Bid Forecasting in Public Procurement

95  Download (0)

Full text

(1)

IN THE FIELD OF TECHNOLOGY DEGREE PROJECT

INDUSTRIAL ENGINEERING AND MANAGEMENT AND THE MAIN FIELD OF STUDY

INDUSTRIAL MANAGEMENT, SECOND CYCLE, 30 CREDITS STOCKHOLM SWEDEN 2019,

Bid Forecasting in Public Procurement

KARIM STITI

SHIH JUNG YAPE

(2)

This page is intentionally left blank

(3)

Bid Forecasting in Public Procurement

by

Karim Stiti Shih Jung Yape

Master of Science Thesis TRITA-ITM-EX 2019:446 KTH Industrial Engineering and Management

Industrial Management

(4)

Budgivningsmodeller i Offentliga Upphandlingar

av

Karim Stiti Shih Jung Yape

Examensarbete TRITA-ITM-EX 2019:446 KTH Industriell teknik och management

Industriell ekonomi och organisation

(5)

Keywords: Bidding in public procurement, Count data regression, Economically most

advantageous tenders, Lowest price tenders, Machine learning, Multiple linear regression, Non- Master of Science Thesis

TRITA-ITM-EX 2019:446

Abstract

Public procurement amounts to a significant part of Sweden's GDP. Nevertheless, it is an overlooked sector characterized by low digitization and inefficient competition where bids are not submitted based on proper mathematical tools. This Thesis seeks to create a structured approach to bidding in cleaning services by determining factors affecting the participation and pricing decision of potential buyers. Furthermore, we assess price prediction by comparing multiple linear regression models (MLR) to support vector regression (SVR). In line with previous research in the construction sector, we find significance for several factors such as project duration, location and type of contract on the participation decision in the cleaning sector. One notable deviant is that we do not find contract size to have an impact on the pricing decision. Surprisingly, the performance of MLR are comparable to more advanced SVR models. Stochastic dominance tests on price performance concludes that experienced bidders perform better than their inexperienced counterparts and companies place more competitive bids in lowest price tenders compared to economically most advantageous tenders (EMAT) indicating that EMAT tenders are regarded as unstructured. However, no significance is found for larger actors performing better in bidding than smaller companies.

Examiner

Pontus Braunerhjelm

Comissioner

Tendium AB

Supervisor

Almas Heshmati

Contact person

Farzad Khoshnoud

Approved

2019-06-14

Bid Forecasting in Public Procurement

Karim Stiti Shih Jung Yape

(6)

Examensarbete TRITA-ITM-EX 2019:446

Godkänt

2019-06-14

Sammanställning

Examinator

Pontus Braunerhjelm

lm

Uppdragsgivare

Tendium AB

Handledare

Almas Heshmati

Kontaktperson

Farzad Khoshnoud Budgivningmodeller i Offentliga Upphandlingar

Karim Stiti Shih Jung Yape

Offentliga upphandlingar utgör en signifikant del av Sveriges BNP. Trots detta är det en förbisedd sektor som karakteriseras av låg digitalisering och ineffektiv konkurrens där bud läggs baserat på intuition snarare än matematiska modeller. Denna avhandling ämnar skapa ett strukturerat tillvägagångssätt för budgivning inom städsektorn genom att bestämma faktorer som påverkar deltagande och prissättning. Vidare undersöker vi prisprediktionsmodeller genom att jämföra multipel linjära regressionsmodeller med en maskininlärningsmetod benämnd support vector regression. I enlighet med tidigare forskning i byggindustrin finner vi att flera faktorer som typ av kontrakt, projekttid och kontraktsplats har en statistisk signifikant påverkan på deltagande i kontrakt i städindustrin.

En anmärkningsvärd skillnad är att kontraktsvärdet inte påverkar prissättning som tidigare forskning visat i andra områden. För prisprediktionen är det överraskande att den enklare linjära regressionsmodellen presterar jämlikt till den mer avancerade maskininlärningsmodellen. Stokastisk dominanstest visar att erfarna företag har en bättre precision i sin budgivning än mindre erfarna företag. Därtill lägger företag överlag mer konkurrenskraftiga bud i kontrakt där kvalitetsaspekter tas i beaktning utöver priset. Vilket kan indikera att budgivare upplever dessa kontrakt som mindre strukturerade. Däremot finner vi inger signifikant skillnad mellan större och mindre företag i denna bemärkning.

(7)

This page is intentionally left blank

(8)

Acknowledgements

We would like to express our deep and sincere gratitude to our thesis advisor Pro- fessor Almas Heshmati for his continuous support and guidance within the field of statistical analysis. His broad experience and expertise was valuable for us through different part of our thesis. We could not have imagined a more suitable candi- date in counselling us than Professor Almas. Beside our advisor, we would also like to thank the people who helped us in Tendium, mainly Farzad Khousnoud, Peter Vesterberg and Tim Lachmann. Together with Farzad we developed the idea of forecasting public procurement in the Swedish cleaning industry. Peter and Tim provided insight in data handling and model constructions which was helpful for the end result.

Finally, we gratefully acknowledge the support and continuous love of our parents.

Their influence throughout our education is what have driven our passion and the completion of this thesis.

Jung Yape and Karim Stiti Stockholm, June 2019

(9)

Table of Contents

1 Introduction 1

1.1 Background . . . 1

1.2 Purpose . . . 3

1.3 Problem Formulation . . . 3

1.4 Sustainability Aspect . . . 4

1.5 Scope . . . 4

1.6 Report Structure . . . 5

2 Previous Research in Sealed Bid Auctions 6 2.1 Measuring Tender Participation . . . 6

2.1.1 Probability of Winning Tenders . . . 6

2.1.2 Determining Number of Participants in Tenders . . . 7

2.1.3 Factors Influencing the Bid/No Bid Decision . . . 8

2.2 Price Prediction Models in Sealed Bid Auctions . . . 9

2.2.1 Predicting Bid Prices Using Statistical Models and Machine Learning . . . 10

2.3 Assessing EMAT tenders . . . 12

2.4 Green Public Procurement - Environmental Quality Criteria . . . 13

3 Empirical Framework 16 3.1 Multiple Linear Regression Analysis . . . 16

3.2 Model Validation . . . 17

3.2.1 Multicollinearity . . . 17

3.2.2 Residual Diagnostics . . . 18

3.2.3 Variable Transforms . . . 19

3.3 Model Selection . . . 20

3.3.1 Selective Criteria . . . 20

3.3.2 K-fold Cross-Validation . . . 21

3.4 Poisson Regression Models . . . 21

3.4.1 Negative Binomial Regression . . . 23

3.5 Support Vector Regression . . . 25

3.6 Probit Regression . . . 26

3.7 Stochastic Dominance . . . 27

3.8 Confidence Intervals Using Non-Parametric Bootstrap . . . 27

3.9 Joint Distribution Function with Position Performance . . . 29

3.10 Other Statistical Models . . . 30

3.10.1 Chi-Square Test . . . 30

(10)

4 Data and Methodology 31

4.1 Data Collection and Limitations . . . 31

4.2 Variable Description . . . 32

4.3 Competitors Affect On Price . . . 34

4.4 Assessing Tender Participants . . . 34

4.5 Predict Price Performance . . . 36

4.5.1 Comparing Multiple Linear Regression and Support Vector Regression . . . 36

4.5.2 Inference for experience, size and tendering method with Stochas- tic Dominance . . . 38

4.6 Assessing Quality Performance . . . 38

5 Results 40 5.1 Bid/no Bid Decision . . . 40

5.1.1 Number of Bidder’s Effect on Price . . . 40

5.1.2 Fitting a Distribution the Participation Data . . . 41

5.1.3 Factors Contributing to Participants With Regression . . . 45

5.1.4 Impact of Environmental Criteria on Participation . . . 51

5.1.5 Bid/No Bid Decision for Individual Participants . . . 51

5.2 Predicting Price . . . 53

5.2.1 Factors Affecting Pricing . . . 53

5.2.2 Comparing SVR And MLR Models for Price Prediction . . . . 54

5.2.3 Price Range with Non-parametric Bootstrap . . . 56

5.2.4 Stochastic Dominance for Spread . . . 58

5.2.5 Price Performance with Spread Variable . . . 60

5.3 Competitor Performance in EMAT tenders . . . 61

6 Analysis of Results 63 6.1 Number of Competitors . . . 63

6.2 Bid/No Bid Logistic Regression . . . 66

6.3 Predicting Price . . . 66

6.3.1 Stochastic Dominance and Non-Parametric Bootstrap Analysis 68 6.4 Quantifying Quality . . . 69

7 Conclusions 71 8 Suggestions for Future Research 73 Bibliography 74 Appendix 80 A. Literature Review . . . 80

(11)

B. Bid/No-Bid Probit Regression . . . 81 C. Diagnostics . . . 82 D. Price Prediction . . . 84

(12)

1 Introduction

In this section public procurement auctions are introduced, the objectives and im- plications of our thesis are described, the scope explained and finally we detail the report structure.

1.1 Background

The purchase of goods and services by a public organization from external sources is termed public procurement. It has a sizeable affect on world trade amounting to more than 1.3 trillion euro each year. In EU it accounts for around 16 % of GDP and during 2016 the EU put in new rules intended to open up the public procure- ment market within Europe. The stated goal was to streamline processes and make it easier for smaller companies to participate in the market (European Commission 2017). The total value of public procurement contracts in Sweden was estimated to 683 billion SEK which is a 17 % share of GDP. In 2017, 18525 contracts were announced and 39 % of those were in the construction sector (Upphandlingsmyn- digheten 2019).

Public procurement contracts are awarded by Swedish local government in a process known as sealed bid auctions meaning no bidder knows what the other participants have bid (Upphandlingsmyndigheten 2019). This is a broadly used auction method not only in public procurement but also in private procurement, especially in the construction sector (Brook 2016).

There has been a steady decline from an already low level of the average number of participants in public procurement auctions in Sweden, in particular the cleaning industry. Today, there are on average 4.3 bidders per contract. It is the goal of the Swedish government to increase competitiveness and make public procurement more efficient (Upphandlingsmyndigheten 2019). The market is plagued by laws that make the process static and inefficient which subsequently leads to inexperienced parties winning auctions. Contracts where the winner is determined by combining an assessment of quality with price have also not been effective (Ink¨opsr˚adet 2016).

(13)

The bidding process in cleaning services in particular has been characterized by bids under the recommended price winning. As a result, serious actors are electing not to participate (Fastighetsfolket 2017). Part of the improvement process is to evaluate how artificial intelligence can be used by the government in public procurement to increase security and improve processing time. In addition, they aim to make the market more transparent by providing access to more data (Regeringskansliet 2019).

We perform our analysis in this thesis by drawing on both existing literature directly from cleaning in public procurement and the construction industry. We believe this paper contributes to the existing literature in several ways. Firstly, it provides an updated look at factors affecting the bid/no bid and pricing decision of bidders in public procurement cleaning using factors initially discovered in the construction industry. Secondly, we find that linear models perform in line to more advanced support vector regressions. Thirdly, using models that have not been applied to public procurement before we show that the experience of the bidder is more im- portant when it comes to performance in tenders than company size. This follows as more frequent bidders perform better than less frequent bidders and have smaller confidence intervals in their bids; indicating that with experience comes structure in bidding. Finally, we show companies tend to bid more evenly in lowest price tenders compared to EMAT tenders. All together, our results show that one can draw infer- ence of bidding behaviour with straightforward mathematical models and as more structured data is made available with time a complete bid forecasting model can be built.

(14)

1.2 Purpose

The Swedish Upphandlingsmyndigheten is hoping to streamline and digitize the public procurement sector in general and the cleaning services in particular. It is a sector plagued by low competition and inefficiency. Our thesis seeks to understand and improve the low participation rate in cleaning services’ tenders by contributing to digitizing the sector. We do this by evaluating pricing models and participa- tion models that will make the bidding easier and more transparent. In addition, considering the perceived problems with economically most advantageous tenders (EMAT), we also intend to study whether there is a difference in how companies perform in EMAT in relation to lowest price tenders.

1.3 Problem Formulation

Considering the industry inefficiencies, an important question to pose is whether there is in fact any structure to the bidding behavior of participants or if they act randomly. This thesis will seek to understand whether models can be developed for the behavior of competitors within the Swedish cleaning service industry and in that case what models are best suited. The approach to these problems is to divide them into two main areas of study: The bid/no bid decision of competitors and predicting bid prices. To do this we must first determine factors that affect the decision-making of companies in the sector, then we will explore whether simple linear regression models or more advanced machine learning methods perform better.

Research Question 1 (RQ1): What factors contribute to companies bidding in public procurement?

Research Question 2 (RQ2): What factors affect the pricing decision in public procurement?

(15)

Research Question 3 (RQ3): Are multiple linear regression or support vector re- gression models best suited for price prediction in public procurement?

Research Question 4 (RQ4): How does bidder performance differ in EMAT ten- ders compared to lowest price tenders?

1.4 Sustainability Aspect

This paper will explore sustainability through the public procurement contracts that are EMAT tenders. We will study these contracts to determine what impact the quality criteria based on environmental factors has on participation. This results in the following research question:

Research Question 5 (RQ5): Does participation increase or decrease when en- vironmental quality criteria are included in EMAT tenders?

1.5 Scope

Our research will only focus on public procurement contracts in the cleaning services sector in central and the south of Sweden from 2016-2019. Within the cleaning sector we focused on sanitation and standard cleaning of floors and windows. For price analysis, we only look at floor care. Some of the companies participating in these tenders are not Swedish but no distinctions are made between Swedish and foreign firms. Previous research presents numerous attributes that have an affect on bidding in other sectors as well as in the cleaning industry. We limit our thesis to those that are most quantifiable and are accessible to us from our database.

Limitations in the data will be further explored in section 4.1. The study methods used will mainly consist of regression analysis but some inference will be drawn from stochastic dominance and non-parametric bootstrapping.

(16)

1.6 Report Structure

The paper is organized as follows. Section 2.1 starts off by going trough research in tender participation with section 2.1.3 in particular detailing findings when looking at factors affecting the bid/no bid decision. Section 2.2 provides an overview of existing literature pertaining to predicting bid prices and determinants of the pricing decision. The literature review concludes with section 2.3 describing the difficulty in judging economically most advantageous tenders and 2.4 that looks specifically at the impact of environmental quality criteria. All of the mathematical models used in this thesis are presented next. Section 4 then describes the data and details its limitations as well as defining key variables. In addition, it is exhaustively explained how we intend to apply the methods that have been introduced in section 3. We outline each approach in the order they will be presented in the results section.

Results will be presented in section 5 for fitting tender participation into a known distribution and the regression models. Price prediction model comparison and price performance is shown next and we finally present the assessment of EMAT tenders.

Section 6 and 7 analyzes and concludes the results. Finally, suggestions for further research are presented in section 8.

(17)

2 Previous Research in Sealed Bid Auctions

Using past research we hope to find good models that can be used for our thesis.

For tender participants there are some existing studies in public procurement for cleaning services that we can build on. For price prediction and EMAT assessment the research is more sparse and we seek studies in other sectors such as construc- tion.

2.1 Measuring Tender Participation

2.1.1 Probability of Winning Tenders

Multiple and logistic regression can be applied in determining probabilities of win- ning tenders. Data from one specific bidding firm in the Polish construction industry allowed Malara and Mazurkiewcz (2012) to model the winning probability through a binary logistic regression model. The binary response variable is partially deter- mined by qualitative variables such as the type of tender, size of the procurer and the presence of partner contractors, and partially by quantitative variables such as number of competitors, lowest price bid and highest price bid.

Results in Malara and Mazurkiewcz (2012) model gave the suppliers either an output of 0 as in loosing the tender or 1 as in winning the tender. Rounding between 0 and 1 are done accordingly with standard mathematical procedures. Although Malara and Mazurkiewcz do not forecast any optimal bid range or optimal bid price, their contribution could still be useful for this study. Their method of determining winning probabilities can be incorporated in other auction bidding theories that both utilize quality and price to find and optimal bid. Lastly, it is imperative to note that the model Malara and Mazurkiewcz propose is restricted to one firm’s probability of winning, which may not be satisfactory in a large competitive setting with many actors.

Malara and Mazurkiewcz work is pertinent for this thesis, not due to their procedure of measuring the probability of winning tenders, but rather for what factors that

(18)

could contribute firms to participate in tenders. Furthermore, their mathematical theory could be of significance for this thesis since they apply binary regression models well aligned with probit regression and the probability of a firm participating in tenders.

2.1.2 Determining Number of Participants in Tenders

There have been varying results regarding the effect of number of participants on the tender outcome. An analysis of the so called bid spread, defined in section 4.2, in auctions did not show any significant effect by either number of competitors or contract size (Drew et al. 2001). However, determining the number of participants in a contract may be pertinent due to simple supply demand theory; the more bidders in a contract, the harder it becomes for firms to profit and the cheaper it becomes for buyers. Several studies have centered around understanding how different factors affect the participation rate of contracts in different industries.

Augustin and Walter (2010) found in their study on operator changes that project duration, i.e. longer contracts, usually increased the participation rate in contracts.

When studying competitive bidding Beck (2011) found that season was statistical significant when describing the number of participants in tenders. Contracts starting during summer or at the beginning of the year had lower participation rate than contracts that started mid autumn or mid spring. Although indications that both time and seasonal components might affect the amount of participants in contracts, it is important to be critical. Influencing factors may vary for different industries depending on the type of project, the risk firms undertake and the amount of capital firms bind during a certain time period (Agerberg and ˚Agren 2012).

A more explanatory procedure for determining number of participants in contracts was presented by Vigren (2017). In his study, Vigren used count data regression models to determine what contract characteristics that affected the number of bids for public transport bus contracts. The main finding from the study was that most contract features changed participation in tenders by around 0.1 − 0.5 bidders. The factors he looked at included, project duration, number of other tenders available, geography, a firm’s current workload and whether the contract was evaluated based

(19)

on lowest price or economically most advantageous criteria. He compared ordinary least-square to Poisson Regression, Generalized Poisson Regression, Truncated Pois- son Regression and Truncated Generalized Poisson. The OLS regression performed worse than the different Poisson models. In particular he found that project du- ration increased the number of participants while tenders that are evaluated on EMAT decrease the number of participants as with the number of other tenders available to bid, possibly indicating that some firms have limited capacity to bid.

Finally, Vigren found that tenders with combined contracts did not affect the overall participation.

Over the years the participation rate of contracts ranging from the timber industry to the construction industry has been found to vary depending on factors such as the type of project (Drew and Skitmore 2006; Athey et al. 2011), client relationship (Bageis and Fortune 2009), project location (Azman 2014), project duration (Au- gustin and Walter 2010) and project size (Al-Arjani 2002; Benjamin 1969; Drew and Skitmore 2006; Lundberg et al. 2015). To further understand important attributes that may contribute to the bidding participation rate, it is relevant to study factors’

influence on single firm’s bidding participation.

2.1.3 Factors Influencing the Bid/No Bid Decision

Numerous studies have been made on which factors that are most important when assessing the bid/no bid decision and overall competitiveness for contracts in dif- ferent sectors. One study in the construction industry, performed by Cheng et al.

(2010), indicated variables such as project size, type of project, time available for tender preparation, current workload, expected number of competitors, tendering method and project duration to be important for a firm’s decision to bid in a con- tract (remaining factors in Cheng et. al. study are illustrated in table 21). In comparison to other studies which uses various statistical models they implement a questionnaire to determine important factors contributing to firms’ bid/no bid decisions. Cheng et. al. gathered key influencing factors from renowned market participants, weighed their relative importance within the industry and finally gave them points that described factors’ significance to contracts. Ballesteros-P´erez et

(20)

al. (2016) took a similar approach as Cheng where they focused on anticipating the participation of individual bidders. They found that contract size was significant and thus affected the likelihood of individual bidders to participate in contracts.

Furthermore, bidders that have not previously participated in a auction are impor- tant to consider in tender forecasting models, since excluding them would limit the predictive accuracy (Ballesteros-P´erez et al. 2016)

Fu (2003) measured in his doctoral thesis the effect of contractor’s bidding expe- riences on competitiveness in recurrent bidding. His work is pertinent in multi- attribute tendering theory since he incorporates other important factors to assess competitive bidding. Well aligned with Cheng et al. (2010) he studied how fac- tors contributes to bid/no bid contract decision, Fu found that features such as client relationship, a firm’s previous experience, project size and project location to be important when determining competitiveness mainly within the construction industry.

By comparing studies in the construction industry (Cheng et al. 2010; Fu 2003) and public transport industry (Vigren 2017), there is a further strong indication that common factors to assess in bid/no bid decision models are project size, project location and the workload (in some studies called market conditions) of firms.

Conclusively, the number and identity of participants auctions in economics have been challenging to forecast. There are few models that provide accurate solutions or predictions, thus further strengthening the fact that the area of multi-attribute auction theory and assessment of factors contributing to competitive bidding to be a fairly unexplored field of study. In addition, there are no good models to predict specific number of key competitors (Ballesteros-P´erez et al. 2015).

2.2 Price Prediction Models in Sealed Bid Auctions

In this section we review past research to identify attributes that affect the pricing decision of a bidder to use in our regression analysis. There have been several studies in this area and Takano et al. (2018) categorized them into three buckets:

statistical models, multi-criteria utility models and artificial-intelligence (AI) based

(21)

models. We focus on statistical and AI models by presenting the results of previous attempts to use machine learning and least-square regression to predict prices in sealed bid auctions in procurement. In addition to these models we would also argue the prevalence of models based on game theory. Friedman, a prominent researcher in bidding theory, neglected these model arguing game theory models were only functional when the number of bidders are predictable and few Friedman (1956), a rare occurrence in this types of auctions.

2.2.1 Predicting Bid Prices Using Statistical Models and Machine Learn- ing

Based on an extensive literature review it was found that factors affecting the bid decision of companies in the construction sector can be categorized into seven ma- jor groups; project characteristics, economic Characteristics, bidding characteris- tics, contract Characteristics, owner characteristics, company characteristics and opportunity Characteristics. Some of the most prominent attributes within these categories were project size, investment risks, time for tender preparation, type of contract, relationship with the owner, current workload and need for work (Polat et al. 2016). The paper further compared a machine learning method called ar- tificial neural network with least-square regression. They found that both models performed equally with good predictive accuracy.

(22)

In one paper least-square regression was applied to forecast a bidding range. They applied logistic regression and found a model with a very high model fit (Petrovski et al. 2015). An advantage of this model is that it can easily take in to account several factors that impact the bidding decision, both quantitative and qualitative.

Artificial intelligence tools have been used since the 1990s to tackle bidding problems.

Methods include artificial neural networks (Hegazy and Moselhi 1994; Li 1996), case- based reasoning (Dikmen et al. 2007) and fuzzy set theory (Fayek 1998).

A paper that instead looks at itemized bids is Jung and Kim (2019) that provided a forecasting model to using a machine learning approach called random forest method to estimate bidding ranges with the help of random forest variable selection and regularized linear regression approaches. They validated their model by finding that the actual winning bid always was in the proposed range. Lastly, they argued that the predictive power of the suggested model could be improved by using better datasets.

Petrovski et al. (2015) used Support vector regression with a Radial Basis Function (RBF) kernel to arrive at a model using two attributes, tender preparation and price received, and predict prices in the construction sector in Macedonia by only 2.5 % mean absolute percentage error

Instead of looking at regression models some studies have focused on trying to fit a distribution model to bids. One study (Ballesteros-P´erez and Skitmore 2017) as- sessed seven different distributions including Uniform, Weibull and different versions of the log-normal distributions. They found that the 3-parameter log normal gave the best results while Weibull, Log-Uniform and Uniform performed badly. They noted that the Weibull giving such poor results was surprising since it is widely used to model bid variability.

(23)

2.3 Assessing EMAT tenders

EMAT contracts are not simply awarded to the lowest price bidder. Instead each company is evaluated by a set of quality criteria. The criteria either results in a price discount for good scores, price penalty for bad scores or is translated into a score that combined with a price score results in a final bid score. Both the criteria to be included and subsequent assessment mechanism is up to each procurement entity to choose. There are certain guidelines from upphandlingsmyndigheten regarding appropriate quality scores (Upphandlingsmyndigheten 2019).

Yu et al. (2013) argue that few adequate models exist for EMAT tenders due to the inherent difficulty in measuring the difference in price that comes from variance in the quality of service or product. They tackle EMAT tenders by estimating a bidding range that takes into account quality scores by introducing a price elasticity of quality (PEQ) model. This measure is reminiscent of the definition of price elasticity of demand found in economics, with the demand replaced by a quality variable. The quality is defined by factors such as capabilities, experience and management skills.

Using this model they are able to present a method to estimate a bidding range.

The bidding range is solved with a graphical analysis tool known as geometric graph analysis (GGA) proposed by Wang et al. (2007). The key finding from their paper was that both the most competitive and profitable strategies suggest choosing the same quality level in the bid. Meaning that regardless of bidding strategy there exists a given optimal quality level so that the quality and pricing aspects can be kept separate.

Ballesteros-P´erez et al. (2015) developed a method to assess the position of a bidder in EMAT tenders using a position performance coefficient. They found that the both the Beta distribution and the Kumaraswamy’s distribution fits the position perfor- mance coefficient. In addition to calculating a distribution of the likely position a bidder will have in a future auction they model the number of participants in a bidding process with the Laplace distribution. They did this because the likelihood that you are placed second when there are three participants will likely be different than when there are ten bidders. They then arrived at their final result by creating a joint probability distribution. This distribution gives the probability of a competi-

(24)

tor placing in any given position. Thereby a bidder can assess the performance of its competitors in an EMAT tender. The authors raise three drawbacks with their research with the biggest being that they neglect to account for non-economic ra- tional bidding and cover pricing, defined as a participant finding it in their interest to bid in an auction without the intention to win.

2.4 Green Public Procurement - Environmental Quality Cri- teria

Green public procurement (GPP) can be used as a tool by public organizations to achieve environmental quality objectives. Overall, there seems to be an increased usage of environmental criteria (Von Oelreich and Philip 2013). The extent to which GPP is used however differs between countries in EU because it is voluntary.

In Sweden, environmental criteria were used in 40-60 % of tenders while in EU as a whole it was less than half that (Renda et al. 2012).

Aldenius and Khan (2017) listed several important factors featured in previous lit- erature that have an effect on the outcome of GPP. These included strategy and goals since research has shown that top level staff in government have an impact on the degree to which GPP is taken into account when setting goals. When GPP directives were more voluntary than mandatory then factors other than sustainabil- ity were prioritized in the procurement process. What is lacking in GPP research is studies detailing how specific regions strategically use public procurement to pro- mote environmental objectives and what challenges it implies. Another key factor driving the use of GPP was found to be costs. Studies have shown that procurement entities perceive the inclusion of environmental criteria as cost ineffective and that is slows down the process. Moreover, the size of public organizations in different regions may explain varying success of GPP. Aldenius and Khan (2017) presented a study conducted in Norway that showed that larger municipalities have imple- mented GPP criteria to a larger extent than smaller ones. Finally Aldenius and Khan (2017) described the existence of legal uncertainties regarding the application of GPP criteria as well as a lack of knowledge of the advantages of GPP and life cycle costs. In fact, this lack of knowledge and training in environmental criteria are more

(25)

critical factors to the future success of GPP rather than budgetary considerations (Testa et al. 2013).

An argument for green public procurement (GPP) is that public sector parties can in- fluence producers and consumers to reduce their impact on the environment through their purchasing power. However, Lundberg et al. (2016) assessed the ability of GPP to achieve environmental objectives and found its potential as an environmental pol- icy to be limited in terms of how polluting firms choose to adapt to the environmental requirements posed by the public sector and invest in greener technologies. In fact, they argued it can be counterproductive. They concluded by stating that GPP must aim for environmental standard beyond the technology of the procurement firms and to be designed with clear environmental objectives in mind.

The Swedish public procurement agency Upphandlingsmyndigheten has put forth sustainability criteria that should be used in public procurement contracts. They can be divided into four subcategories. It is up to each individual procurement en- tity to choose which criteria and to what degree to use them. The four categories are: 1. Qualification criteria, 2. Technical specification, 3. EMAT criteria, 4. Con- tract criteria. For cleaning services there are specific criteria that a procurement entity may choose to use. Qualification criteria are used for the bidders to prove that they works systematically with environmental considerations. ISO 14001 certificates are therefore often required to participate in contracts. It is an international envi- ronmental management system standard that aims to decrease the environmental footprints of companies. The minimum requirements is to work proactively with regard to negative impact on the environment as well as to meet national laws.

The procurement entity should accept substitute documents showing that a com- pany meet the requirements in the system standard if it currently does not hold the certificate (Upphandlingsmyndigheten 2019).

The consequences of including environmental criteria in public procurement auctions has been considered. Lundberg et al. (2015) presented with a negative binomial re- gression that environmental criteria, together with other variables such as Tendering Method and Project Size, does in fact have statistical significance when describing the number of competitors in tenders. Their argument is that it will decrease the

(26)

number of tender participants and thereby lower competition. On the other hand it might lead to increased competition because it incentivizes suppliers that already deliver sustainable solutions to participate more. Then, if these companies out- number those that do not focus on sustainability than the overall effect could be increased participation (Lundberg et al. 2009).

To conclude this section, it is clear from our review that research pertaining to bidding participation, bid forecasting related directly to the cleaning public pro- curement sector is relatively limited. Thus justifying our thesis on bidding in public procurement contracts.

(27)

3 Empirical Framework

3.1 Multiple Linear Regression Analysis

To model the relationship between a dependent variable and independent variables a multiple regression model (MLR) can be used. The dependent variable can also be referred to as the response variable. The extended model has the following mathematical notation

Yi = β0+ β1x1+ β2x2+ ... + βkxk+ i, (1) where, Yi is the dependent variable, β0 is the intercept, βk are the regression coeffi- cients, β0 is the intercept, xk the independent variables, also referred to as explana- tory variables, and i the random error terms. MLR assumes that the relationship between the variables are linear (Montgomery et al. 2012).

In matrix form the regression model is expressed as

Y = Xβ + , (2) where

Y =

Y1

Y2 ... Yn

, X =

1 X11 X12 ... X13

1 X21 X22 ... X23 ... ... ... . .. ... 1 Xn1 Xn2 ... Xnk

β =

β0 β1 ... βk

,  =

1

2 ...

n

, (3)

where Y is a nx1 vector of observations. X is a nxp matrix of the independent variables, β is px1 vector of regression coefficients and  the random errors in an nx1 vector.

(28)

Estimation of model parameters is done with the ordinary least-square approach (OLS). The least-square estimators are obtained by minimizing the sum of squares of the errors: 0. We obtain the least-squares normal equations

X0X bβ = X0Y, bβ = (X0X)−1X0Y, (4) In a regression model two types of independent variables are used: quantitative variables and qualitative variables. The first type are continuous variables. Dummy variables are qualitative variables and take values 1 or 0 to indicate a categorical effect that can shift the outcome (Montgomery et al. 2012).

3.2 Model Validation

3.2.1 Multicollinearity

The presence of multicollinearity can increase the uncertainty in the model by in- creasing the standard errors of estimated coefficients. The first step to detect mul- ticollinearity is by inspecting the correlation matrix of the independent variables.

These are obtained by the unit length scaled values give from

wij = Xij − Xj

s1/2jj , i = 1, 2, ..., n, j = 1, 2, ..., k (5) where k is the number of independent variables without the intercept, Xj is the mean of the independent variables in j th row and sjj = Pn

i=1(Xij − Xj)2. The correlation matrix is now obtained by multiplying two matrices W of the scaled values.

W0W =

1 r12 r13 ... r1k r12 1 r23 ... r2k ... ... ... . .. ...

r1k r2k r3k ... 1

(6)

(29)

An additional multicollineraity diagnostic is the variance inflation factor (VIF).

According to James et al. (2013) and Montgomery et al. (2012) a VIF value exceeding 5 or 10 is a strong indication of collinearity between the variables. A benefit of the VIF over the simple cross-correlation is that it is conditional on other explanatory variables. For the ith independent variables the VIF is

V IFi = 1

1 − R2i, i = 1, 2, ..., p (7) Where R2i is the coefficient of determination that is the result of using the ith independent variables in a regression against the other independent variables. The coefficient of determination is further explained below.

3.2.2 Residual Diagnostics

The use of the multi-linear regression model requires some assumptions to hold:

• Approximate linear relationship between the dependent variable and indepen- dent variables

• The errors are normally distributed by e ∼ N (0, σ2)

• The errors are uncorrelated The residuals are defined as

ei = Yi− ˆYi, i = 1, 2, ..., n (8) where Yi is the ith observation and ˆYi the fitted value. Plotting the residuals is a good way to investigate the key assumptions underlined above . In particular one can look at the studentized residuals to detect outliers or extreme values (Montgomery et al. 2012). They are defined as

ri = ei

pMSres(1 − hii), i = 1, 2, ...n (9)

(30)

where hii is found in the ith diagonal element of the hat matrix

H = X(X0X)−1X0, (10)

M Sres is the residual mean square defined as

M Sres = SSres

n − p, (11)

where SSres is defined in section 3.3.1

The Studentized residuals may be used in Quantile-Quantile (QQ) plots. to check if the errors are normally distributed. QQ-plots are sample order statistics plotted against theoretical quantiles from a standard normal distribution. Non-normality can be spotted in such a plot (Thode 2002).

3.2.3 Variable Transforms

The Box-Cox method can be used to try to remedy non-normality by transforming the dependent variable. The power transformation of the ith observation Yiλ is defined as

Yi(λ) =

Yiλ−1

λ ˙Yλ−1, λ 6= 0 Y ln(Y˙ i), λ = 0

(12)

where ˙Y = ln−1[n1Pn

i=1lnYi] corresponds to the geometric mean of the observations and Yi(λ) is the transformed dependent variable (Montgomery et al. 2012).

(31)

3.3 Model Selection

3.3.1 Selective Criteria

Model selection in regression analysis can be done by the all possible regression method. It fits all possible combinations of the regressors and selected the best model according to some selective criteria. For k regressors there are 2k possible combinations.

A common selective criteria is the coefficient of determination, R2. It measures what amount of the variance in the dependent variable that can be predicted with the independent variable (Montgomery et al. 2012). R2 is defined as

SSres=

n

X

i=1

(Yi− ˆYi)2, (13)

SST =

n

X

i=1

(Yi− Y )2, (14)

R2 = 1 − SSres

SST , (15)

where Y is the dependent variable mean, Yi is the ith observation and ˆYi is value estimated by the regression. Finally we also use the Akaike Information Criteria (AIC) and Bayesian information criterion (BIC) defined as

AIC = −2ln(L) + 2p (16)

In the OLS regression this becomes

AIC = nln(SSres

n ) + 2p (17)

(32)

The BIC is defined as

BIC = ln(n)p − 2ln(L) (18)

where, L is a likelihood function for a specific model. A lower AIC and BIC value indicates better fit (Montgomery et al. 2012)

For prediction in regression analysis a frequently used criteria is the root-mean square error (RMSE) defined as

RSM E =

r Pn

i=1(ˆyi− yt)2

n , (19)

where ˆyiis the predicted value, yithe corresponding observed value and n the number of observations (Montgomery et al. 2012).

3.3.2 K-fold Cross-Validation

K-fold cross-validation is a rigorous method for prediction model validation in re- gression analysis. It separates the data into k-subsamples of which the model is tested on k-1 samples and validated on the remaining sample (Montgomery et al.

2012)

3.4 Poisson Regression Models

The dependent variables used in this paper are count data, meaning they are non- negative integer values. The probability mass of the distribution for count data is limited to a non-negative range as opposed to the the normal distribution (Cameron and Trivedo 2005). Consequently, the standard OLS method might fail.

The Poisson regression model is based on the Poisson distribution with a probability mass function

(33)

P r[Y = y1|xi] = exp(−λiyi i

yi! , yi = 0, 1, 2..., (20) with yi as response variable, independent variables x, parameters λi and first and second order moments

E[Y ] = V ar[Y ] = λi, (21)

So the expected value of the response variable is:

E[yi|xi] = λi = exp(x0i)β, (22)

Meaning it is non-linear expressed as an exponential parameterization of Y. It is estimated with a maximum likelihood technique and log-likelihood function (Green, 2003).

The Poisson model requires equidispersion and it does not hold the model may give uncertain standard errors (Cameron and Trivedo 2005). Choosing an appropriate model thus requires investigating the response variable. Underdispersion would indicate that the standard errors may be overestimate and thus leading to false insignificant results (Hilbe 2014). A remedy if the data is found to be over-or underdispersed is to use the Generalized Poisson distribution (Consul, 1989). This extends the Poisson distribution in the above equation to:

P r[Y = y1|xi] =

λiexp(−λi−yi)(λi+yiγ)y i−1

yi! , yi = 0, 1, 2...,

0, f or y˙i m, when γ < 0

(23)

This model introduces an additional parameter dispersion parameter γ lying in the range max[-1, λi/m] < γ ≤ 1 with a negative value indicating underdispersion and γ = 0 reduces it to the standard Poisson distribution. The moments are:

E[Y ] = λi

1 − γ, (24)

(34)

V ar[Y ] = λi

(1 − γ)3, (25)

To allow for interpretation of the coefficients they are transformed by taking the exponent. Then they can be interpreted as a percentage change in the number of counts/bids (Hilbe 2014).

To address the fact that the count data in this thesis (participation in tenders) does not have any zero counts we extend the empirical model with truncation at zero.

3.4.1 Negative Binomial Regression

The Negative Binomial regression is a generalized linear regression which in similar- ity to the Poisson regression can be used for count data. The dependent variable Y in Negative Binomial regression is a count of the number of times an event occurs (Zwilling 2013). A convenient parameterization of the Negative Binomial distribu- tion is given by

p(y) = P (Y = y) = Γ(y + 1/α) Γ(y + 1)Γ(1/α)

 1

1 + αµ

1/α αµ 1 + αµ

y

, (26)

where µ > 0 is the mean of Y and α > 0 is the heterogeneity parameter. The parameterization is derived as a Poisson-gamma mixture, or as the number of failures before the (1/α)th success, though 1/α is not required to be an integer (J.M. Hilbe 2011).

According to J.M. Hilbe (2011), the traditional negative binomial regression model, designated as the NB2 model, is defined as

lnµ = β0+ β1x1+ β2x2+ ... + βpxp, (27) where the predictor variables x1i, ..., xpi are given and the regression coefficients β0, β1, ..., βp are to be estimated using maximum likelihood estimation.

(35)

Given a random sample of n subjects, observe for i the dependent variable y, and the predictor variables x1i, ..., xpi. Following vector notation can be made for β = (β0, β1, ..., βp)T and predictor data can be gathered in to the following ma- trix X

X =

1 x11 x12 . . . x1p 1 x21 x22 . . . x2p

... ... ... . .. ... 1 xn1 xn2 . . . xnp

Designating the ith row of the matrix X to be xi, and exponentiating equation (26), the distribution in equation (27) can be written as

p(yi) = P (Y = yi) = Γ(yi+ 1/α) Γ(yi+ 1)Γ(1/α)

 1

1 + αexjβ

1/α

αexjβ 1 + αexjβ

yi

,

where i = 1, 2, ..., n. Maximum likelihood estimation is applied to estimate the unknown parameters α and β. The likelihood function is defined as

L(α, β) =

n

Y

i=1

p(yi) =

n

Y

i=1

Γ(yi+ 1/α) Γ(yi+ 1)Γ(1/α)

 1

1 + αexjβ

1/α

αexjβ 1 + αexjβ

yi

,

and the log-likelihood function is

lnL(α, β) =

n

X

i=1

(yilnα + yi(xjβ) − (yi+ 1

α)ln(1 + αexjβ) + lnΓ(yi+ 1

α) − lnΓ (yi+ 1) − lnΓ(1 α)) The values of α and the regression coefficients β that maximize lnL(α, β) will be the maximum likelihood.

(36)

3.5 Support Vector Regression

Initially, Support Vector Machines were developed to solve classification tasks, but it can also be used to tackle regression problems. The kernel function is used to map lower dimensional data to higher dimensional data. Radial Basis Function (RBF) is an often recommended kernel function (Petrovski et al. 2015).

To assess the quality of estimation SVR uses a loss function called -insensitive loss function proposed by Vapnik (Vapnik and Chapelle 1999). It measures the error of approximation and is defined by

|y − f (x, w)|=

0, if |y − f (x, w)|≤ ,

|y − f (x, w)|− otherwise

(28)

Where,  is the insensitive zone, f (x, w) is a vector of the predicted values, y is a vector of the true values and w is vector of the unknown wights coefficients. The interpretation of the model is that when difference between the predicted value and true value is less than  the error is put to zero and thus no included in the model.

The SVR is defined as minimizing the error given by

R = 1

2||w||2+C(

l

X

i=1

|y − f (xi, w)|), (29)

Where the hyperparameter C is chosen and its value impacts the value of approxi- mation error and ||w||

The hyperparameters C and gamma (γ) act like regularization hyperparamters and are used to mitigate overfitting. If the model is overfitting then γ should be reduced, and if it is overfitting, it should be increased. The C parameter works the same way (Aurelien 2017).

(37)

3.6 Probit Regression

In determining the probability of winning binary logistic regression can be applied in accordance to Malara and Mazurkiewcz (2012). In their model they define the binary explanatory variable Y , the quantitative variables Xi, i = 1, 2, 3...., n and the qualitative variables Zj, j = 1, 2, 3...., m. Both quantitative and qualitative variables should be collected through historical data from several tenders committed by one firm.

The binary logistic regression model expresses probabilities in terms of so called odds instead of the classic method where one divide # of successes through # of trials (Peng et al. 2002). Contrary to the classical method of calculating probabilities, Malara et al. calculate the odds as the ratio of # of successes to the # of failures.

Thus, the odds can be defined as,

logit(p) = ln(odds) = ln( p

1 − p) = Y = β0+ β1x1+ β2x2+ ... + βkxk+ , (30) p denoted the likelihood of the occurrence of an event so that the probability p ∈ [0, 1] and  is the error term of the regression model. β is the unknown vector of regression parameters, where β = (β0, β1, ..., βk)T. Equation (30) can also be written in the form,

P (Y ) = eβ1x12x2+...+βkxk

1 + eβ1x12x2+...+βkxk, (31)

(38)

3.7 Stochastic Dominance

Assume F (x) and G(x) are continuous cumulative distributions functions of X and Y. Then stochastic dominance of first order (FSD) is defined as

F (x) ≤ G(x), (32)

To test for first order stochastic dominance the Kolmogorov-Smirnov test is widely used. The test statistic is defined as (Schmid and Trede 1996)

n,m = sup

x∈R

{ ˆGn− ˆFm}, (33)

where ˆGn and ˆFm are Empirical Cumulative Distribution Functions (ECDFs) for the data with n and m data points. This method has been used before in analysis of income distribution (Hestmati and Maasoumi 2000).

3.8 Confidence Intervals Using Non-Parametric Bootstrap

Non-parametric bootstrap generates additional data by re-sampling from the orig- inal dataset with replacement. Bootstrapping is a powerful tool particularly when assessing prices since it does neither assume distribution model or require any model as inputs. The purpose of the non-parametric bootstrap in this thesis is to enable further study of mainly the distribution of unit prices. The non-parametric boot- strap method applied in this thesis will be in accordance to what is described in the literature Risk and Portfolio Analysis - Principles and Methods by Hult et al.

(2012).

Consider the observations x1, ..., xn of independent and identically distributed ran- dom variables X1, ..., Xn. The aim is to estimate some quantity θ = θ(F ) that de- pends on an unknown empirical cumulative distribution function F of Xk. In the case of this thesis θ could be the unit prices θ =R xdF (x) giving ˆθobs = (x1+ ... + xn)/n.

Construct thereafter a confidence interval for θ with confidence level q, where q is

(39)

usually set to 95%. Since the empirical cumulative density function F is unknown, one method of constructing a confidence interval is to simulate large samples form F to approximately compute θ as the empirical estimate (Hult et al. 2012).

More samples are generated by randomly drawing with replacement n times from the set of observations {x1, ...., xn} to produce {X1, ..., Xn}. The amount of bootstraps required for good results usually vary but a general rule of thumb is minimum to or more than 599 bootstrap iterations (Wilcox 2010). The generated sample points Xk are assumed to be independent and Fn-distributed (uniformly distributed on the set of the original observations {x1, ..., xn}). Some Xk : s will be equal even though the xk are all different. Fn is denoted as the empirical cumulative distribution of X1, ..., Xnand ˆθ = θ(Fn) for the estimate of θ based on the samples {X1, ..., Xn}.

Even though {X1, ..., Xn} is not a sample from F , it has most of the features of a sample from F as long as n is sufficiently large. In particular, the probability distribution of ˆθ is likely to be close to the probability distribution of ˆθ. While the probability distribution of ˆθ is unknown (since F is unknown), the probability distribution of ˆθ can, with sufficiently large N, be approximated arbitrarily by repeated re-sampling N times. An approximate confidence interval Iθ,q for θ with confidence level q using the non-parametric bootstrap method is constructed as follows.

(40)

1. For each j in the set {1, ..., N } draw with replacement n times from the sample {x1, ..., xn} to obtain sample {X1(j), ..., Xn(j)} and the corresponding empirical cumulative distribution function Fn∗(j).

2. Compute the estimates ˆθj = θ(Fn∗(j)) of θ and the residuals Rj = ˆθobs− ˆθj for j = 1, ..., N .

3. Compute the confidence interval for the confidence level q Iθ,q = (ˆθobs+ R[N (1+q)/2+1,N ], ˆθobs+ R[N (1−q)/2+1,N ]), where R1,N ≤ ... ≤ RN,N is the ordering of the sample {R1, ..., RN}

3.9 Joint Distribution Function with Position Performance

As described in section 2.3 we use the model that allows us to calculate the probabil- ity curve that shows the likely position to be occupied by a given bidder that takes into account the total number of bidders. The general expression for the position performance joint probability curve using the kumaraswamy for bidder i is defined as

Ji P DF (x = j, αi, βi, m, b) =

Nk=+∞

X

Nk=jk

kum P DF (x, α, β) ∗ Laplace P DF (x, m, b) (34) Where x is the position in a tender, Nk is the number of participants, αi and βi are distribution parameters for the kumaraswamy distribution, and m, b are parameters for the laplace distribution that was chosen in the paper.

(41)

3.10 Other Statistical Models

3.10.1 Chi-Square Test

Pearson chi-square test statistic can be applied in order to compare different distri- butions and assess the goodness of fit. The test statistic compares observed probabil- ities with expected probabilities of success and failure at each group of observations (Montgomery et al. 2012). Define the expected number of successes and expected number of failures as niπˆi and ni(1 − ˆπi) respectively. The Pearson chi-square test statistic can thus be formulated as,

χ2 =

n

X

i=1

((yi− niπˆi)2

niˆπi +[(ni− yi) − ni(1 − ˆπi)]2 ni(1 − niˆπi)

)

=

n

X

i=1

(yi− niπˆi)

niˆπi(1 − ˆπi) (35)

The goodness-of-fit test statistic above is comparable with a χ2-distribution with n − p degrees of freedom. Large p-values for the test statistic implies that a model or distribution has a satisfactory fit to the data.

(42)

4 Data and Methodology

Due to the limited amount of research that has focused solely on the cleaning service sector we seek to test models employed in the construction sector and see how well they can be translated. Research in public procurement auctions are often characterized by limited data and to remedy this we apply other methods in addition to regression analysis. Computation of models and choice of variables will be inspired by the studies presented in the literature review. The key focus of this thesis is to assess tender participation and pricing decisions. We will study two key dependent variables in each area.

For the bid/no bid decision we choose to look at all bidders collectively through count data regression as well as compare behavior on an individual basis with probit regression. For pricing we will assess floor care unit prices and the spread, both will be defined in section 4.2.

4.1 Data Collection and Limitations

We have two separate datasets. One set consists of 409 sealed bid auctions in pub- lic procurement from 2016-2019 in Stockholm County, ¨Osterg¨otland County, Sk˚ane County and V¨astra G¨otaland County. However, there are several rows with missing data and after removing them we are left with 278 observations. Each contract contains information regarding, project duration, project location, procurement en- tity, tender preparation time, tendering method (EMAT or lowest price), number of participants and their submitted bids. For the individual company bid/no bid decision we use the same data as for the collective study.

For the spread variable, not all contracts contained detailed information on bids for all participants and since this is required to construct the spread dependent variable we are left with in total 285 points for all 15 most frequent bidders.

(43)

The other dataset contains unit prices submitted by the 15 most frequent bidders on floor care. This set amount to 123 points from 2016-2018. These where chosen so that we could compare large to small companies and frequent to less frequent bidders with enough data points. An advantage with our data is that it does not only contain successful bids; i.e., the data base contains offers by tender participants who were outbid. In sealed-bid auctions the opposite is normally the case and a typical limitation of the data (Kleijnen and Schaik 2011)

4.2 Variable Description

• Bid Spread: The difference between the lowest and second lowest bid. Used as a response variable. Will be used as a response variable in section 5.1.1

BS = B1B−B2

1

• Competitiveness: Measuring the spread between a company is bid and the winning bid. Will be used as a response variable in section 5.5

Ci = B1B−Bi

1

• Current Workload: We measure workload by the number of simultaneous ten- ders that are offered on the market when a company makes the decision to bid within a given time interval. Either five or ten days. We define two con- tracts to be simultaneous if they have at least ten overlapping days for tender preparation.

• EMAT: In economically most advantageous tenders there are selective criteria other than price taken into consideration when ranking bidding proposals.

Subsequently, bidding the lowest price is not a guaranteed winning strategy (Pla et al. 2014).

• Experience: It is defined as the number of similar tenders a company has par- ticipated in during the last three years. It will be used to categorize companies

Figure

Updating...

References

Related subjects :