Selecting the Flexible Last-Mile Delivery Models Using Multicriteria Decision-Making

Postal service providers can reorganise the last-mile delivery process within the scope of universal service and apply some of the flexible models for the organisation of the delivery. In this paper, the question of the selection of Flexible Last-Mile Delivery Models (FLMDMs) is treated using multicriteria decision-making. We have identified four different sustainable last-mile delivery models with an emphasis on the number of delivery workers. One postal service provider from Europe was selected, where the proposed FLMDMs were tested. The proposed last-mile delivery models are ranked using Multiple Criteria Decision Analysis (MCDA) techniques. In this context, MCDA techniques are used to make a comparative as - sessment of alternatives. The obtained results suggest the AB delivery model as the optimal choice for the last-mile delivery and complete allocation of the number of delivery workers.


INTRODUCTION
In the past period, harmonisation of the postal market and a common regulatory framework for the postal sector have been put into effect.The goal is to achieve a single market for postal services throughout the European Union Postal Directives [1,2,3].Directives ensure the provision of universal postal service (UPS) of a certain quality, available to all service users at affordable prices throughout the territory of that state on a permanent, transparent, impartial basis, under the supervision of the national regulatory authority.The national legislation of every member state provides a detailed description of the service itself, which results in great differences in legislation and practice.Differences are reflected in the definition of the scope of the universal area.Quality of universal postal service refers to the delivery time, and member states define in national legislation the time of transportation process via the postal network.Minimum five-day delivery with the possibility of an exemption (which is agreed upon with the national regulatory authority) is mandated [3].Due to this possibility, the postal service provider can reorganise the last-mile delivery process within the scope of universal service and apply some of the flexible models for the organisation of the delivery process.
Last-mile delivery includes a set of operations that enable the delivery of items to recipients directly at their home or business addresses.It is the most important phase in the value chain of the postal service business because it completes the technological process, the recipient receives the item and satisfies their need.The postal, i.e. service providers in general, are the most represented last-mile delivery providers.Nowadays, when the needs of users are increasingly expressed in terms of sending and receiving items containing correspondence or goods, service providers through the provision of the last-mile delivery represent an integral part of the daily functioning of society.In addition to the advantages for the users, last-mile delivery also generates large costs for the operators as one of the main challenges facing the operators and service providers.It makes up a large portion of an operator's shipping costs even if processes go smoothly.It accounts for just over half of an order's total shipping costs.Key factors driving up this cost include fuel consumption (frequent start-stop and spending more time on the road), diverse and complex routes, substantially more drivers, tight delivery times and failed delivery.However, the challenge is to find a sustainable environment in which the organisation of the delivery processes can occur.Human factor remains the key to the optimal performance of the last-mile delivery, as well as customer satisfaction.
In this paper, we have identified four different models of the last-mile delivery, within the scope of the UPS, intending to reduce the last-mile delivery costs by optimising the number of delivery workers.The selected model can be adjusted depending on the legal regulations and obligations of the country whose service provider is observed (possibility of introducing priority and non-priority mail, number of delivery days for universal postal service, i.e. the frequency of delivery, etc.).Furthermore, the proposed and selected flexible models can be applied to the delivery process of any service provider dealing with the UPS.
The main motivation of this research is to find a sustainable way in optimising the last-mile delivery in each variant of the delivery model (a variant is an alternative in the process of ranking by the Preference Ranking Organisation Method for Enrichment Evaluations -PROMETHEE and Additive Ratio Assessment -ARAS methods), i.e. an optimal number of workers for the last-mile delivery.This will allow for: -optimisation of the number and size of delivery areas and last-mile delivery routes (the area that is covered by a delivery worker) -optimisation of fleet and number of employees -reduction of unproductive working hours and easier redistribution of resources within the postal network.
The specific goals of the research are to ensure the complete allocation of the required number of technological workers in the delivery (the number of delivery workers), by applying the originally proposed, flexible solution (models) for the organisation of the last-mile delivery.
For a better understanding, the research procedure performed in this paper is presented in Figure 1.

Figure 1 -Research procedure
The paper is organised in the following way.Section 2 presents a review of related literature.In Section 3 the development of flexible last-mile delivery models (FLMDM) is elaborated.In Section 4 the application of the methodology was carried out on a real-life example based on observed postal service provider and the results are presented.This section is divided into two subsections.The first subsection explains and applies the PROMETHEE method for obtaining the rank of the alternatives, while the second one elaborates on the ARAS method for obtaining the final rank of the alternatives (last-mile delivery models).The conclusions and directions for further research finally follow in Section 5.

LITERATURE REVIEW
According to the EU [1], a postal network is a system of organisation of all kinds of resources used by a designated universal postal service provider to collect postal items based on universal service obligation (USO) throughout the territory, directing and handling items from the access point to the distribution centre and distribution to the addresses indicated on the items.It consists of (1) "first-mile collection" (from pick-up of mail to the first mail processing step, including therefore post offices and collection boxes), (2) processing and handling of postal items, including transportation, and (3) "last-mile delivery" to either a PO Box or to the addressee [4].

Obtaining statistical data of the service provider
Definition of delivery models (4 last-mile delivery models), subsection 3.2 Combination of the inputs (Table 1), subsection 3.1 Obtaining the outputs (Table 2), subsection 3.3 Ranking of the proposed models by the PROMETHEE and ARAS methods, section 4 The criteria for establishing a postal network are often combined depending on the geographical and demographical characteristics of a country.For example, Gracin and Stipetić [5] propose a modular procedure of designing postal network units.Mostarac et al. [6] analyse the concept of spatial accessibility in the postal system as well as the spatial characteristics of the research area.Boldron et al. [7] show that it may be desirable to scale down the national deadlines of mail delivery and restrict it to specific geographic areas.The liberalisation of the market resulted in the commercialisation of the service and far-reaching rationalisation of service provision processes [8].
The most important factors for the success of logistic providers are sustainability and delivery options [9].Sustainability can be seen through the triple bottom line, which focuses on three dimensions: people, planet and profit [10].The 2030 Agenda for Sustainable Development is, among other goals, dedicated to promoting productive employment and decent work for all [11].
Sustainability has been investigated by scholars in different research areas, as well as in the field of last-mile delivery.Klein and Popp [12] investigate how sustainability influences consumers' acceptance of delivery models in e-commerce.Thomas et al. [13] determine how sharing sustainability information about the last--mile delivery options affects consumer behaviours, while Ignat and Chankov [14] conclude that sustainability affects consumers' choice of delivery method.Mucowska [15] provided an extensive literature analysis in the field of sustainable last-mile delivery, where it is evident that the sustainable approach for delivery workers has not been dealt with.However, the workforce remains crucial to last-mail delivery, despite automation [16].Bates et al. [17] emphasised the advantages of the human factor for the delivery processes.
Studies dealing with personnel and the workforce in the postal sector are scarce.Malhotra et al. [18] created the linear programming model for scheduling personnel in the United States postal distribution stations.Demazière and Mercier [19] refer to the singularities of the postal delivery officers' activities and their engagement with delivery areas.Flecker et al. [8] deal with the transformation of public services from the perspective of postal workers where only the social dimension of postal workers is considered, not their technological contribution to the postal value chain.
The last-mile delivery represents the most expensive and problematic part of the entire supply chain process and usually impacts the profits of companies as well as the customer experience [20].Moreover, the entrance of new private competitors on the market, due to its gradual liberalisation [3], represents an additional factor pushing the postal operators towards more a cost-effective management of their technological processes [21].Further studies focus on the cost and performance optimisation of parcel delivery [22].Chromcová and Švadlenka [23] deal with optimisation in the light of the reconstruction of the postal transportation network, only in the parcel segment.Bruno et al. [24] propose and analyse two different strategies for rationalising post boxes, from demographic to spatial distribution criteria.Turska et al. [25] tried to optimise the route of the postal carrier of the selected delivery area through the solution of the traveling salesman problem.The authors Niroomand and Nsakanda [26] address the issue of improving collection flows in a public postal network while considering the contractor's obligations.
Furthermore, Laseinde and Mpofu [27] provide a solution to the last-mile challenges in postal operations.Sandoval et al. [28] address a last-mile logistic design problem faced by a courier and delivery company in Chile, although the same problem is likely to arise in the last-mile delivery operation of other postal companies.Yilmaz et al. [29] investigate the last-mile delivery models from the perspective of the growing e-commerce demands and focus on the delivery methods used by most delivery companies.
Alizadeh and Lahiji [30] discuss the provision of a multicriteria decision-making tool that allows customers to examine and choose, with certitude, the best possible delivery service.In the paper Wang et al. [31], the aim is to evaluate some key last-mile delivery companies in Vietnam regarding their sustainability performance by a fuzzy multi-criteria decision-making (F-MCDM) based framework.Krstić et al. [32] define innovative sustainable last-mile solutions and evaluate their potential application in the real-life logistics system of the city.
In the field of human resources, Polychroniou and Giannikos [33] present fuzzy multicriteria decision-making (MCDM) methodology for selecting employees.The purpose of the Widianta et al. [34] paper is to compare the four methods of multicriteria decision-making (MCDM) for the application of employee placement under predetermined criteria.Pourkhodabakhsh et al. [35] have identified factors affecting employee turnover using effective machine learning, meta-heuristic algorithms and multicriteria decision-making.
Selecting the best personnel among many alternatives is a multicriteria decision-making problem.Demirci and Kılıç [36] used three multicriteria decision-making techniques to solve recruitment problems via finding the optimal candidate for a job position.Dağdeviren [37] described a hybrid model which employs an analytic network process (ANP) and modified TOPSIS for supporting the personnel selection process in manufacturing systems.Korkmaz [38] used the TOPSIS (Technique for Order Performance by Similarity to Ideal Solution) method, which is one of the multicriteria decision-making techniques, as a personnel selection method in the logistics sector.
According to our knowledge, there is no evidence in the literature about the possible methodology to determine the optimal, sustainable and flexible model of the last-mile delivery process for a service provider from the aspect of optimising the number of delivery workers.

DEVELOPMENT OF THE FLEXIBLE LAST-MILE DELIVERY MODELS (FLMDM)
One postal service provider from Europe was selected, where the proposed FLMDMs were tested.The proposed last-mile delivery models are ranked using the Multiple Criteria Decision Analysis (MCDA) techniques.In this context, the MCDA techniques are used to make a comparative assessment of alternatives.These methods allow several criteria to be considered simultaneously in a complex situation and they are designed to help decision-makers to integrate different options, which reflect the opinions of the involved actors, in a prospective or retrospective framework [39].In recent decades, the decision support system has been constantly growing in the field of transportation planning.A review of the PROMETHEE method in transportation was presented by Oubahman and Duleba [40].In this paper, PROMETHEE is use as an outranking method to support decisions in selecting the FLMDM.To compare results obtained with PROMETHEE, we used the ARAS method to get a final rank of alternatives, i.e. last-mile delivery models.
The research proposed in this paper suggests delivery models that are independent of customer geography.Variables for optimal, flexible organisation of delivery are simplified and they do not depend on geographies.Our goal is to simplify inputs for the selection process, eliminating constraints such as traffic congestion, the ability to find parking in urban environments, etc.Such endeavours contribute to the creation of sustainable last-mile delivery models.Main inputs include a volume of items, the number of delivery norm minutes and the existing number of delivery workers.Specific processes of the last-mile delivery (on foot, bicycle, car, etc.) and the covered road distance are already included in the norm minutes.As a result, using the optimised number of workers would lead to lower wage costs and mail delivery deadlines.This approach can serve in the decision-making process for the postal sector (Figure 2).decision-making (MCDM) methodology for selecting employees.The purpose of the Widianta et al. [34] paper is to compare the four methods of multicriteria decision-making (MCDM) for the application of employee placement under predetermined criteria.Pourkhodabakhsh et al. [35] have identified factors affecting employee turnover using effective machine learning, meta-heuristic algorithms and multicriteria decision-making.
Selecting the best personnel among many alternatives is a multicriteria decision-making problem.Demirci and Kılıç [36] used three multicriteria decision-making techniques to solve recruitment problems via finding the optimal candidate for a job position.Dağdeviren [37] described a hybrid model which employs an analytic network process (ANP) and modified TOPSIS for supporting the personnel selection process in manufacturing systems.Korkmaz [38] used the TOPSIS (Technique for Order Performance by Similarity to Ideal Solution) method, which is one of the multicriteria decision-making techniques, as a personnel selection method in the logistics sector.
According to our knowledge, there is no evidence in the literature about the possible methodology to determine the optimal, sustainable and flexible model of the last-mile delivery process for a service provider from the aspect of optimising the number of delivery workers.

DEVELOPMENT OF THE FLEXIBLE LAST-MILE DELIVERY MODELS (FLMDM)
One postal service provider from Europe was selected, where the proposed FLMDMs were tested.The proposed last-mile delivery models are ranked using the Multiple Criteria Decision Analysis (MCDA) techniques.In this context, the MCDA techniques are used to make a comparative assessment of alternatives.These methods allow several criteria to be considered simultaneously in a complex situation and they are designed to help decision-makers to integrate different options, which reflect the opinions of the involved actors, in a prospective or retrospective framework [39].In recent decades, the decision support system has been constantly growing in the field of transportation planning.A review of the PROMETHEE method in transportation was presented by Oubahman and Duleba [40].In this paper, PROMETHEE is use as an outranking method to support decisions in selecting the FLMDM.To compare results obtained with PROMETHEE, we used the ARAS method to get a final rank of alternatives, i.e. last-mile delivery models.
The research proposed in this paper suggests delivery models that are independent of customer geography.Variables for optimal, flexible organisation of delivery are simplified and they do not depend on geographies.Our goal is to simplify inputs for the selection process, eliminating constraints such as traffic congestion, the ability to find parking in urban environments, etc.Such endeavours contribute to the creation of sustainable last-mile delivery models.Main inputs include a volume of items, the number of delivery norm minutes and the existing number of delivery workers.Specific processes of the last-mile delivery (on foot, bicycle, car, etc.) and the covered road distance are already included in the norm minutes.As a result, using the optimised number of workers would lead to lower wage costs and mail delivery deadlines.This approach can serve in the decision-making process for the postal sector (Figure 2).

Figure 2 -Research approach
The existing way of organising the required number of technological working places and delivery workers for the last-mile delivery and calculation of the norm minutes does not allow accurate insight into costs by postal operators and their economy.Also, such a situation neglected legal possibilities (introduction of priority and non-priority mail and the possibility of introducing a new

Recieved outputs
Ranking of the proposed models

Figure 2 -Research approach
The existing way of organising the required number of technological working places and delivery workers for the last-mile delivery and calculation of the norm minutes does not allow accurate insight into costs by postal operators and their economy.Also, such a situation neglected legal possibilities (introduction of priority and non-priority mail and the possibility of introducing a new mandatory number of working days for delivery in the scope of the universal postal service).It also does not stimulate the optimisation of the organisational structure and the rationalisation of the number of workers in the post offices in a self-sustainable way.In this regard, some of the basic activities of the paper are: -Identification of the norms applied in the delivery of items at the observed service provider.The norm represents the time required to perform individual service during a particular process.Norms are expressed in minutes by two decimal places; -Identification of the volume of items of the observed service provider; -Identification of the existing number of technological working places and delivery workers by post offices of the observed service provider.
To develop an FLMDM, it is necessary to define possible alternatives that may appear in the delivery of postal items to find out which solution is optimal for the observed service provider, by applying multicriteria decision-making.In addition to the alternatives, the criteria on which the alternatives are evaluated must also be defined.As alternative solutions, the following have been proposed: 1) Delivery of items 6 times a week in all delivery areas (existing solution); 2) Delivery of items 5 times a week (minimum provided by law) in all delivery areas; 3) Six-day delivery in delivery areas located in municipal places and five-day delivery in other delivery areas (6/5 delivery).Municipal places are places where the administrative centre of the municipality is located.They are the focal point of the municipality; 4) Delivery of items according to the AB delivery model, which implies the legal introduction of priority and non-priority mail.
Moreover, the ranking of alternatives was performed by applying multicriteria analysis according to the following proposed criteria: 1) Labour costs (direct and indirect) 2) Additional costs of using modern means of delivery (electric bicycles, motorcycles, vehicles, etc.) 3) The impact of the alternative on stimulating the introduction of new postal services 4) The impact of the alternative on the improvement of business relations with the economy (large users) and elements of the state structure (municipalities, local communities, etc.).
According to the census, the observed country has a total of 619,211 inhabitants [41].Having in mind the requirements stated in EKIP [42], an observed service provider with 140 post offices (units) meets the following requirements: − 13,812 km 2 [41]/157 units (post offices) = 87.97km 2 by one post office.− 619,211 inhabitants/157 units = 3944,01 inhabitants by one post office.
It should be noted that the observed service provider delivers postal items 6 times per week.The independent regulatory body may determine a different performance of the universal postal service.Due to the significant reduction of collection activities in the most expensive areas (rural areas), the reorganisation of geographical coverage is required.This was a challenge for the authors and one of the motives to deal with the topic processed in this paper.Reorganisation through the FLMDM will keep the financial, personal and territorial accessibility of the population in rural areas.

Phase I: Preparation of the input data
Currently, the delivery of postal items is being performed six days a week, with the exemption to deviate from the required obligation that cannot exceed 10% of the total number of households.These deviations may relate to: − households located more than 500 m from the public road, − households to which there is no suitable road for access to an operator, − households located in hilly and mountainous areas with extremely difficult access conditions.
In accordance with these deviations, the service provider has been given the opportunity to reorganise the last-mile delivery process within the scope of universal service and apply some of the flexible, sustainable models proposed in the paper.
In the first phase of the research, three basic variables were considered as input data for further calculations.1) The first variable is the norms that are applied in the delivery of items at the observed service provider.
Based on the norms, the realised norm minutes were calculated based on the volume of items, by last-mile delivery routes.The realised norm minutes based on the travelled distance were also calculated, to obtain the total realised norm minutes needed to calculate the productivity of the last-mile delivery routes.
2) The second variable is the volume of delivered items by the observed service provider.The number of delivered registered and unregistered items monthly, for legal entities and individuals (given in Table 1), was identified by post centres, post offices in post centres and their respective last-mile delivery routes.money order annually and monthly).Data are obtained from the application implemented by the observed postal service provider within the adopted Methodology for standardisation of the collection and processing of statistical data [43].Due to the extensiveness of the data, only a part is shown.In Table 1, the calculation of the average number of registered and unregistered monthly mail was performed (AMRM-Average Monthly Registered Mail and AMUM-Average Monthly Unregistered Mail), respectively.We need this information to forecast the number of priority mail.
3) The third used variable is the existing number of technological working places of delivery workers by post offices of the observed service provider.As with the second variable, the number of counter clerks and the number of workers in delivery were identified by post centres, post offices in post centres and their respective last-mile delivery routes (given in Table 1).The observed service provider, in the current organisation of the last-mile delivery (six days per week, without optimisation), has 280 delivery workers [44].The goal is to reduce this number by alternative last-mile delivery models proposed further in this paper.
The norm minutes that quantify the delivery process, the volume of items and the number of delivery workers provide starting variables in the process of optimising the last-mile delivery.In this direction, the already mentioned four alternatives are recognised as possible models of the last-mile delivery organisation and they represent the second phase of development of a solution proposal, the phase of creating an FLMDM of an observed service provider.

Phase II: Alternatives as Flexible Last-Mile Delivery Models (FLMDM)
In this phase, alternatives that represent possible solutions for the organisation and optimisation of the last-mile delivery process are developed.Below is a description of each, noting that the calculations were made based on data when the observed service provider did implement a category of priority mail.
Alternative 1: Delivery of items 6 times a week in all delivery postal network units of the observed service provider (existing solution).The existing solution for the last-mile delivery implies a six-day delivery of items.Delivery covers all delivery areas, with the existing number of delivery workers.
Alternative 2: Delivery of items 5 times a week (minimum provided by law) in all delivery postal network units of the observed service provider.This alternative in terms of organising the last-mile delivery allows switching from six-day delivery of items to five-day delivery.
Alternative 3: Delivery of items 6 times a week in the delivery postal network units at the seat of the municipality and in all other postal network units 5 times a week.This alternative would significantly reduce the costs of the postal network (service provider) while maintaining the quality of services.
Alternative 4: Delivery of items by the AB delivery model (implies a legal definition of priority and non--priority mail).The AB delivery model implies the organisation of the delivery area in such a way that all items for which the delivery deadline is longer than D+1 (next day delivery), arrived at the destination post office in the days before the delivery deadline, are grouped by recipient address and delivered on one of the next working days.
By introducing the AB delivery model, the process of delivering non-priority mail has changed with increasing productivity and delivery efficiency.By reducing the number of delivery points to delivery workers on their daily routes, the time required to complete the delivery is reduced, as is the length of the delivery route itself.Applying such a model would reduce labour costs and transportation costs.This centralised delivery model leads to a reduction in the number of delivery workers in certain areas, the use of more cost-effective ways of moving through the last-mile delivery route and a greater number of deliveries per day per delivery worker.
The AB model proposes priority mail that is delivered daily and non-priority mail delivered to half of the last-mile delivery route every other day (days A and B).During the A days, priority mail is delivered (in this case the observed service provider in a base year did not have a category of priority mail and we applied an expert estimate of 10% of registered items per last-mile delivery route) as well as half quantities of non-priority mail (registered and unregistered items).Priority mail and the other half of the non-priority mail would be delivered on day B. From the aspect of the quality of service, introducing the AB model maintains the required quality standards.Non-priority mail would be delivered within D+2 and priority mail within D+1.

Phase III: Finding the optimal FLMDM using the PROMETHEE and ARAS methods
A ranking of possible alternatives (delivery models) was performed to confirm the selection of the optimal framework for the organisation of the last-mile delivery in the observed service provider.This can be achieved by using multicriteria analysis for various delivery models based on the existing situation and the conditions in which delivery is performed in advanced postal administrations in the European Union.For this purpose, the PROMETHEE and ARAS methods were applied as methods of multicriteria analysis.Before ranking, the output variables should be obtained, as a part of inputs for the multicriteria analysis performed in Section 4.
The structure of the output data is described in Table 2, where only a part of the obtained outputs is shown due to the extensiveness of the data.The output data are calculated on the basis of service provider's input data presented in Table 1.The postal network consists of post centres (from 1 to 14), post offices and last-mile delivery routes.Transportation means are not considered.The list of the output acronyms is shown in Appendix.
Output variables for each last-mile delivery route are described as follows.
Estimated Priority Mail Monthly: EPMM=0.1‧AMRM.Based on the experiences of European countries and the analysis of independent regulatory agencies in the region, it was determined by an expert's estimate that this number is around 10% of registered mail.The experts considered the Universal Postal Union statistics database, annual reports of European postal operators and regulatory bodies, as well as European postal statistics.This output variable is estimated in the described way for the postal service providers that have not yet introduced the category of priority mail.In case there is a category of priority mail at the observed provider, the actual volume of priority mail will be taken for further analysis.In the case of the provider observed in this paper, the analysis was performed on data from one base year and the provider introduced priority mail in the next year.
Estimated Non-Priority Mail Monthly: ENPMM=0.1‧AMRM+AMUM.Furthermore, in Table 2, the data obtained from the observed postal service provider, which refers to the current system of six-day delivery, are presented by post offices.The data on realised services by volume of items Achieved Norm Minutes Based on the Volume of Items -for delivery (ANMVID) and distance travelled Achieved Norm Minutes Based on the Road Distance -six-day delivery (ANMRD6) are specially stated.Achieved Norm Minutes Based on the Volume of Items -for delivery (ANMVID) are shown in norm minutes based on statistical records and obtained as follows: Norm Minutes for Postal Items Sent by Individuals: NMSI=AMRM‧2.2(the statistical norm for this type of postal item) + AMUM‧0.2(the statistical norm for this type of postal item).
Norm Minutes for Postal Items Sent by Legal Entities: NMSLE=AMRM‧2.5 (the statistical norm for this type of postal item) + AMRMO‧2 (the statistical norm for this type of item)) + AMUM‧0.2(the statistical norm for this type of postal item).
According to the above, we get that: ANMVID=NMSI+NMSLE The variable Achieved Norm Minutes Based on the Road Distance -six-day delivery (ANMRD6) also provides statistical data on the norm minutes based on the road distance, i.e. distance travelled.These data contain differentiation in standardisation depending on whether the road in the last-mile delivery route is crossed on foot, by moped or by bicycle.
The next output variable is the Estimated Norm Minutes Based on the Road Distance (ENMRD) for different delivery systems monthly.That variable presents predicted new norm minutes for the travelled road distance for different systems (flexible models, i.e. alternatives) of delivery, per month.The travelled road distance will be different for different alternatives, i.e. last-mile delivery models (the volume of services does not change because the demand for the service remains the same).Thus, for five-day delivery, a 20% reduction in travelled road distance per last-mile delivery route is estimated compared to the current six-day model, and, accordingly, the ENMRD for five-day delivery is calculated as: ENMRD5=ANMRD6‧0.8For 6/5 delivery, ENMRD6/5 was calculated separately for postal units at the seat of the municipality (as a six-day delivery (variable ANMRD6) and especially in all other postal network units (as a five-day delivery (variable ENMRD5)): For the AB delivery model for each last-mile delivery route the ENMRD is reduced by 50% (delivery of non-priority mail every other day) and increased by the norm minutes based on the road distance for priority mail (10% of the travelled road distance in six-day delivery).
6 ( 6 0.1) 2 The next output variable is the estimation of the total achieved norm minutes for different delivery systems on a monthly basis (TANM).It implies the total number of norm minutes based on the road distance and based on the volume of items (for delivery), per month, for the appropriate delivery model (alternative).This means the following: for the six-day delivery model TANM6=ANMVID+ANMRD6, for the five-day delivery model TANM5=ANMVID+ENMRD5, for the 6/5 delivery model TANM5/6=ANMVID+ENMRD5/6, for the AB delivery model TANMAB=ANMVID+ENMRDAB.
Based on the previously described and obtained variables, the productivity of the last-mile delivery routes for different last-mile delivery systems (EP) is estimated, per month.It is expressed as a percentage and is obtained by dividing the total number of achieved norm minutes for each delivery model by 8800 norm minutes.The number of 8800 norm minutes was taken based on a 40-hour working week (regardless of the delivery system).The norm for 8-hour working hours is 400 minutes, so we get that: 22 working days per month ?400 minutes = 8800 norm minutes monthly, for the six-day delivery model .The following set of output variables represents the optimised number of delivery workers for different last-mile delivery models.Table 2 shows the optimal number of delivery workers per post centre, with belonging post offices (for example, for post centre 1, there are 8 belonging post offices.In Table 2 the numbers of workers 12, 11, 12, 10, 13, 12 and 13 are optimised numbers of workers sufficient for delivery at post centre 1, due to the four delivery models, respectively).
Estimates of the number of delivery workers were made in two variants, with and without working replacement (for example vacation or sick leave periods).
In the variant of Estimated Number of Delivery Workers Without Replacement (ENDWWithoutR) we have for every delivery model by post centre per month as follows: − for the six-day delivery model In this way, the number of employees who are 100% productive is obtained.The procedure was done for each delivery model, as presented.As shown in Table 2, we obtained the number of 184, 171, 181 and 158 delivery workers, respectively.Having in mind the fact that for the current last-mile delivery organisation within the scope of the USO, the observed service provider engages 280 delivery workers, we can conclude that our approach, proposed in this paper, gives better and more rational results.
Furthermore, as it has already been shown, the number of delivery workers with replacement is estimated, for different models of delivery on a monthly basis by post centres (EDWWithR).It was previously established that it is necessary to provide 8% of the reserve of delivery workers for replacement during the holidays.This means: − for the six-day delivery model EDWWithRAB EDWWithoutRAB EDWWithoutRAB = + ⋅ By summing up the data, the total number of required delivery workers was obtained, with replacements, by post centres.As shown in Table 2, the optimal number of workers is significantly less than the current (198, 185, 196, and 171, respectively).
In the end, the labour costs are calculated for each delivery model for the estimated number of delivery workers without replacement (LCWithoutR) and with replacement (LCWithR), as presented below: − for the six-day delivery These data, which refer to labour costs with replacements for various last-mile delivery models were used as input data for the multicriteria analysis, using the PROMETHEE and ARAS methods.The ranking of alternatives is discussed in detail in Section 4.

RESULTS AND DISCUSSION
This paper provides insight into the implementation of multicriteria decision-making in the field of the last-mile delivery models evaluation and selection, with the aim to obtain an optimised number of delivery workers.This section couples two possible methods to solve the defined problem: the PROMETHEE method to select the best last-mile delivery model and then the ARAS to compare the results and come to a more confident conclusion to the presented problem.

Application of the PROMETHEE method to obtain the rank of the last-mile delivery models
Results are obtained according to the following phases.
Phase 1: Construction of an evaluation matrix.A double-entry table for the selected criteria and alternatives has been compiled by using quantitative data.This matrix accounts for deviations of evaluations on pairwise comparisons of two alternatives (a and b) on each criterion.
Phase 2: Identification of the preference function P j (a, b) for each criterion j.The preference function is used to determine to what extent alternative  is preferred to alternative  and it translates the difference in evaluations of the two alternatives into a preference degree.These preferences are represented in a numerical scale ranging between 0 and 1.The value "1" represents a strong preference of alternative a over b, whereas "0" represents the indifferent preference value between the two alternatives [39].The PROMETHEE requires defining the preference function of each criterion, the choice between six preference functions depends on the decision-maker, who must define the preference or the indifference thresholds.Figure 3 shows preference function characteristics.
Phase 3: Calculation of the overall preference index Π(, ).The overall preference index Π(, ) represents the intensity of preference of  over  and it is calculated as follows: where Π(a, b) is the overall preference intensity of  over b with respect to all the K criteria, w j is the weight of criterion , and P j (a, b) is the preference function of  over  with respect to criterion .Π(a, b) ∼0 implies a weak global preference of a over b, whereas Π(a, b) ∼1 implies a strong global preference of a over b.
Phase 4: Calculation of the outranking flows, i.e. positive flow Φ + () and negative flow Φ − ().In the PRO-METHEE method, two flow measures can be determined for each alternative.There is a positive flow (it shows how much the alternative a outperforms other alternatives) and negative flow (it shows how much other alternatives outperform alternative a) Phase 5: Comparison of the outranking flows to define the alternatives' complete ranking by calculating the net flow.The comprehensive ranking is important in the case of detecting incomparability between criteria, it equals the difference between leaving and entering flow.The higher the net flow, the better the alternative is performing.Only two relations between alternatives are concluded for the comprehensive flow, which are preference and indifference relations.
The value of the net flow belongs to [-1,1] interval and the sum of the net flows computed in a problem equals 0, because the amount of entering flows is the same as the leaving flows.−1 ≤ Ф() ≤ 1 (5) The first step is to identify the alternatives and then to determine the criteria based on which the ranking of the set of alternatives was performed.The four delivery models described in the previous sections are taken as alternatives.Alternatives are ranked based on four criteria.Expert opinion was used to define the criteria, assign weight coefficients to each criterion and determine the type of preferential function of the PROMETHEE method.The result of the analysis is determining alternatives of the highest rank (priority).
The following last-mile delivery models were used as alternatives in the application of the PROMETHEE method: A1 -the six-day delivery, A2 -the five-day delivery, A3 -the combination of six-day and five-day delivery (6/5 delivery), A4 -the AB delivery.
To define the criteria, a proposal of four criteria was given, using the opinion of experts.The following criteria were set by the analysis of expert opinion: K1.Labour costs (direct and indirect) -labour costs are a very important criterion because these costs represent the largest part of the operating costs of the service provider.For each of the proposed alternatives, the number of delivery workers was calculated and labour costs were obtained according to this indicator (in the example verified here, we note that the costs were taken approximately based on the estimate that the average salary of a delivery worker is approximately 500 euros).K2.Additional costs of using modern means of delivery (electric bicycles, motorcycles, vehicles, etc.) -this criterion became important especially with the fourth alternative because in that case electric scooters or mopeds are introduced in all the last-mile delivery routes.K3.The impact of the alternative on stimulating the introduction of new postal services -the introduction of new services can be considered in all four alternatives, although the importance of this criterion is the weakest in the existing delivery organisation (Alternative 1).With each subsequent alternative, the importance of this criterion is stronger because it opens new opportunities for offering services by reorganising the delivery area and adapting to the needs and requirements of users.K4.The impact of the alternative on the improvement of business relations with the economy ("Large users") and elements of the state structure (municipalities, local communities, etc.) -the impact of this criterion is strongest with the fourth alternative because the introduction of the AB delivery model (which implies the existence of priority mail services) gives a great opportunity to key (big) users and elements of state structure to use priority mail that would be delivered every day.In fact, these entities (key users and elements of state structure) are expected to be the "big users" of priority mail.
The PROMETHEE method provides the ability to select preferred functions from a set of offered function types.Thus, the choice of the generalised criterion according to the intensity of preference was made.Then, the weight coefficients of the criteria were determined, so that the experts estimated that the first two criteria weight 0.3 and the other two weight 0.2 (Table 3).The sum of these criteria must be equal to 1.
After defining all alternatives and criteria, the next step is to minimise or maximise the values of each criterion in terms of economy, as well as to form a generalised criterion for each criterion based on preference functions.Table 3 shows the most important values for each criterion: minimised or maximised value, relative weighting coefficients and preference function for each criterion.Then, certain parameters P and Q (based on the type of preference function), minimum and maximum values for each criterion, mean and standard deviation.
Table 3 contains numerical input data for calculation that are entered from Table 2 (labour costs of the estimated number of delivery workers for different delivery systems with replacement) and the labour cost function is maximised (1-value by alternatives).The function of the costs of using modern means of delivery was maximised (1-value by alternatives).Input data for criterion 3 are also entered, as well as for criterion 4. Furthermore, the data on the importance of the criterion is entered (the sum must be 1).
Using the PROMETHEE method, alternatives are ranked based on the value of net flow Φ(), which is shown by Equation 4. The term "net flow" implies the validity of the alternative in the sense that the higher the value, the better the alternative, i.e. the alternative will have higher priority.In our case of determining the optimal FLMDM, the pure flow value indicates the priority of the delivery model as an alternative.
The results of the application of the PROMETHEE method are shown in Table 4. Based on the obtained results and the ranking of alternatives, it can be concluded that the highest ranking (priority) of the alternative is the A4-AB delivery model.The results suggest the implementation of the AB delivery model.Regarding the robustness of the obtained results, it is necessary to point out that we can expect that this alternative would be sufficient for seasonal increases in volumes and would have sufficient personnel capacity.During such periods it is recommended to use the AB model with the replacements because then full personnel capacity is engaged.

Application of the ARAS method to obtain the rank of the last-mile delivery models
For the selection of alternatives, the Additive Ratio Assessment (ARAS) method is applied.It is evident in the literature that the ARAS method was combined with many other MCDM methods.There are several real-life studies where the ARAS method was used, for example [45−48].The ARAS method is one of the re- cently developed multicriteria decision-making methods developed by [49].A procedure to solve the problems of multicriteria decision-making by applying the ARAS method can be described through the following steps [48].
Step 1. Forming the decision-making matrix and determining the weights of the criteria.A decision-making matrix consists of feasible alternatives rated on criteria.In this step, the expert determines the optimal performance rating for each criterion.If the expert has no preferences, then the optimal performance ratings can be determined as: max where x 0j is the optimal performance rating in relation to the j th criterion.
Step 2. Normalise decision-making matrix R=[r ij ].In this step, the normalisation is done by the following equation: where r ij is the normalised performance rating of the i th alternative in relation to the j th criterion.
Step 3: Definition of weighted normalised decision matrix V=[v ij ].The weighted normalised performance ratings are calculated by using the following formula: where v ij is the weighted normalised performance rating of the i th alternative in relation to the j th criterion.
Step 4. Determine the value of the optimality function where S i is the value of the optimality function of i th alternative.
Step 5. Calculate the degree of utility for each alternative.The calculation of the utility degree Q i of an alternative a i is by applying the following formula: where Q i is the degree of the utility of the i th alternative, and S i and S o are the optimality criterion values, obtained from Equation 9.The calculated values Q i are between 0 and 1.
Step 6. Rank the alternatives and/or select the most efficient one.The considered alternatives are ranked by ascending Q i , i.e. the alternatives with the higher values of Q i have a higher rank and the alternative with the largest value of Q i is the best-placed one.
The obtained results of the ARAS method application are presented in the following tables.The initial decision-making matrix is presented in Table 5.The next step is normalisation of the input data and it is presented in Table 6.The normalised weighted values, the values of the optimality function, as well as the degrees of the utility of the alternative are presented in Table 7.The results obtained from the ARAS method confirm the results obtained by the PROMETHEE method.The alternatives, i.e. the last-mile delivery models obtain the same rank through both methods.The AB model is the best ranked model for delivery organisation in the observed case.

CONCLUSIONS
Results obtained in this paper represent an assessment of the optimal flexible model for the organisation of the last-mile delivery of a service provider within the scope of universal postal service.Using the multicriteria decision analysis, the paper compares four delivery models: 6-day delivery service (existing solution), 5-day delivery service, 6-day delivery service for municipal places/5-day for other areas, and an AB delivery model with priority and non-priority mail.
Choosing an optimal FLMDM and optimisation of the number of delivery workers using multicriteria decision-making is introduced in this paper for the first time.Relevant variables that evaluate the business of the service provider are included.In that sense, the paper treats data related to the number of postal items and the number of norm minutes individually and in total by services and last-mile delivery routes, and the number of delivery workers as the basic input variables.Using these input data, an optimised number of delivery workers were obtained, as well as the productivity of the last-mile delivery routes for each delivery model.All inputs were processed through four flexible models of delivery organisation, which represent four alternatives in the model of multicriteria analysis.The goal was to get a model, i.e. the highest-ranking alternative to show which delivery model is the most suitable for the observed service provider with an emphasis on the optimised number of delivery workers.
To qualitatively apply the proposed models, it is necessary to: − ensure comprehensive collection and processing of statistical data regarding the volume of services performed at the last-mile delivery routes, − provide monitoring of the monthly travelled road distance in the last-mile delivery routes, primarily with the aim of recording and accurately standardising the share of the travelled road distance in the total productivity of delivery workers, − ensure regular updating of the number of technological jobs and delivery workers.
In accordance with the results, the following is proposed: when any service provider with the universal postal service obligation meets the legal requirements regarding the application of all proposed alternatives (category of priority mail has been introduced), it is recommended that the provider (operator) organises the last-mile delivery according to the flexible models proposed in this paper.Depending on the specifics of each service provider and available data, the results will vary for the last-mile delivery organisation.Specifically, for the postal service provider observed in this paper, the recommended optimal organisation of the last-mile delivery is in accordance with a flexible model of alternative 4 -the AB model.This is confirmed by the PROMETHEE and ARAS methods by ranking the proposed alternatives according to the defined criteria.The AB model is a type of dynamic model of delivery organisation that includes, among other things, monitoring contracts with large customers and, depending on that, merging and creating last-mile delivery routes.In that sense, it would be possible to create daily last-mile delivery routes following the daily number of postal items for delivery.That is the main advantage of a dynamic delivery model.Another main advantage of the dynamic AB delivery model would be the optimised redistribution of the number of workers and the reduction of human resources costs.All delivery workers would be distributed to the last-mile delivery routes according to actual daily needs.
Having in mind the fact that for the current last-mile delivery organisation the observed service provider engages 280 delivery workers (six-day delivery, without optimisation), we can conclude that our approach gives better and more rational results.All proposed FLMDMs offer the optimal number of workers for the last-mile delivery, which significantly reduces the labour costs of service providers and reflects financial sustainability.Even in the case of a currently implemented delivery model (six-day delivery, without optimisation), better results and improvements are obtained with our approach.
The authors believe that the obtained results may represent a general guideline for any service provider.Improvements in the number of delivery workers and labour costs are evident regardless of the proposed flexible model applied in the last-mile delivery organisation.In this paper, according to the PROMETHEE and ARAS, the AB delivery model gives the best results, but the other models also reach significant savings in the number of workers at the level of the entire postal network.In our research, we decided to use the PROMETHEE and ARAS methods because they are an efficient decision-making support deployed in case of a finite number of criteria.
Future research would include the elaboration of a detailed model of the AB delivery and its application in real conditions to see whether the solutions of the delivery model presented in this paper have found practical application.Furthermore, new forms of postal locations (franchises, agencies, mobile post offices) were not dealt with in this research.Moreover, the expansion of the network for collecting items (by increasing the number of postal mailboxes), the expansion of the retail network, the optimisation of transport and the installation of a collective postal mailbox in less populated rural areas were also neglected.Future models should encompass these inputs as well.It would also be beneficial to expand the optimal flexible model, by including other input variables, such as demographic and geographic characteristics, financial indicators of the post offices and centres, etc.

Appendix: The summary of output acronyms
i is the number of the last-mile delivery routes within the observed post centre − for the five-day delivery model

∑
where pc is the number of post centres at the observed provider and 500 is the cost of salary per delivery worker (average salary is €500) − for the five-day delivery

Table 1
contains a number of counter clerks and a number of delivery workers engaged in post centres (from PC1 to PC14).For every post office belonging to the competent post centre current last-mile delivery routes are listed.Table 1 also contains the volume of items whose senders are legal entities (registered mail annually and monthly, unregistered mail annually and monthly) and the volume of items whose senders are individuals (registered mail annually and monthly; unregistered mail annually and monthly; registered

Table 1 -
Part of the input data calculation

Table 2 -
Output data calculation

Table 4 -
Ranking of alternatives based on net flow values

Table 3 -
Input for the multicriteria analysis

Table 5 -
The initial decision-making matrix

Table 6 -
Normalisation of the initial decision-making matrix

Table 7 -
Normalised weighted values, values of optimality function and the degrees of the alternative utility Estimated Number of Delivery Workers for six-day delivery, monthly, without replacement, by post centre EDWWithoutR5 pc Estimated Number of Delivery Workers for five-day delivery, monthly, without replacement, by post centre EDWWithoutR6/5 pc Estimated Number of Delivery Workers for 6/5 delivery, monthly, without replacement, by post centre EDWWithoutRAB pc Estimated Number of Delivery Workers for AB delivery, monthly, without replacement, by post centre EDWWithR6 pc Estimated Number of Delivery Workers for six-day delivery, by post centre, monthly, with replacement EDWWithR5 pc Estimated Number of Delivery Workers for five-day delivery, by post centre, monthly, with replacement EDWWithR6/5 pc Estimated Number of Delivery Workers for 6/5 delivery, by post centre, monthly, with replacement EDWWithRAB pc Estimated Number of Delivery Workers for AB delivery, by post centre, monthly, with replacement pc Labour Costs for AB delivery, with replacement