An integrated model for supplier selection in the public procurement sector of defence

Abstract

Public procurement in defence includes the supplier selection issue. The purpose of this article is to suggest a model that combines Analytic Hierarchy Process with Voronoi Diagrams/Thiessen Polygons and Reilly’s law in order to propose a way to effectively use European Directive 2009/81/article 23. It also endeavours to expand the model by providing tools that increase its applicability, as well as providing a flexible and cost-effective tool for supplier selection to public procurement managers, allowing quick decision-making. It is also applicable in the correspondent private sector.

Points for practitioners

The model attempts to enrich supplier selection methods in the public procurement of defence. Its analysis may assist in: assessing potential suppliers more objectively, using a combination of well-established tools; presenting results to management that may reduce budgetary planning and avoid supply disruptions; enhancing the spirit of cooperation among departments of an organization/agency. It allows the joining of mathematics with experience and an important aspect of the legal frame in the public procurement of defence. Practitioners may also conclude that it is expandable to other sectors due to its flexibility.

Keywords

Analytic Hierarchy Process public procurement Reilly’s law security of supply Thiessen Polygons Voronoi Diagrams

Introduction

Public procurement in defence, otherwise called military logistics, presents interest for the security of a country (logistics also have a military context; see Webster’s, 1993). It is an important financial aspect of a Ministry of Defence (MoD) function since the money spent for that purpose is usually a significant part of its budget. Several data support this. For example, the combined defence budgets of the European Union (EU) add up to €180 billion (Institute for Security Studies, 2005). Additionally, in 2011–12, the largest spender in the total procurement expenditure of the UK central government was the MoD, reaching an amount of £20.1 billion (UK National Audit Office, 2013). Furthermore, in 2009, contract obligations for the US MoD included $330 billion for defence-related supplies and services (Apte et al., 2011). This financial significance, the ascertainment that attracting a great number of potential suppliers in public procurement in order to maximize reliable competitiveness is a common strategy (Laios, 2010), the importance of fiscal transparency in the smooth functioning of public procurement (Berkay and Üstüner, 2015; Herald, 2012) and the fact that handling the supplier agenda is a part of military leadership (Wong et al., 2003) lead to the conclusion that selecting an efficient supplier constitutes a major precondition for an MoD’s stable functioning.

Defence procurement in the EU is governed by European Directive (ED) 2009/81,¹ which established the legislative framework for the procurement of defence- and security-related articles and provided the path for the establishment of a European defence equipment market. Nevertheless, defensive equipment remains one of the main concerns for each EU member state because of its importance to their sovereignty, and purchasing procedures in this sector are naturally distinguished by the importance of their efficient ends, achieving high levels of Security of Supply (SoS). SoS focused on Critical Application Items (CAI), constitutes the triggering issue for the construction of this integrated supplier selection model. SoS is a term introduced by article 23 of ED 2009/81. SoS introduces each country’s ability to specify the characteristics of procurement in defence so that it works in favour of their interests. It may imply a variety of requirements designed in favour of each nation’s specific interests, including, for example, the provision of critical services and maintenance to ensure support for purchased equipment throughout its life-cycle (ED 2009/81). CAI refers to the essential items for a weapon system’s performance or operation, or the operating personnel (USA DoD, 2006). Consequently, after citing a short analysis of the aforementioned terms, it may be concluded that a public procurement case, under the characteristics of those terms, will need a solid, thus mathematically and experience-based, supplier selection procedure since its outcome may affect sensitive sectors in defence (i.e. the safety of personnel).

The objective of this article is to suggest a way to effectively use article 23 of ED 2009/81 by combining an Analytic Hierarchy Process (AHP) and Voronoi Diagrams (VD) within the frame of a supplier selection procedure for CAIs and the specificities of the armed forces (i.e. sensitive equipment, quick decision-making, etc.). The main contribution of this article is that it manages to provide an efficient supplier selection model that incorporates two seemingly irrelevant tools (AHP and VD) in the military procurement area under the ED 2009/81 and a heuristic law of economics – Reilly’s law of retail gravitation. It also demonstrates the fact that a private sector tool for supplier selection (AHP) is practicable in public procurement procedures and vice versa as it provides the ground for a visualized tool, and thus easy-to-understand application, for implementing SoS through computational geometry (VD).

It is hoped that the current study will enrich the defence literature by exploring and applying scientific and systematic theories of group decision support and geometrical structures in the supplier selection problem of the defence area. It combines well-structured and widely used methods with data in a professional area where, to the best of our knowledge, there is still work to be done. To support its contribution in the supplier selection area even better, Table 1 presents the results of research and a review of that area for unrestricted documents, where no combined use of AHP and VD seems to appear. The article is organized as follows: in the next section, parts of the relevant literature are reviewed and the areas of AHP and VD are introduced. Afterwards, the development of the model, its application in real locations and more geographical tools are presented. Finally, concluding remarks, managerial implications, limitations and directions for future research are cited.

Table 1.

A short review of supplier selection approaches/methods.

Supplier selection approaches/methods
Evaluation/selection technique	Authors
Mixed Integer Programming	Ware et al. (2014a)
Analytic Hierarchy Process	Al Harbi (2001), Byun (2001), Ware et al. (2014b)
Case-based Reasoning	Ng and Skitmore (1995)
Analytical Network Process	Wadhwa and Ravindran (2007)
Total Cost of Ownership	Degraeve et al. (2000)
Principal Component Analysis	Petroni and Braglia (2000)
Data Envelopment Analysis	Liu et al. (2000)
Optimization Models	Apte et al. (2011)
Statistical Analysis	Verma and Pullman (1998)
Standardized Unitless Rating Outranking Methods	De Boer et al. (1998)
Mathematical Models	Deng et al. (2014)
Integrated Fuzzy AHP	Sen et al. (2010)
Fuzzy PCA	Lam et al. (2010)
Integrated AHP and DEA	Sevkli (2010)
Integrated AHP and GP	Kar (2014)
Integrated Fuzzy and Cluster Analysis	Bottani and Rizzi (2008)

Note: AHP: Analytic Hierarchy Process; DEA: Data Envelopment Analysis; GP: Goal Programming; PCA: Principal Component Analysis.

Literature review

In this section, the results of the literature review for AHP and VD in the supplier selection area, and Reilly’s law in general, are presented. Supplier selection is a Multi Criteria Decision Making (MCDM) issue and it may become the most important decision in procurement (Mobolurin, 1995). Efficient supplier selection reduces purchasing costs and improves corporate competitiveness (Ghodsypour and O’Brien, 2001); therefore, it may reduce defence budgets. The relevant literature generally discusses the properties that should distinguish such a process, the ways to reach the optimal supplier, the qualitative and quantitative criteria, and the trade-offs among them (Cheragi et al., 2004; De Boer et al., 2001; Degraeve et al., 2000; Dickson, 1966; Ho et al., 2010; Weber et al., 1991). That literature also demonstrated that no single appropriate approach exists for each supplier selection case and that supply managers usually deal with uncertainty and adopt different selection criteria (Degraeve et al., 2000; Ho et al., 2010; Lee et al., 2003), as well as that no hybrid AHP–VD/Reilly’s law model seems to have been applied. Besides its supportive role in this study, Table 1 may assist readers who would like to deepen their knowledge of supplier selection issues.

In the literature on procurement, the need for public–private sector cooperation to resolve procurement issues has been highlighted (Choi, 2010; Institute for Security Studies, 2005; Tadelis, 2012). Consequently, the use of AHP – a popular, thus experienced, tool of the private sector supplier selection area (Ho et al., 2010) and more accurate than other scoring methods (Ghodsypour and O’Brien, 1998) – allows optimism with regards to the preservation of accuracy in the correspondent public sector process.

The first component of this model is the AHP, a systematic and flexible MCDM methodology that increases the efficiency of attributing weights to criteria (Laios, 2010). Its ability to provide an effective decision-making process is seen in Kerr and Tindale (2004) and it may incorporate qualitative and quantitative factors (Perçin, 2006). AHP is divided into three general steps (Deng et al., 2014). Initially, a hierarchical structure is established by recursively decomposing the decision-making problem. Then, a pairwise comparison matrix is constructed to indicate the relative importance of alternatives, and, finally, the priority weights of alternatives are calculated. The recognition of the AHP as an acceptable supplier selection tool has been proved by the number of papers that have used it for that purpose (Al Harbi, 2001; Byun, 2001).

VDs and Thiessen Polygons (TPs) constitute the second part of the model. A VD is a geometrical construct that permits the decomposition of a given space to a specified family of subsets in the space. The basic concept of a VD is as follows (Emiris, 2008; Novaes et al., 2009): given a finite set of distinct 0 and isolated points in a continuous space, all locations in that space are associated with the closest – in the sense of a given distance – member of the point set. It is the technique that enables the division of such multidimensional spaces into subspaces. A VD may be based on several other factors than the distance between points, resulting in different kinds of weighted planar VDs, such as the multiplicatively weighted. Schematically, a VD of both cases (ordinary and multiplicatively) is depicted in Figure 1.

Figure 1.

Ordinary (a) and multiplicatively (b) weighted VDs. Source: Novaes et al. (2009).

VDs have received attention due to three main reasons (Aurenhammer, 1991): first, they arise in nature in various situations; second, they present interesting mathematical properties; and, third, they have proved to be a powerful tool in solving seemingly unrelated computational problems. Therefore, they have been used in several sectors of science, such as computational geometry, urban planning and so on. In the area of defence, VDs have been used in military command-and-control matters (Kim and Hoffmann, 2003), while their use for procurement issues seems to focus on logistics and transportation districting issues rather than in supplier selection (Galvão et al., 2006; Novaes et al., 2000, 2009).

Reilly’s law constitutes the basis for studies on the location of retail stores (Minagawa and Sumiyoshi, 1999). Originally issued in 1931 as The Law of Retail Gravitation by William Reilly (1931), and inspired by Isaac Newton’s Law of Gravity, it proposed a similar formula for identifying retail trading areas. This law suggested that two large cities draw retail trade from a smaller intermediate city or town in direct proportion to some power of the population of these two large cities and in inverse proportion to some power of the distance of each of the cities from the smaller intermediate city. In an alternative formulation, if it is assumed that two large cities draw retail trade competitively from a smaller intermediate city, then the use of this formula permits the determination of which competing large city would finally ‘win’ in drawing the trade of the intermediate city.

Factors like mission and ground severely affect the acquisition function of a military support system (Hellenic MoD, no date[a]; USA DISAM, 2007). In defence, the need for flexible mathematical tools that produce measurable and user-friendly results in order to reach optimum solutions exists in several defence-related documents (Defence Acquisition University, 2010; Hellenic MoD, no date[a], 2002; USA DoD, 2008a). The review of the military logistics literature showed that mathematical modelling exists as a concept, but to the best of our knowledge, no clear use of an integrated AHP–VD model accompanied by Reilly’s law is observed therein.

This study aims to fill this gap by proposing an integrated AHP–VD model for an effective implementation of article 23 of ED 2009/81 in order to use it in the supplier selection area. The proposed model combines AHP with VD, which visualises ground partitions, as well as Reilly’s law. Simultaneously, it emphasizes two prerequisites of the military doctrine HDAL/SK-31-15 (Hellenic MoD, no date[a]) that participate in shaping this article’s idea of how Reilly’s law could be implemented in supplier selection in defence. The building, the solution and the application processes of the proposed model are presented hereinafter.

The development of the AHP–VD model

General terms and conditions of the model

For the analysis of the model, four randomly selected Hellenic geographical places (cities) were introduced, assuming that military depots exist in favour of a defence procurement agency under a public legal frame. Figure 2 shows these cities (marked in red), which are Ioannina, Kozani, Larissa and Thessaloniki; for the purposes of this article, they will be called ‘cities’ or ‘depots’. Additionally, it is assumed that four suppliers selected from an original set that satisfies the prerequisites of Hellenic Law 3978/11² have reached the final supplier selection stage, using the same means of transport to supply. The national defence procurement law (Hellenic Law 3978/11) completely transposed ED 2009/81 into Hellenic legislation, thereby adopting the concept of SoS and allowing us to use Hellenic cities for this model.

Figure 2.

View of the cities.

An expert team (ET) was created by four senior procurement officers, with two of them being specialized in CAI, which is assumed to be part of the aforementioned defence procurement agency. Its creation was preferred as several authors argue in favour of it inter-temporally for the amelioration of public procurement processes such as supplier selection, which requires interdepartmental cooperation (Ballou, 2004; Laios, 2010; Mpasaras, 2012; Seidman, 1969). The idea of creating teams was also recognized as one of the best commercial practices in USA defence procurement (USA GAO, 1998). An ET may be a path along which experience is combined with academic knowledge; thus, it may produce practical results close to real-world situations, acknowledging the fact that experience in the field of military procurement really matters (Pagonis, 1992; (Hellenic MoD, no date[a]).

The ET, assisted by the authors, performed the AHP for the calculation of the cities’ weights. Then, it constructed VDs/TPs aiming at an optimum location for the potential CAI supplier/s. Additionally, the ET considered the ‘Hellenic doctrine for army logistics’ (Hellenic MoD, no date[a]) and made an effort to enrich the model by presenting two cases in a hypothetical example since a real-world one might risk exposing restricted information.

AHP for the cities

AHP is a suitable technique for decision-making (Kar, 2014). Figure 3 depicts schematically the implementation of the AHP. The overall objective is at the top of the hierarchy and the criteria that may influence the decision-making process are located at the second level. The assigned weights represent the importance of the cities (alternatives to be ranked), indicating how effectively the ET thinks that they may support selected kinds of military operation. Consequently, the necessary steps before the application of the AHP would be to determine and analyse the criteria that participate in the formulation of the aforementioned weights.

Figure 3.

The hierarchical structure of the depot selection model. Note: GWC = ground and weather characteristics.

In military planning, the following criteria should be considered during the planning of a supportive operation (Hellenic MoD, no date[a]):

The mission.

The operational environment divided into: ground and weather characteristics (GWC) and the enemy state.

The size of the force to be supported.

The duration of the support operation.

The cost of the support operation.

The availability of the means and the respective support equipment.

The ET evaluated three of the aforementioned criteria (marked in italics) in order to assign weights to the cities, whereas for the rest criteria, no realistic assumptions could be made in this article with unrestricted data. Two cases of a hypothetical scenario were examined, assuming the existence of an infantry battalion within national boundaries, which were to support the battalion (force) in the Attack and the Movement to Contact (MtC) kinds of military operations. An Attack is an offensive movement supported by fire, while an MtC is a type of offensive operation that develops a situation and establishes or regains contact, which also sets favourable conditions for subsequent tactical actions (USA DoD, 2008b). A short explanation has been provided since the AHP model relies on the characteristics of the supportive mission for each one.

Then, the criteria should be analysed to clarify their content. The criterion ‘Availability’ corresponds to a time period that the four potential suppliers would be willing to state contractually within which they would be able to provide any CAI for the weaponry requested by the battalion. For this, suppliers collaborate with the procurement agency from the early stages of the model and are urged to present realistic capabilities. This criterion enhances strong cooperation between the two parties, which is a procurement strategy for critical products (Laios, 2010).

The criterion ‘GWC’ evaluates the parameters (provided in the online Appendix, available at http://ras.sagepub.com/) that relate to the characteristics of the ground and weather that affect a supportive operation, such as the ground configuration/altitude and the monthly average rainfall. For example, in the analysis of ground characteristics, a road map of the cities is presented that depicts the respective de-icing equipment (yellow and green schemas). It can be seen that Thessaloniki and Kozani have the most de-icing equipment, implying more severe weather than the other cities, while Ioannina has the poorest road network. Furthermore, a geophysical map of Greece indicates that Ioannina and Kozani are located in a rockier environment than the other cities. A map of the most dangerous parts of roads for 2014 shows that the main road to Ioannina from Patras has two such separate parts of a total length of 13 km, while the main road to Thessaloniki from Athens, being the same road to Larissa, has one part measuring 15 km long. Slow movements on dangerous roads extend the time for supplying the acting force. Furthermore, bad weather conditions may disallow winter operations since they may render supply impossible.

Climatological data were used for the evaluation of each city’s weather characteristics. It can be noted that the monthly average rainfall in Ioannina is significantly higher than in Larissa, while the respective levels between Thessaloniki and Kozani differ only slightly. The monthly average wind speed appears higher in Thessaloniki. Larissa has the biggest monthly average temperature and Kozani has the lowest average one. Heavy rainfall levels harden the support of an operation that requires a constant supply of fuels and/or ammunition. Moreover, stricter safety measures are required for the personnel, the vehicles and the equipment involved. Respectively, high temperatures incommode works in the depots and facilitate night support operations, when the ambient temperature is lower.

The aspects of the ‘Mission’ criterion are mainly derived by the military characteristics of the logistics involved in supporting each kind of operation. Attack is mainly characterized by the large consumption of ammunition and fuels, and by many human injuries/casualties (Hellenic MoD, no date[a]). Respectively, MtC is mainly characterized by the large consumption of fuel, the small consumption of munitions, reduced human injuries/casualties and an extended road network devoted to logistics needs (Hellenic MoD, no date[a]). For a better rendition of the mission, the safety of the troops that would operate in each city was also of concern. The level of safety required for the military facilities may determine the number of troops that would be dispatched from the operating force for safety duties, resulting in weakening the force from its main mission (Attack or MtC). Official crime statistics (shown in the online Appendix, available at http://ras.sagepub.com/) were used as an indicating factor about that number and seem to imply an augmenting tendency of crime incidents in the prefectures of Thessaloniki and Larissa; thus, the respective safety forces should be more in these prefectures.

The ET performed pairwise comparisons for all possible combinations of criteria by assigning numerical values based on their relative importance with respect to the alternatives and their corresponding parent elements (see Figure 2). Saaty’s (1980) nine-point scale of intensity was used for the calculation of the numerical values (see Table 2).

Table 2.

The scale of intensity.

Saaty’s intensity of importance scale
Definition	Intensity of importance
Equally Important	1
Moderately more important	3
Strongly more important	5
Very strongly more important	7
Extremely more important	9
Intermediate values	2, 4, 6, 8

For the two kinds of operation, the pairwise comparisons of the criteria and the alternatives are shown in the findings of Tables 3 and 4, where the preferences of the ET among the criteria and their respective weights are provided. Table 3 presents the results for Attack, where Mission is the most important criterion, followed by GWC and Availability. After the evaluation of the three criteria for each depot, the ET determined that Depot 1 may better support that kind of operation, followed by D4, D2 and D3.

Table 3.

The criteria and depot scores for Attack.

Weighting scores for criteria	Mission	GWC	Availability		Sum of scores
Weighting scores for criteria	0.546	0.273	0.180		1
AHP scores for depots	D1	D2	D3	D4
AHP scores for depots	0.352 (Larissa)	0.229 (Kozani)	0.088 (Ioannina)	0.328 (Thessaloniki)	0.999 (due to number rounding)

Table 4.

The criteria and depot scores for MtC.

Weighting scores for criteria	Mission	GWC	Availability		Sum of scores
Weighting scores for criteria	0.383	0.417	0.2		1
AHP scores for depots	D1	D2	D3	D4
AHP scores for depots	0.314 (Larissa)	0.343 (Thessaloniki)	0.120 (Kozani)	0.220 (Ioannina)	0.997 (due to number rounding)

Table 4 presents the results for MtC, where GWC is the most important criterion, followed by Mission and Availability. After the evaluation of the three criteria for each depot, the ET determined that Depot 2 may better support that kind of operation, followed by D1, D4 and D3.

This article’s required calculations for the AHP scores were made manually. This may reveal an insignificant but existing limitation of the AHP. In cases of numerous pairwise comparisons, when there are numerous criteria and alternatives, the calculations should be executed with specialized software for the AHP; otherwise, they would be time-consuming and tiresome. For example, in this research, the judgement matrixes for comparing the criteria and the alternatives were 3 × 3 for the criteria comparisons and 4 × 4 for the alternatives under each criterion. The relevant kind of software may also calculate the consistency ratio (CR), which evaluates the degree of validity in basic AHP pairwise comparisons and shows if a comparison matrix suffers from inconsistencies. In this article, the CR of the criteria judgement matrixes and the respective ones for the alternatives fluctuated from 0.8 to 0.10, which proves the consistency of these matrixes as it is below 0.10 (Deng et al., 2014).

VDs/TPs for the cities

The principles of government sourcing in the standard operating procedures of UK departments and government procurement (UK Government Procurement, 2012) include the use of visual tools and visual management in order to achieve lean sourcing for shorter lead times and less bureaucracy. Visual management is a way of displaying information to drive the performance of a process, and VD may assist towards that direction since it is an efficient visualization tool (Emiris, 2008). For the construction of the VD, the ET considered two important documents. The first was the ‘Defence management guidelines’ of the Hellenic armed forces (General Kostarakos, 2012), where it is stated that one of the key targets is to ensure the maximum level of availability and maintainability of the existing weaponry. The second was article 23 of ED 2009/81, where it is written that:

The contracting authority/entity may require, among others, a commitment from the tenderer to establish and/or maintain the capacity required to meet additional needs required by the contracting authority/entity as a result of a crisis, according to terms and conditions to be agreed and a commitment to ensure that possible changes in its supply chain during the execution of the contract will not affect adversely compliance with these requirements.

The ET concluded that TPs have properties that may assist in reassuring the requirements of the two aforementioned documents in the supplier selection process. Analytically, cities are centres of TPs, defining an area of influence, so that any location inside the polygon is closer to that city than any other location within the plane (Greece). Consequently, adding a requirement for a potential supplier to establish a facility devoted to the supply of the agency’s depots within the boundaries of a TP would imply its ability to procure faster and safer for the depot that is in the respective TP than in any other location within the plane, assisting the force to achieve greater levels of availability for its weaponry. Crisis response would be more secured if an obligation of maintaining a safety stock in that facility was included as a contractual requirement. ArcGIS 10.2.2 software was used for the production of the TPs and additional relevant data (i.e. catchment areas and geostatistical indices). Figure 4 depicts the cities’ TPs and their respective areas in km² where storage facilities should be established.

Figure 4.

TPs for the cities.

Further on, a simplification of Reilly’s law constitutes the basis for what is proposed to add flexibility in the model. Converse (1949) suggested that the Point of Indifference (PoI)/Breaking Point (BP) in Reilly’s law for trade flow between two cities (A and B) is provided by the following formula:

{BP}_{a, b} = D_{a, b} / [1 + (P_{a} / P_{b})^{1 / 2}],

where D_a,b is the distance between A and B and P_a/P_b is the relative size/population, or alternatively the ratio of appropriateness/attractiveness, of A and B. The BP is the point where the appropriateness of two cities is equal. In this article, it is suggested that P_a and P_b are the scores derived from the AHP, the cities are the points from where distances are calculated, and the customer is the battalion undertaking the two operations. BP may provide an estimation of how a battalion’s supply decisions could be shaped. If the BP is significantly larger for A, then a potential ‘customer’ could decide to supply from a different depot than those indicated by a TP. This could imply bigger loads of fuels, food supply and ammunition, respectively, as routes become longer and rarer. Consequently, supply routes are characterized by the involvement of less hardship for the personnel and means of transport but bigger vehicles and roads to use. Moreover, a battalion that moves near the separating line of two TPs may choose the supply depot based on the aforementioned formula. Table 5 provides the results for the PoIs concerning the two operations. The numbers in the BP/PoI columns show the radius of the circle that represents the catchment area of each city.

Table 5.

The depot scores of the cities for Attack and MtC.

	OPERATION: ATTACK	OPERATION: MtC
CITY/DEPOT	PoI-BP (LARISSA)	PoI-BP (LARISSA)
LARISSA
THESSALONIKI	66314.46049	61223.7883
KOZANI	60889.88667	50716.94188
IOANNINA	68306.10157	84350.46501
	PoI-BP (THESSALONIKI)	PoI-BP (THESSALONIKI)
LARISSA	53487.78951	58578.4617
THESSALONIKI
KOZANI	65003.68958	57320.26787
IOANNINA	94804.29769	128702.287
	PoI-BP(KOZANI)	PoI-BP(KOZANI)
LARISSA	30444.94333	40617.88812
THESSALONIKI	40295.96889	47979.39061
KOZANI
IOANNINA	36233.914	61078.31337
	PoI-BP (IOANNINA)	PoI-BP (IOANNINA)
LARISSA	65936.37843	49892.01499
THESSALONIKI	113461.1565	79563.16723
KOZANI	69953.72333	45109.32396
IOANNINA

Figures 5 and 6 depict the catchment areas along with the initially calculated TP. Each city’s appropriateness may be compared and described by the relative size of the circles that osculate and have the same colour. For example, Larissa seems to be the most attractive city for a battalion in both operations as its catchment area is geographically much larger than its TP. The difference becomes obvious for MtC if those areas in Larissa and Ioannina are compared. This application of Reilly’s law could also be used as a tool for assisting decision-making in reorganization/relocation issues as it may demonstrate which depot may be substituted by another.

Figure 5.

The catchment areas for Attack.

Figure 6.

The catchment areas for MtC.

An analysis of the spatial point distribution

ArcGIS 10.2.2 software produces results that could increase the applicability of the model. Herein, the use of certain geostatistical indices of spatial centrality and spatial dispersion is based on the coordinates of Greek prefectures’ capital cities, and sufficient sample data (N ≥ 30) complying with normality assumption for their distribution (Koutrouvelis, 2000). It may assist decision-makers by providing useful information for selecting a potential location for new storage facilities. The spatial median provides the point of the distribution where all the Euclidean distances are minimized, and the spatial mean is the geographical mean defined by the coordinates of all cities. The measurement of the variance in relation to the spatial mean is given by the standard distance, which defines how the points (cities) are distributed around the spatial mean. Figures 7 and 8 depict these three indices, from which it is inferred that the spatial mean and the spatial median are close to each other and that the standard distance scheme covers a significant part of the plane encompassing most of the cities.

Figure 7.

The standard distance circle and the spatial mean point.

Figure 8.

The spatial median point.

The aforementioned indices may also suggest a way to efficiently apply the legal frame for the implementation of the offsets in a contractual process. If an offset relates to the construction of a storage depot, these indices could be used as objective tools for the selection of its location. Herewith, these indices demonstrate that besides the fact that the spatial mean and median represent geographical points close to each other, they are near the city of Lamia, which already has military facilities. Consequently, if Lamia was selected as a new supply depot, it would be near the geographical points that minimize all distances from other cities, simultaneously providing significant cover for the Hellenic territory. This fact, combined with the exploitation of Lamia’s existing military facilities, could reduce the respective construction and transportation costs.

Conclusions and managerial implications

The model of this article may be practicable in several real-world applications in non-defensive areas as well. It provides objectivity as it combines well-established geometrical tools with a popular process that benefits from the experience of an ET. It attempts to weld theory with practice under a common denominator: the requirement for a solid and cost-effective supplier selection tool. The overall usefulness of this model could be its applicability in the defence public procurement area due to its innovative character. AHP and VDs have proven to be capable of evaluating pure military operational characteristics and embodying them in defence logistics. As a consequence, this model has shown that it embraces the principles of cooperation and interoperability, which are principles of military logistics (Hellenic MoD, 2014 ). Agility is a principle that fits in this model since AHP may adapt to new parameters inserted in the model and evaluate different operational situations in an efficient manner. Agility also bolsters the model’s ability to work in the private procurement sector as the factors that produce the AHP scores and the VDs could be replaced by others that describe such a procurement situation, like the factors contained in the formation of cost-plus contracts, a procurement tool seen much in the private sector (Tadelis, 2012). AHP and VD present the advantage of flexible and adaptable structural elements being able to fit with private or public procurement rules. The model successfully introduced computational geometry into the supplier selection area of public defence procurement and demonstrated its benefits in CAI, where time and distance parameters really matter.

Sufficiency, another military logistics principle (Hellenic MoD, 2014 ), is covered by SoS. The model makes the concept of SoS clearer and indicates how sufficiency in products may be supported by a warehouse’s optimal location. It also constitutes a tool for introducing the idea of SoS from the early stages of a supplier selection procedure, making this process less bureaucratic and strengthening early cooperation with the suppliers. The model also indicated that SoS may be linked to the risk of guaranteed supply (Spanjer, 2007), showing another aspect of its applicability in both sectors of procurement since successful SoS policy is vital for any company that aspires for high levels of uninterrupted supply services.

Managerial implications of this model lie on its actual results. Managers can conclude that it would not only be effective in real-world applications, but it would also supply them with a tool that uses computational geometry in a friendly and easy-to-understand geographical output requiring little time to present to top management. Moreover, the model may reduce the time needed for decision-making by simplifying and visualizing information for complex military factors like ground and weather. Finally, the application of Reilly’s law and the spatial point distribution analysis may reduce the subjectivity of decisions and endeavour to inculcate the idea of budgetary savings, adopting the military logistics principle of economy (Hellenic MoD, 2014 ). It may also puzzle the decision-makers during the contractual process about the location requirements that would serve the purpose of the contract best (f.e. contracts for supply chain management that are affected by the position of the storage facilities and their respective distance).

Limitations and future research directions

While this study has provided the frame for the identification of an effective supplier, by no means has it answered all questions concerning this issue and all its sources/references are available unrestricted. Reilly’s law presumes the geography of the area is flat without any geographical obstacles that could alter the results of this study. An additional limitation for this model is that it was designed for critical items in two kinds of operations. Consequently, the model cannot be applied to other operations without the re-evaluation of their characteristics. AHP also requires software in cases of numerous criteria and alternatives (see earlier). Possible future inquiry would be to develop a fuzzy approach to the AHP and to import other applications of the VD/TP in the model, such as the minimum Euclidean spanning tree.

Footnotes

Funding

This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.

Notes

Christodoulos Nikou is a public employee in the defence logistics sector. He received his PhD in supply management from the Department of Industrial Management and Technology, School of Maritime and Industrial Studies, University of Piraeus, Greece. His research interests include logistics and supply chain management. His work has been published in journals such as Journal of Public Procurement, Journal of Mathematics and System Science and SPOUDAI Journal of Economics and Business, as well as chapters in volumes published by Springer.

Socrates J. Moschuris is an Associate Professor of Logistics and Supply Management at the Department of Industrial Management and Technology, School of Maritime and Industrial Studies, University of Piraeus, Greece. His research interests include logistics and supply management. His work has been published in journals such as Omega, European Journal of Marketing, Production and Inventory Management Journal, International Journal of Operations and Production Management, Industrial Marketing Management, Journal of Supply Chain Management and EuroMed Journal of Business.

Ioannis Filiopoulos is a public employee in the defence sector. He received his MSc in Geoinformatics from the School of Rural & Surveying Engineering, National Technical University of Athens, Greece. His research interests include spatial analysis, geographical information systems, photogrammetry and airborne mapping. He is a member of the Technical Chamber of Greece.

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