, it is vital for manufacturers to keep the fluctuations into account when manufacturers determine their permanent workforce. However, the cost savings of using this stochastic model instead of a deterministic model depend heavily on the diversity of the demand. Moreover, the hour wage of temporary workers and the threshold point of the allowable ratio of permanent workers are important factors for the outcomes of this model. In settings, where a manufacturer has established a low threshold point and the costs of using temporary workers are low, the cost savings of this stochastic model will increase compared to a deterministic model. Furthermore, a MTO manufacturer with a homogenous workforce should always use a model that considers all the effects of a non-homogenous workforce and the effects of fluctuated and uncertain demand. The use of a stochastic model or a deterministic model depends heavily on the diversity of the uncertain demand.
33
7. Conclusions
This research aims to fill the literature gap with concern to planning a non-homogenous workforce of MTO manufacturers under demand variability. A new two-stage stochastic model was developed to plan the non-homogenous workforce. This new model considers the main effects of a non-homogenous workforce and use overtime hours and temporary workers to make the workforce flexible against demand variabilities. The results are very promising for MTO manufacturers, where they could save up 5 percent of their total workforce cost when they use temporary workers to make their workforce flexible. However, the value of the stochastic model depends heavily on the diversity of the fluctuated and uncertain demand. Anyway, a MTO company should use a stochastic model when the diversity of the fluctuated and uncertain demand is high.
34
8. References
Attia, E. A., Duquenne, P., & Le-Lann, J. M. (2014). Considering skills evolutions in multi-skilled workforce allocation with flexible working hours. International Journal of Production Research, 52(15), 4548-4573.
Bard, J. F., Morton, D. P., & Wang, Y. M. (2007). Workforce planning at USPS mail processing and distribution centers using stochastic optimization. Annals of Operations Research, 155(1), 51-78.
Chen, C. S., Mestry, S., Damodaran, P., & Wang, C. (2009). The capacity planning problem in make-to-order enterprises. Mathematical and computer modelling, 50(9-10), 1461-1473.
De Bruecker, P., Van den Bergh, J., Beliën, J., & Demeulemeester, E. (2015). Workforce planning incorporating skills: State of the art. European Journal of Operational
Research, 243(1), 1-16.
Higle, J. L. (2005). Stochastic programming: Optimization when uncertainty matters. Tutorials in operations research, 3053.
Hillston, J. (2003). Model validation and verification. Edinburgh: University of Edinburgh.
Lee, T. (2004). The effect of workers with different capabilities on customer delay. Computers and Operations Research, 31(3), 359-381.
Li, N., & Li, L. X. (2000). Modeling staffing flexibility: A case of China. European Journal of Operational Research, 124(2), 255-266.
Norman, B. A., Tharmmaphornphilas, W., Needy, K. L., Bidanda, B., & Warner, R. C. (2002). Worker assignment in cellular manufacturing considering technical and human skills. International Journal of Production Research, 40(6), 1479-1492.
Sadjadi, S. J., Soltani, R., Izadkhah, M., Saberian, F., & Darayi, M. (2011). A new nonlinear stochastic staff scheduling model. Scientia Iranica, 18(3), 699-710.
35
Sillekens, T., Koberstein, A., & Suhl, L. (2011). Aggregate production planning in the
automotive industry with special consideration of workforce flexibility. International Journal of Production Research, 49(17), 5055-5078.
Song, H., & Huang, H. C. (2008). A successive convex approximation method for multistage workforce capacity planning problem with turnover. European Journal of Operational Research, 188(1), 29-48.
Techawiboonwong, A., Yenradee, P., & Das, S. K. (2006). A master scheduling model with skilled and unskilled temporary workers. International Journal of Production
Economics, 103(2), 798-809.
Voss, C., Tsikriktsis, N., & Frohlich, M. (2002). Case research in operations management. International Journal of Operations & Production Management, 22(2), 195–219.
