A methodology for the strategic design of city logistics networks and its application in Turkish automotive spare parts industry

Abstract

City logistics approaches and modeling struggles have a significant role in urban areas in increasing the efficiency of logistics operations and reducing traffic jams and their environmental effects. By developing an effective distribution network for cities, it is possible to compete with the changing world and satisfy flexible customer requirements. In this study, as a real-world case, a city logistics model for Istanbul metropolitan area is designed using multi-objective linear programming that considers the different objectives of the stakeholders in cities by integrating the fuzzy Choquet integral technique in a multi-level distribution network for the automotive spare part industry. This paper makes decisions regarding the amount of product flowing among the echelons, the amount of stock to be kept in the warehouses, and the product delays allowed. While minimizing the transportation cost, holding cost and emission levels during these decisions, the study also aims to maximize the service quality in the warehouses. The model is applied to a logistics network of fifty demand points and thirty time periods which can be considered a middle or large-scale problem. In the model, it is also decided to transport the products with electric or fuel vehicles. In the transport sector, electric vehicles are the key to meet future needs for social, health and other human services. The results are discussed under different scenarios. This research allows the use of such a model in making strategic decisions for the distribution network design in big cities.

Keywords

Fuzzy Choquet integral electric vehicles multi-criteria decision making city logistics mathematical modeling

1 Introduction

City logistics plays a key role in transportation operations for satisfying the customer demands in urban areas and significantly affects the environment, energy consumption and reduction of traffic jams. With the increase in urban population, freight related decisions for city areas are becoming more critical. For this reason, it is an important success factor in urbanization. In addition, companies can make decisions to be more competitive by considering different scenarios regarding their distribution networks. As a strategic level decision, the distribution network design problem determines the best facility locations and optimal flows of products among the facilities to support a given supply chain strategy. It always aims to optimize sources, save on costs and provide quality services. A well-designed network model satisfies customer demands at a specified service level with the lowest cost. Besides, a number of different stakeholders, such as shippers, residents, receivers and local authorities, etc., in cities have various and sometimes conflicting objectives. Including the different priorities of various stakeholders is a crucial success factor for an efficient city logistics domain. They are complicated organizations that display complex relationships and trade-offs among the various decision policies. While the cost is more important for a specific decision-maker, the other decisions can be related to time or other factors like accessibility, environment, etc.

The literature review shows that the types of modeling studies exist for city logistics. These studies provide various city logistics models according to stakeholders, objective functions and methods. Furthermore, there are many diverse categorizations of city logistics stakeholders, and each has different expectations. The local authority is among the most remarkable stakeholders [6, 15, 16, 19, 33]. Local authorities aim to provide a quality life to residents in the city. One of the studies in this area focuses on urban freight transport for some Swedish cities and works on urban transport operation planning from the perspective of local authority [18]. According to this study, the local authority is a powerful organization to perform the official rules and procedures that significantly affect the logistics services in urban areas. Thus, it is essential to know the measures, such as the cause-and-effect relationship. In this study, a valuable method is presented for comprehending the cause-and-effect approach, which helps to elucidate the process and outlines the necessary steps.

Most of the studies in the literature are related to a different stakeholder priority, but a few are focused on multiple stakeholders. According to Taniguchi et al., taking into account the multiple stakeholders is essential in city logistics analyses as it involves different views of stakeholders [30]. The authors of [10] and [33] represented this perspective in their studies. They argue that factors such as stakeholder involvement with different objectives demonstrate the forces behind urban freight transportation. Holguin-Veras proposes a similar modeling approach that considers the customer, government, carrier and producer for urban freight transportation [11].

There are some studies that include implementation of network planning for the areas. The optimization of the distribution network design problem is generally tried to be solved by mathematical models. In addition, there is a wide range of studies in which the problems have been resolved by using heuristic models. Ishii et al. [13] and Jayaraman & Ross [14] represent deterministic models and solve these problems by using mathematical programming approaches. Syarif et al. [28] worked on a network planning problem using the genetic algorithm. This designed model decides on the selection of the production areas and distribution centers. Moreover, Tuzkaya and Önüt presented a model-based holonic approach to minimize inventory and delay costs for manufacturers, warehouses and suppliers [31].

Other modeling approaches propose stochastic programming models and offer solution algorithms for many supply network problems, including uncertainty [9, 22, 23]. In [26], Santoso et al. worked on stochastic programming and designed a distribution network model. They presented a method that includes a sampling approach (SAA schema) and the Benders decomposition algorithm. In this study, two distribution networks are evaluated to show the importance of the stochastic approach and underline the effectiveness of the offered solution method. Some other studies [3, 18, 25] can be given as examples that solved network design problems by fuzzy approaches used in different stages of the solution process.

Poor air quality and its environmental effects in urban areas are becoming a serious problem for citizens. There are also studies that examine the issue of poor air quality in urban areas. These studies propose many different options to have lower emissions in the cities. One option is using electric vehicles instead of fuel vehicles in urban freight transport. Electric vehicles have undergone substantial technological advancements in recent years [29]. Giordano et al. compare diesel and electric pickup trucks by evaluating their economic and environmental effects on city logistics and highlight the use of battery electric vehicles, which plays a critical role in having lower emissions [8]. This study provides an opportunity for the government and companies to evaluate the effects of diesel and battery electric vehicles on health, environmental and economic issues. Urzua-Morales et al. proposed a logistics model for last-mile deliveries using various vehicles such as diesel vehicles, bicycles and electric vehicles. The authors analyzed the environmental impact of air pollution in terms of vehicle type [32, 36]. Pelletier et al. and Juan et al. discuss the search for electric vehicles for freight transportation and their challenges [15, 21]. According to Taniguchi et al. [30], transportation operations lead to many problems. Transportation functions that are environmentally sustainable and economically efficient are the ideal option for urban areas.

Based on the existing literature, the main contribution of this paper is to find a compromise solution to the conflicting objectives of city logistics. Although companies focus on their internal costs, such as transportation, delaying and inventory costs, environmental sensitivity is also reflected in decisions with industry and customer pressure. Traditional businesses are limited to focusing solely on the cost factor or even just one aspect of cost during decision-making, which results in making strategic errors. As a result, the motivation of this study is to consider the strategic and operational decisions of the enterprises together and to take into account many factors while finding the global optimum. Here, the model is applied to a network planning problem of a company in the automotive industry in Turkey and the results are analyzed. This company provides automotive spare parts for its customers. The management of the spare parts distribution network is especially critical in terms of inventory costs. The companies generally keep stock at all echelons of the supply chain and the number of items in the automotive spare part industry is high. Customer demand is unstable, and a high level of service is always expected. This renders the process challenging to manage, and the effectiveness and efficiency of logistics operations become crucial for urban areas such as Istanbul.

Another motivation of this study is proposing a solution strategy by using either goal programming and fuzzy Choquet integral methods for a multi-level and multi-product city logistics network. The main advantage of the study is to accomplish the different objectives of the stakeholders in the city while minimizing the sum of total transportation costs, inventory costs, punishment costs for delayed products and emission levels in the urban areas and maximizing the service quality level of warehouses. While trying to find an optimal solution for this distribution network, it integrates fuzzy Choquet integral approach to weight the main customer warehouses.

In the literature, there are many aggregation methods such as Simple Arithmetic Average (SA), Simple Weighted Average (SWA), Geometric Average or Geometric Weighted Average. These traditional aggregation techniques ignore the interdependency or interrelation between the criteria. However, Choquet integral is one of the powerful solution methods for decision making problems with using fuzzy logic. This method allows to consider the interaction between all possible combinations of criteria. It plays an important role for flexibility during aggregation process. Choquet integral is a method which changes the way decision makers interpret logical values and solves the problem for non-linear situations since it does not need to assume the independence of each criterion.

In this study, Choquet integral is used to evaluate main customer warehouses with multiple criteria. When other methods are used to determine the overall performance of warehouses, the interactions among the criteria are ignored. This shows that the warehouses’ performance for one criterion does not have any relation with their performance of other criteria which is generally not true for a real-world case.

Electric vehicles are becoming more and more popular throughout the world industry, offering a range of unique benefits such as a big contributing factor on reducing the emission level. This proposed model also makes a decision between electric and fuel vehicles in urban freight transportation under uncertainty (Fig. 1).

Fig. 1

The proposed methodology.

2 Mathematical model design

The proposed model is designed for an automotive industry transportation network. The inspired company has a local warehouse and automotive spare parts distribution network in a metropolitan city. There are two levels from the local warehouse to the main customer warehouses and from main customer warehouses to demand points. Furthermore, direct transportation from the local warehouse to demand points is possible as another alternative (Fig. 2). The model is generated to select fuel and electric vehicles in city logistics operations. It also calculates the number of products that must be transported between facilities, the number of delayed products and inventory for main customer warehouses in each time slot. The presented model also satisfies customer demands under capacity constraints.

Fig. 2

Network structure of the model.

The problem has multiple objectives that try to minimize the total transportation costs, inventory costs, punishment costs for delayed products and emission levels in the urban area. The used notation and mathematical form of the network model are given below;

Indices

i: Index of the demand points

j: Index of the vehicle types

k: Index of the main customer warehouses

m: Index of the time period

l: Index of the product types

t: Index of the permitted delaying time to demand points

Decision variables

QLw_mklj: Quantity of product l transported from local warehouse to main customer warehouse k with vehicle type j during period m

QCw_kmilj: Quantity of product l transported from main customer warehouse k to demand point i with vehicle type j during period m

QLe_milj: Quantity of product l transported from local warehouse to demand point i with vehicle type j during period m

In_mlk: Inventory level of product l at main customer warehouse k during period m

Dl_mli: Quantity of delayed product l to demand point i during period m

Parameters

a: Maximum permitted delaying time

CLw_klj: Transportation cost per product l from local warehouse to main customer warehouse k with vehicle type j

CCw_kilj: Transportation cost per product l from main customer warehouse k to demand point i with vehicle type j

CLe_ilj: Transportation cost per product l from local warehouse to demand point i with vehicle type j

CW_lk: Waiting cost per product l in main customer warehouse k

CD_li: Unit punishment cost for delayed product l to demand point i

D_mil: Demand of product l for demand point i during period m

Acw_k: Capacity of main customer warehouse k

A_LW: Local warehouse capacity

Qss_lk: Safety stock quantity per product l in main customer warehouse k

Si_lk: Initial inventory per product l in main customer warehouse k

Sd_li: Delayed product l level at the beginning for demand point i

Tcw_ikj: The transportation time between main customer warehouse k and demand point i with vehicle type j

Tlw_kj: The transportation time between local warehouse and main customer warehouse k with vehicle type j

Tle_ij: The transportation time between local warehouse and demand point i with vehicle type j

E: Emission level in the urban area

W_k: Weighting value of main customer warehouse k acquiring by Choquet integral method

The formulation of the model can be found in Equations (1) (19).

The first objective function (1): Minimization of total transportation costs

$\begin{matrix} Min = \sum_{m}^{M} \sum_{k}^{K} \sum_{l}^{L} \sum_{j}^{J} {CLw}_{klj} ({QLw}_{mklj}) \\ + \sum_{m}^{M} \sum_{i}^{I} \sum_{l}^{L} \sum_{j}^{J} {CLe}_{ilj} ({QLe}_{milj}) \\ + \sum_{m}^{M} \sum_{i}^{I} \sum_{l}^{L} \sum_{k}^{K} \sum_{j}^{J} {CCw}_{kilj} ({QCw}_{kmilj}) \end{matrix}$ (1)

The second objective function (2): Minimization of total inventory holding costs

$\begin{matrix} Min = \sum_{m}^{M} \sum_{l}^{L} \sum_{k}^{K} {CW}_{lk} (\sum_{j}^{J} {QLw}_{(m - {Tlw}_{kj}) klj} \\ - \sum_{i}^{I} \sum_{j}^{J} {QCw}_{(m + {Tcw}_{ikj}) kilj} + {In}_{(m - 1) lk}) \end{matrix}$ (2)

The third objective function (3): Minimization of penalty costs for delayed products

$\begin{matrix} Min = \sum_{l}^{L} \sum_{m}^{M} \sum_{i}^{I} {CD}_{li} (\sum_{k}^{K} \sum_{J}^{J} \\ (D_{mil} - {QCw}_{kmilj} - {QLe}_{milj}) + {Dl}_{(m - 1) li}) \end{matrix}$ (3)

The fourth objective function (4): Minimization of emission level in urban area

$\begin{matrix} Min = \sum_{k}^{K} \sum_{m}^{M} \sum_{i}^{I} \sum_{l}^{L} \sum_{j}^{J} {QCw}_{kmilj} E \\ + \sum_{m}^{M} \sum_{k}^{K} \sum_{l}^{L} \sum_{j}^{J} {QLw}_{mklj} E \\ + \sum_{m}^{M} \sum_{i}^{I} \sum_{l}^{L} \sum_{j}^{J} {QLe}_{milj} E \end{matrix}$ (4)

The fifth objective function (5): Maximization of service quality level for warehouses

$\begin{matrix} Max = \sum_{k}^{K} \sum_{m}^{M} \sum_{i}^{I} \sum_{l}^{L} \sum_{j}^{J} W_{k} {QCw}_{kmilj} \\ + \sum_{m}^{M} \sum_{k}^{K} \sum_{l}^{L} \sum_{j}^{J} W_{k} {QLw}_{mklj} \\ + \sum_{m}^{M} \sum_{i}^{I} \sum_{l}^{L} \sum_{j}^{J} {QLe}_{milj} \end{matrix}$ (5)

Subject to;

$\begin{matrix} \sum_{k}^{K} \sum_{j}^{J} {QLw}_{(m - {Tlw}_{kj}) klj} + \sum_{k}^{K} {In}_{(m - 1) lk} \\ ⩾ \sum_{i}^{I} \sum_{k}^{K} \sum_{j}^{J} {QCw}_{(m + {Tcw}_{ikj}) kilj} \forall_{m, l} \end{matrix}$ (6)

$\begin{matrix} \sum_{k}^{K} \sum_{j}^{J} {QLw}_{(m - {Tlw}_{kj}) klj} \\ - \sum_{i}^{I} \sum_{k}^{K} \sum_{j}^{J} {QCw}_{(m + {Tcw}_{ikj}) kilj} \\ + \sum_{k}^{K} {In}_{(m - 1) lk} = \sum_{k}^{K} {In}_{mlk} \forall_{m, l} \end{matrix}$ (7)

$\begin{matrix} D_{mil} ⩽ \sum_{t}^{m + a} \sum_{k}^{K} \sum_{j}^{J} {QCw}_{ktilj} + \sum_{t}^{m + a} \sum_{j}^{J} {QLe}_{tilj} \\ - \sum_{t}^{m} D_{(t - 1) il} \forall_{m, i, l} \end{matrix}$ (8)

$\begin{matrix} D_{mil} - \sum_{k}^{K} \sum_{j}^{J} {QCw}_{kmilj} - \sum_{j}^{J} {QLe}_{milj} \\ + {Dl}_{(m - 1) li} = {Dl}_{mli} \forall_{m, i, l} \end{matrix}$ (9)

${In}_{mlk} ⩾ {Qss}_{lk} \forall_{m, l, k}$ (10)

$\sum_{l}^{L} {In}_{mlk} ⩽ {Acw}_{k} \forall_{m, k}$ (11)

$\sum_{l}^{L} \sum_{j}^{J} {QLw}_{mklj} ⩽ A_{LW} \forall_{m, k}$ (12)

${In}_{(0 l) k} = {Si}_{lk} \forall_{l, k}$ (13)

${Dl}_{(0 l) i} ⩾ {Sd}_{li} \forall_{l, i} .$ (14)

${QLw}_{mklj} ⩾ 0 \forall_{m, k, l, j}$ (15)

${QCw}_{kmilj} ⩾ 0 \forall_{k, m, i, l, j}$ (16)

${QLe}_{milj} ⩾ 0 \forall_{m, i, l, j}$ (17)

${In}_{mlk} ⩾ 0 \forall_{m, l, k}$ (18)

${Dl}_{mli} ⩾ 0 \forall_{m, l, i}$ (19)

As the first constraint of the model, Equation (6) ensures that the total transported quantity of lth product in (m - Tlw_kj)th period from local warehouse to kth main customer warehouse and main customer warehouse inventory level in (m-1)th period must be greater than or equal to the total quantity of lth product which is transported in mth period from main customer warehouse to demand point in order to meet the need in (m + Tcw_ik)th time period. Equation (7) gives the main customer warehouse stock quantity per product in mth period. Equation (8) satisfies the demand of the demand points for each product in no more than (m + a) periods. Equation (9) gives the delaying quantity for each demand point in mth period. Equation (10) guarantees that the overall stock quantity per product in the main customer warehouse must be greater than or equal to safety stocks. Equations (11) and (12) are capacity constraints for local warehouses and main customer warehouses, respectively. Equations (13) and (14) provide the initial stock level and delayed quantity at the beginning, respectively. The last five equations of the model are non-negativity constraints of decision variables.

3 Solution approaches

The proposed multi objective and multi-level logistics network model is solved by goal programming. The service quality of main customer warehouses which is very critical in the network design is weighted by fuzzy Choquet integral approach. These solution approaches are explained below briefly.

3.1 Fuzzy Choquet integral method

Choquet integral is one of the solution methods for decision-making problems using the fuzzy measure. It is a method that changes decision-makers’ interpretation to logical values and solves the problem with mathematical accounting. The use of fuzzy logic allows this method to designate importance to all criteria groups by considering the interaction between all possible combinations of criteria, and it provides flexibility for adunation. Some studies include Choquet integral method to solve decision-making problems [1, 4, 24, 27, 35]. The main steps to perform Choquet integral is indicated below:

m is supposed to be the number of dimensions and n_j is the number of criteria in j. dimension.

Step 1: Criteria i, respondents’ linguistic choices for importance level, detected service and the tolerance area of anticipated service are investigated.

Step 2: Responder t and criteria i show the importance level by the fuzzy measure ${\overset{ˇ}{A}}_{i}^{t}$ , detected service by ${\overset{ˇ}{p}}_{i}^{t}$ and the tolerance area of anticipated service by ${\overset{ˇ}{e}}_{i}^{t}$ , where t = 1,2, … ,k, i = 1,2, … ,n_j, j = 1,2, … ,m and k is the number of responders.

Step 3: Average ${\overset{ˇ}{A}}_{i}^{t}$ _, ${\overset{ˇ}{p}}_{i}^{t}$ and ${\overset{ˇ}{e}}_{i}^{t}$ into ${\tilde{A}}_{l}$ ${\tilde{p}}_{l}$ and ${\tilde{e}}_{l}$ , respectively, using Equations (20) (22) below.

$\begin{matrix} {\tilde{A}}_{l} & = \frac{\sum_{t = 1}^{k} A_{i}^{\lor t}}{k} \\ = (\frac{\sum_{t = 1}^{k} a_{i 1}^{t}}{k}, \frac{\sum_{t = 1}^{k} a_{i 2}^{t}}{k}, \frac{\sum_{t = 1}^{k} a_{i 3}^{t}}{k}, \frac{\sum_{t = 1}^{k} a_{i 4}^{t}}{k}) \end{matrix}$ (20)

$\begin{matrix} {\tilde{p}}_{l} & = \frac{\sum_{t = 1}^{k} p_{i}^{\lor t}}{k} \\ = (\frac{\sum_{t = 1}^{k} p_{i 1}^{t}}{k}, \frac{\sum_{t = 1}^{k} p_{i 2}^{t}}{k}, \frac{\sum_{t = 1}^{k} p_{i 3}^{t}}{k}, \frac{\sum_{t = 1}^{k} p_{i 4}^{t}}{k}) \end{matrix}$ (21)

$\begin{matrix} {\tilde{e}}_{l} & = \frac{\sum_{t = 1}^{k} e_{i}^{\lor t}}{k} \\ = (\frac{\sum_{t = 1}^{k} e_{i 1}^{t}}{k}, \frac{\sum_{t = 1}^{k} e_{i 2}^{t}}{k}, \frac{\sum_{t = 1}^{k} e_{i 3}^{t}}{k}, \frac{\sum_{t = 1}^{k} e_{i 4}^{t}}{k}) \end{matrix}$ (22)

Step 4: Normalize the service quality per criteria by using Equation (23) where $\tilde{f_{l}} \in \tilde{F} (S)$ is a fuzzy-valued function.

${\tilde{f}}_{i} = ‖_{\propto \in [0, 1]} {\tilde{f}}_{i}^{\propto} = ‖_{\propto \in [0, 1]} [f_{i, \propto}^{-}, f_{i, \propto}^{+}]$ (23)

Step 5: $\tilde{F} (S)$ represents all fuzzy-valued functions ${\tilde{f}}_{l}$ . $p_{i}^{- \propto}$ and $e_{i}^{- \propto}$ are α-level cuts of ${\tilde{p}}_{i}$ and ${\tilde{e}}_{i}$ for ∝ ∈ [0, 1].

${\bar{f}}_{i}^{\propto} = [f_{i, \propto}^{-}, f_{i, \propto}^{+}] = \frac{p_{i}^{- \propto} - e_{i}^{- \propto} + [1, 1]}{2}$ (24)

Step 6: Equation (25) gives the service quality of dimension j.

$(C) \int \tilde{fd} \tilde{g} = \propto \in [0, 1] (C) \int f_{\propto}^{-} {dg}_{\propto}^{-}, (C) \int f_{\propto}^{+} {dg}_{\propto}^{+}$ (25)

Where ${\bar{g}}_{i}$ : $P (S) \to I (R^{+}), {\bar{g}}_{i} = [g_{i}^{-}, g_{i}^{+}], {\bar{g}}_{i}^{\propto} = [g_{i, \propto}^{-}, g_{i, \propto}^{+}]$ and^¯ $f_{i} : S \to I (R^{+}), f_{i} = [f_{i}^{-}, f_{i}^{+}] for i = 1, 2, 3, \dots, n_{j}$

For this service quality value to be calculated, a λ value and the fuzzy measures g (A (i)) , i = 1, 2, …, n, are needed. These can be obtained from the following Equations (26) (28).

$g (A_{(n)}) = g ({S_{(n)}}) = g_{n}$ (26)

$\begin{matrix} g (A_{(i)}) = g_{i} + g (A_{(i + 1)}) \\ + λ g_{i} g (A_{(i + 1)}), where 1 ⩽ i < n \end{matrix}$ (27)

$1 = g (S) = {\begin{matrix} 1 / λ {\prod_{i = 1}^{n} [1 + λ g (A_{i})] - 1} if λ \neq 0 \\ \sum_{i = 1}^{n} g (A_{i}) if λ \neq 0 \end{matrix}$ (28)

Where A_i∩ A_j = ∅ for all i,j = 1,2,3, … ,n and i≠j and λɛ (-1, ∞]. Let μ be a fuzzy measure on (I, P(I)) and an application $f : I \to R^{+} .$

The Choquet integral of f with regard to μ is defined by Equation (29):

$(C) \int fd μ = \sum_{i = 1}^{n} (f (σ (i)) - f (σ (i - 1))) μ (A_{(i)})$ (29)

Where σ is a permutation of the indices in order to have f (σ (1))⩽ … ⩽ fσ (n)) , A_(i) = { σ (i) , …, σ (n) } and f (σ (0)) = 0 by convention [5, 13].

Step 7: Assemble all measured service quality into overall service quality, which is represented by a fuzzy number $\tilde{Y}$ .

Step 8: Suppose that the affiliation of $\tilde{Y}$ is $μ_{\tilde{Y}}^{(x)}$ ; defuzzify the fuzzy number $\tilde{Y}$ into a crisp value y and compare the total performance of the alternatives.

3.2 Goal programming method

Satisfying the objective functions in a compromise solution requires additional linear programming approaches. The goal programming methodology provides a solution for a multi-objective model. Goal programming minimizes the deviations between the target values of the objectives, so the overachievement of the target d+ and underachievement of goal d^– should be minimized to 0. Goals are converted to constraints by introducing these deviational variables. Furthermore, a target value is given (b_i), which must be achieved for each objective. Equations (30) (32) provide a generalized model for this type of programming:

$MinZ = \sum_{i \in m} (d_{i}^{+} + d_{i}^{-})$ (30)

$\sum_{j \in n} a_{ij} x_{j} - d_{i}^{+} + d_{i}^{-} = b_{i}$ (31)

$\begin{matrix} d_{i}^{+} . d_{i}^{-} = 0, d_{i}^{+}, d_{i}^{-}, x_{j} ⩾ 0 i = 1, 2, \dots \dots, m \\ j = 1, 2, \dots \dots, n \end{matrix}$ (32)

In the literature, there are different methods to solve goal programming problems. Widespread use one of these methods is preemptive goal programming. The advantage of this approach is handling the priority structure of objectives. In this method, the higher priority objectives must be first satisfied and then the lower priority objectives. After solving the problem for the higher priority objective function, the optimal result is added as a constraint to the model. It continues with the following goals without jeopardizing the previous, more important goals. The priority is judged by the decision-maker [2].

4 An application in the automotive industry

The proposed model is applied to a company in the automotive industry in Istanbul. There are two levels in the network, the first is from local warehouse to main customer warehouses and the second is from main customer warehouses to demand points. Direct transportation from the local warehouse to demand points is another alternative. This multi-level and multi-product model uses fuel and electric vehicles in urban freight transport. The customers also give their demands, and the company realizes a distribution plan considering the transportation costs, total inventory costs, punishment costs for delayed products, service quality level of warehouses and emission level in the urban area. The proposed model considers the different priorities of stakeholders in the city. There are tradeoffs between the objectives, which show differences according to each stakeholder.

4.1 The weighting of main customer warehouses by using fuzzy Choquet integral method

The fifth objective function of the model is the maximization of service quality level for warehouses. This paper suggests using the fuzzy Choquet integral method to weight the main customer warehouses. The efficiency of main customer warehouses is critical to increasing the satisfaction of demand points.

There are two levels from the local warehouse to the main customer warehouses and from the main customer warehouses to demand points. Moreover, direct transportation from the local warehouse to demand points is possible as another alternative. A well-designed network model satisfies customer demands at a specified service level and the lowest cost. The primary purpose of a distribution network design problem is to cover the customer requirements while minimizing the sum of cost items. Therefore, the service quality level of warehouses should be considered to satisfy demand points. In this objective function, a punishment and reward approach is considered as demand points are strongly related to main customer warehouses, and the performance of main customer warehouses is significant for demand points.

High-performer main customer warehouses have precedence over distributions from a local warehouse. For this reason, the main customer warehouses are weighted according to various criteria. This weighting value will be included in the model and used in the fifth objective function as a coefficient (W_k). The fifth objective function will reward the main customer warehouse with the highest weighting value. Firstly, the main criteria (T_n) and also sub-criteria (s_nm) are determined by reviewing the related studies in the literature and taking the opinions of the experts to apply this method (Fig. 3).

Fig. 3

Main and sub-criteria for customer warehouses.

In the next step, each main and sub-criterion is evaluated by an expert group. A nine-linguistic-term scale representing the relationship between trapezoidal fuzzy numbers and degrees of linguistic importance is used in calculating the mathematical equivalents of the linguistic expressions obtained from the experts. The fuzzy numbers parameterize the tolerance area of anticipated service, respondents’ linguistic choices for the importance level, given criteria and perceived service. The tolerance area indicated in Table 1 is obtained as follows: The first two numerical values of the lower linguistic value of a tolerance area in Table 1 are combined with the last two numerical values of the upper linguistic value of the same tolerance area. Please see Table 1 for the details.

Table 1

Importance level, tolerance area of anticipated service and detected service

Criteria	Importance level				Tolerance area of anticipated service				Detected service
T₁	1	1	1	1					A1				A2				A3
s₁₁	0,72	0,78	0,92	0,97	0,72	0,78	1	1	0,93	0,98	0,98	1	0,72	0,78	0,92	0,97	0,58	0,63	0,80	0,86
s₁₂	1	1	1	1	0,93	0,98	1	1	1	1	1	1	0,58	0,63	0,80	0,86	0,72	0,78	0,92	0,97
s₁₃	0,72	0,78	0,92	0,97	0,58	0,63	0,98	1	1	1	1	1	0,72	0,78	0,92	0,97	0,58	0,63	0,80	0,86
s₁₄	0,58	0,63	0,80	0,86	0,32	0,41	0,92	0,97	1	1	1	1	0,72	0,78	0,92	0,97	0,58	0,63	0,80	0,86
T₂	0,93	0,98	0,98	1
s₂₁	1	1	1	1	0,72	0,78	1	1	0,04	0,10	0,18	0,23	0,32	0,41	0,58	0,65	0,04	0,10	0,18	0,23
s₂₂	0,93	0,98	0,98	1	0,72	0,78	0,98	1	0,72	0,78	0,92	0,97	0,93	0,98	0,98	1	0,58	0,63	0,80	0,86
s₂₃	0,72	0,78	0,92	0,97	0,58	0,63	0,98	1	0,72	0,78	0,92	0,97	0,93	0,98	0,98	1	0,58	0,63	0,80	0,86
T₃	0,72	0,78	0,92	0,97
s₃₁	0,72	0,78	0,92	0,97	0,72	0,78	1	1	0,04	0,10	0,18	0,23	0,04	0,10	0,18	0,23	0,58	0,63	0,80	0,86
s₃₂	0,32	0,41	0,58	0,65	0,72	0,78	1	1	0,17	0,22	0,36	0,42	0,04	0,10	0,18	0,23	0,93	0,98	0,98	1
s₃₃	0,17	0,22	0,36	0,42	0,72	0,78	1	1	0,58	0,63	0,80	0,86	0,32	0,41	0,58	0,65	0,72	0,78	0,92	0,97
T₄	0,58	0,63	0,80	0,86
s₄₁	0,72	0,78	0,92	0,97	0,58	0,63	0,98	1	0,32	0,41	0,58	0,65	0,32	0,41	0,58	0,65	0,32	0,41	0,58	0,65
s₄₂	0,58	0,63	0,80	0,86	0,58	0,63	0,92	0,97	0,58	0,63	0,80	0,86	0,58	0,63	0,80	0,86	0,17	0,22	0,36	0,42
s₄₃	0,58	0,63	0,80	0,86	0,32	0,41	0,92	0,97	0,72	0,78	0,92	0,97	0,17	0,22	0,36	0,42	0,04	0,10	0,18	0,23
s₄₄	0,32	0,41	0,58	0,65	0,17	0,22	0,80	0,86	0,72	0,78	0,92	0,97	0,32	0,41	0,58	0,65	0,17	0,22	0,36	0,42

Afterwards, the performance of the service providers is normalized for α= 0 in Table 2. The service quality per criteria is normalized by using Equation (21) where $\tilde{f_{l}} \in \tilde{F} (S)$ is a fuzzy-valued function.

Table 2

Normalized performance of service providers for α= 0

Criteria	Importance level		Normalized performance of service providers
			A1		A2		A3
T₁
s₁₁	0,72	0,97	0,465	0,64	0,36	0,625	0,29	0,57
s₁₂	1	1	0,5	0,535	0,29	0,47	0,36	0,520
s₁₃	0,72	0,97	0,5	0,710	0,36	0,70	0,29	0,640
s₁₄	0,58	0,86	0,515	0,840	0,38	0,83	0,31	0,770
T₂
s₂₁	1	1	0,020	0,255	0,160	0,47	0,020	0,26
s₂₂	0,93	1	0,36	0,625	0,465	0,64	0,29	0,57
s₂₃	0,72	0,97	0,36	0,695	0,465	0,71	0,29	0,64
T₃
s₃₁	0,72	0,97	0,02	0,255	0,02	0,255	0,29	0,57
s₃₂	0,32	0,65	0,085	0,350	0,02	0,26	0,465	0,640
s₃₃	0,17	0,42	0,290	0,57	0,160	0,465	0,360	0,625
T₄
s₄₁	0,72	0,97	0,160	0,535	0,160	0,535	0,160	0,535
s₄₂	0,58	0,86	0,305	0,64	0,31	0,64	0,100	0,42
s₄₃	0,58	0,86	0,375	0,825	0,1	0,55	0,035	0,455
s₄₄	0,32	0,65	0,43	0,9	0,23	0,74	0,155	0,625

In the next step, fuzzy values and fuzzy measures are calculated by using Choquet Integral’s steps. Equation (22) gives $\tilde{F} (S)$ which represents all fuzzy-valued functions ${\tilde{f}}_{l}$ . Please see Table 3 for numerical values.

Table 3

Fuzzy measures for α= 0

Criteria	Importance level		Fuzzy values				Performance of service Provider		Fuzzy values				Performance of service provider		Fuzzy values				Performance of service provider
							A1						A2						A3
T₁			–0,9999		–0,9999				–0,9999		–0,9999				–0,9999		–0,9999
s₁₁	0,72	0,97	A1	1	A2	1	0,46	0,64	A3	0,88	A2	0,99	0,36	0,62	A1	1	A2	0,99	0,29	0,57
s₁₂	1	1	A2	1	A1	1	0,50	0,53	A1	1	A1	1	0,29	0,47	A4	1	A1	1	0,36	0,52
s₁₃	0,72	0,97	A3	0,88	A3	1	0,50	0,71	A2	0,96	A3	0,99	0,36	0,70	A2	1	A3	0,99	0,29	0,64
s₁₄	0,58	0,86	A4	0,58	A4	0,86	0,51	0,84	A4	0,58	A4	0,86	0,38	0,83	A3	1	A4	0,86	0,31	0,77
T₂	–0,9999		–0,9999		–0,9999		–0,9999		–0,9999		–0,9999
s₂₁	1	1	A1	1	A1	1	0,02	0,25	A1	1	A1	1	0,16	0,47	A1	1	A1	1	0,02	0,26
s₂₂	0,93	1	A2	0,98	A2	1	0,36	0,62	A2	0,98	A2	1	0,46	0,64	A2	0,98	A2	1	0,29	0,57
s₂₃	0,72	0,97	A3	0,72	A3	0,97	0,36	0,69	A3	0,72	A3	0,97	0,46	0,71	A3	0,72	A3	0,97	0,29	0,64
T₃	–0,5441		–0,9921		–0,5441		–0,9921		–0,5441		–0,9921
s₃₁	0,72	0,97	A1	1	A1	1	0,02	0,25	A1	1	A1	1	0,02	0,25	A1	1	A1	1	0,29	0,57
s₃₂	0,32	0,65	A2	0,46	A2	0,79	0,08	0,35	A2	0,46	A2	0,79	0,02	0,26	A3	0,32	A3	0,65	0,46	0,64
s₃₃	0,17	0,42	A3	0,17	A3	0,42	0,29	0,57	A3	0,17	A3	0,42	0,16	0,46	A2	0,46	A2	0,80	0,36	0,62
T₄	–0,9574		–0,9998		–0,9574		–0,9998		–0,9574		–0,9998
s₄₁	0,72	0,97	A1	1	A1	1	0,16	0,53	A2	0,94	A1	1	0,16	0,53	A4	0,72	A3	0,99	0,16	0,53
s₄₂	0,58	0,86	A2	0,90	A2	0,99	0,30	0,64	A4	0,58	A3	1	0,31	0,64	A2	0,94	A1	1	0,10	0,42
s₄₃	0,58	0,86	A3	0,72	A3	0,95	0,37	0,82	A1	1	A2	1	0,10	0,55	A1	1	A2	0,99	0,03	0,45
s₄₄	0,32	0,65	A4	0,32	A4	0,65	0,43	0,90	A3	0,72	A4	0,65	0,23	0,74	A3	0,82	A4	0,65	0,15	0,62

In Table 4, the main criteria performance of the service providers is calculated for α= 0. Equation (23) gives the service quality for each main criteria. These are obtained by using equations in step 6.

Table 4

Main criteria performance of the service providers for α= 0

Criteria	The degree of importance		Fuzzy values				Performance of service Provider		Fuzzy values				Performance of service provider		Fuzzy values				Performance of service provider
							A1						A2						A3
T₁			–0,9999		–0,9999		0,50	0,82	–0,9999		–0,9999		0,32	0,80	–0,9999		–0,9999		0,30	0,75
s₁₁	0,72	0,97	A1	1	A2	1	0,46	0,64	A3	0,88	A2	0,99	0,36	0,62	A1	1	A2	0,99	0,29	0,57
s₁₂	1	1	A2	1	A1	1	0,50	0,53	A1	1	A1	1	0,29	0,47	A4	1	A1	1	0,36	0,52
s₁₃	0,72	0,97	A3	0,88	A3	1	0,50	0,71	A2	0,96	A3	0,99	0,36	0,70	A2	1	A3	0,99	0,29	0,64
s₁₄	0,58	0,86	A4	0,58	A4	0,86	0,51	0,84	A4	0,58	A4	0,86	0,38	0,83	A3	1	A4	0,86	0,31	0,77
T₂	–0,9999		–0,9999		0,35	0,69	–0,9999		–0,9999		0,45	0,70	–0,9999		–0,9999		0,28	0,63
s₂₁	1	1	A1	1	A1	1	0,02	0,25	A1	1	A1	1	0,16	0,47	A1	1	A1	1	0,02	0,26
s₂₂	0,93	1	A2	0,98	A2	1	0,36	0,62	A2	0,98	A2	1	0,46	0,64	A2	0,98	A2	1	0,29	0,57
s₂₃	0,72	0,97	A3	0,72	A3	0,97	0,36	0,69	A3	0,72	A3	0,97	0,46	0,71	A3	0,72	A3	0,97	0,29	0,64
T₃	–0,5441		–0,9921		0,08	0,42	–0,5441		–0,9921		0,04	0,34	–0,5441		–0,9921		0,29	0,60
s₃₁	0,72	0,97	A1	1	A1	1	0,02	0,25	A1	1	A1	1	0,02	0,25	A1	1	A1	1	0,29	0,57
s₃₂	0,32	0,65	A2	0,46	A2	0,79	0,08	0,35	A2	0,46	A2	0,79	0,02	0,26	A3	0,32	A3	0,65	0,46	0,64
s₃₃	0,17	0,42	A3	0,17	A3	0,42	0,29	0,57	A3	0,17	A3	0,42	0,16	0,46	A2	0,46	A2	0,80	0,36	0,62
T₄	–0,9574		–0,9998		0,35	0,86	–0,9574		–0,9998		0,12	0,66	–0,9574		–0,9998		0,09	0,56
s₄₁	0,72	0,97	A1	1	A1	1	0,16	0,53	A2	0,94	A1	1	0,16	0,53	A4	0,72	A3	0,99	0,16	0,53
s₄₂	0,58	0,86	A2	0,90	A2	0,99	0,30	0,64	A4	0,58	A3	1	0,31	0,64	A2	0,94	A1	1	0,10	0,42
S₄₃	0,58	0,86	A3	0,72	A3	0,95	0,37	0,82	A1	1	A2	1	0,10	0,55	A1	1	A2	0,99	0,03	0,45
s₄₄	0,32	0,65	A4	0,32	A4	0,65	0,43	0,90	A3	0,72	A4	0,65	0,23	0,74	A3	0,82	A4	0,65	0,15	0,62

The same steps are followed to find the performance of sub-criteria by considering the main criteria. All measured performance values are assembled under overall performance which is represented by a fuzzy number $\tilde{Y}$ in step 7. The total performance (Table 5) obtained from all the sub-criteria is reduced to a fuzzy number by application of Choquet integral steps.

Table 5

Total performance of service provider

Criteria	The degree of		Fuzzy measures				A1		Fuzzy measures				A2		Fuzzy measures				A3
	importance		–0,999		–0,999		0,359	0,803	–0,999		–0,999		0,115	0,669	–0,999		–0,999		0,092	0,560
T₁	1	1	A4	1	A3	1	0,5087	0,8210	A3	1	A4	1	0,3241	0,8058	A4	1	A4	1	0,305	0,751
T₂	0,93	1	A2	1	A2	1	0,353	0,693	A4	0,93	A3	1	0,459	0,708	A2	1	A3	1	0,285	0,638
T₃	0,72	0,97	A1	1	A1	1	0,085	0,423	A1	1	A1	1	0,044	0,343	A3	1	A2	1	0,298	0,604
T₄	0,58	0,86	A3	1	A4	0,86	0,359	0,864	A2	1	A2	1	0,124	0,669	A1	1	A1	1	0,092	0,560

As shown in step 8, the fuzzy number $\tilde{Y}$ is defuzzified into a crisp value. General performance values are shown in Table 6. In Table 7, total performance values are compared. The alternative with the highest total performance value, A1, is ranked as the best. In our model, the weights of the alternatives are used instead of the ranking of alternatives.

Table 6

General performance values and simplification

Criteria	Service provider performance						Simplification
	A1		A2		A3		A1	A2	A3
Total Performance	0,35	0,80	0,11	0,66	0,09	0,56	0,58	0,39	0,32
T₁	0,50	0,82	0,32	0,80	0,30	0,75	0,66	0,56	0,52
s₁₁	0,46	0,64	0,36	0,62	0,29	0,57	0,55	0,49	0,43
s₁₂	0,50	0,53	0,29	0,47	0,36	0,52	0,51	0,37	0,44
s₁₃	0,50	0,71	0,36	0,70	0,29	0,64	0,60	0,52	0,46
s₁₄	0,51	0,84	0,38	0,83	0,31	0,77	0,67	0,60	0,53
T₂	0,35	0,69	0,45	0,70	0,28	0,63	0,52	0,58	0,46
s₂₁	0,02	0,25	0,16	0,47	0,02	0,26	0,13	0,31	0,13
s₂₂	0,36	0,62	0,46	0,64	0,29	0,57	0,49	0,55	0,43
s₂₃	0,36	0,69	0,46	0,71	0,29	0,64	0,52	0,58	0,46
T₃	0,08	0,42	0,04	0,34	0,29	0,60	0,25	0,19	0,45
s₃₁	0,02	0,25	0,02	0,25	0,29	0,57	0,13	0,13	0,43
s₃₂	0,08	0,35	0,02	0,26	0,46	0,64	0,21	0,13	0,55
s₃₃	0,29	0,57	0,16	0,46	0,36	0,62	0,43	0,31	0,49
T₄	0,35	0,86	0,12	0,66	0,09	0,56	0,61	0,39	0,32
s₄₁	0,16	0,53	0,16	0,53	0,16	0,53	0,34	0,34	0,34
s₄₂	0,30	0,64	0,31	0,64	0,10	0,42	0,47	0,47	0,26
s₄₃	0,37	0,82	0,10	0,55	0,03	0,45	0,60	0,32	0,24
s₄₄	0,43	0,90	0,23	0,74	0,15	0,62	0,66	0,48	0,39

Table 7

Performance results

Criteria	A1	A2	A3
Total performance	0,581	0,392	0,326
T₁	0,665	0,565	0,528
s₁₁	0,553	0,493	0,430
s₁₂	0,518	0,378	0,440
s₁₃	0,605	0,528	0,465
s₁₄	0,678	0,600	0,538
T₂	0,523	0,583	0,461
s₂₁	0,138	0,313	0,138
s₂₂	0,493	0,553	0,430
s₂₃	0,528	0,588	0,465
T₃	0,254	0,194	0,451
s₃₁	0,138	0,138	0,430
s₃₂	0,218	0,138	0,553
s₃₃	0,430	0,313	0,493
T₄	0,611	0,397	0,326
s₄₁	0,348	0,348	0,348
s₄₂	0,473	0,473	0,260
s₄₃	0,600	0,325	0,245
s₄₄	0,665	0,485	0,390

4.2 Data collection

This section presents a numerical example that illustrates the model. The data from the database of an automotive company in Turkey. The network with multi-product, multi-echelon and capacitated warehouses transports automotive spare part products from warehouses to demand points (Fig. 2). The unit transportation costs and the transportation times between some echelons are shown in Table 8. The unit transportation cost between the echelons changes according to product and vehicle type. The unit transportation cost of electric vehicles is higher than fuel vehicles due to the high investment cost of electric vehicles. Moreover, the other cost items, which are waiting cost in the main customer warehouse and punishment cost for delayed products to demand points, are given in Table 9.

Table 8
Unit transportation cost values ($/pallet) and transportation times (periods)

Main customer warehouse or demand point no. (k or i) Transportation time from local warehouse to demand point (Tle_ij) Product no. (l) Unit transportation cost from the local warehouse to the main customer warehouse (CLw_klj)

Vehicle type (j) Vehicle type (j) Vehicle type (j) Vehicle type (j)

1 2 1 2

1 2 2 1 6,1 12,2

2 5,4 10,8

3 7,2 14,4

4 6,3 12,6

5 8,9 17,8

2 1 1 1 4,8 9,6

2 6,9 13,8

3 7,5 15,0

4 5,0 10,0

5 7,4 14,8

Main customer warehouse or demand point no. (k or i)	Transportation time from local warehouse to demand point (Tle_ij)	Product no. (l)	Unit transportation cost from the local warehouse to the main customer warehouse (CLw_klj)
1	2	1	2
1	2	2	1	6,1	12,2
2	5,4	10,8
3	7,2	14,4
4	6,3	12,6
5	8,9	17,8
2	1	1	1	4,8	9,6
2	6,9	13,8
3	7,5	15,0
4	5,0	10,0
5	7,4	14,8

Table 9

Waiting cost and punishment cost ($)

Product no.	Waiting cost	Punishment cost
(l)	(CW_lk)	(CD_li)
1	5	5
2	4,5	6,5
3	3	4,5
4	5,5	8
5	4	7,5

The model’s other parameters, which are delayed products at the beginning, capacities for warehouses, starting inventory levels per product and safety stock quantity, are shown in Table 10.

Table 10

Other parameters of the model (pallets)

Main customer warehouse (k)	The capacity of local and main customer warehouse (A_LW and Acw_k)	Product (l)	Safety stock level (Qss_l)	Initial inventory level (Si_l)	Delayed product (Sd_li)
1	50000	1	100	1000	0
2	55000	2	10	100	0
3	45000	3	50	500	0
A_LW	150000	4	1	2	0
		5	40	600	0

In this study, the EEA database is used to identify the emission level. This source provides a different data set for each category of road vehicles. In this study, light commercial vehicles that are designed to carry goods less than 3,5 tonnes are considered. In addition, this paper focuses on CO as one of the major pollutants emitted by road vehicles. According to this report, the emission factor is 2,5166 g/km for the pollutant CO [5].

4.3 Model solution and assessment of the results

In the proposed model, GAMS (23.5) optimization software is used, and a feasible solution is obtained. Fifty demand points give their demands for 30 time periods (monthly demand). The facility realizes a distribution plan considering the transportation costs, inventory costs, punishment costs for delayed products, emission factors and the service quality level of warehouses.

This proposed model makes selection decisions among the fuel and electric vehicles in city logistics operations and calculates the amount of products that must be transported between facilities, the number of delayed products and the stock quantity for main warehouses in each time slot. In addition, the cost of transportation between the echelons is based on the product and vehicle type.

Firstly, the case is solved considering only the transportation cost minimization objective, which aims to transport goods in the urban area with the lowest cost. After solving the problem for the higher-priority objective function, the optimal result is added as a constraint to the model. The new version of the model is solved with the second objective function, which tries to minimize the inventory holding cost. In the same way, the optimal results are added as a constraint in the third, fourth and fifth objective functions, respectively. The optimum results are shown in Table 11. As a result, all the demands of the customers are satisfied with the minimum total cost and emission level, and maximum service level.

Table 11
Objective function values

The optimum result Solution time

1. objective value 134.674,75 00 : 04

2. objective value 336.305,00 00 : 10

3. objective value 570.968,50 00 : 22

4. objective value 908.254,00 00 : 53

5. objective value 1.132.686,80 01 : 02

	The optimum result	Solution time
1. objective value	134.674,75	00 : 04
2. objective value	336.305,00	00 : 10
3. objective value	570.968,50	00 : 22
4. objective value	908.254,00	00 : 53
5. objective value	1.132.686,80	01 : 02

The solution of the first objective function suggests using fuel vehicles with the lowest cost due to the high investment cost of electric vehicles. In the 11th period, main customer warehouses cannot send the products to demand points in the expected time slot, and the local warehouse starts to send products directly to demand points in the 12th period. Due to the capacity constraints, main customer warehouses 2 and 3 store the goods between the 1st and 11th time slots. The initial inventory is transported in the first two time slots and then the model starts to keep safety stock. The results also provide the quantities of the delayed products to demand points as an output of inadequate initial stock and transportation times.

As it can be observed, adding the first optimal result as a constraint into the model increased the objective function value. The second and third objective function results suggest using fuel vehicles instead of electric vehicles. In the fourth objective function, the model aims to decrease the emission level in urban area. The results of the fourth objective function show that electric vehicles are preferred due to their high investment cost. Although the first four objective functions do not prefer to send the products from main customer warehouse 1 (A1), in the fifth objective function the model sends the products from main customer warehouse 1 (A1) due to its high weighting value which is calculated by using Choquet integral method.

There is a tradeoff between the objectives which shows differences according to each stakeholder. The most important point is combining these five objectives here. As highlighted previously, this treatment will fulfill the individual goals of city logistics stakeholders and the overall goal simultaneously.

4.4 Scenario analysis

Once the consequences of this study are reviewed, it is seen that some parameters, such as warehouse volumes and transportation costs, affect the model directly. Different scenarios can be obtained by changing the parameters to illustrate the relations and tradeoffs among model variables. The following section of the study provides an overview of the developed scenarios. These scenarios are listed as follows:

Scenario 1: Under different scenarios, the results are determined considering the higher priority objective. In some cases, environmental concern can be the most critical value for the citizens in the urban area. According to this purpose, the priorities of the objective functions can be changed. In this scenario, the higher priority objective function is the minimization of emission levels as different from the previous model. The first objective function is followed by minimizing the transportation costs, inventory costs, punishment costs for delayed products and maximizing the service quality level of customer warehouses. In this proposed model, the objective function value is 2.371.506,80 $. In this case, the model prefers to use electric vehicles despite their high cost to minimize emissions.

Scenario 2: Eliminating the weighting value calculated using the Choquet integral method for main customer warehouses can be another scenario for applying to real-life problems. In this scenario, in the fifth objective function, the model did not prefer to send the products from main customer warehouse 1 (A1) despite its high weighting value, which is calculated using Choquet integral method and continued to send the products from the main customer warehouses 2 and 3.

Scenario 3: Increasing 4 times the starting inventory level of the products can be another case to analyse. Increasing the initial inventory level decreases the transported product quantity from a local warehouse to the main customer warehouse. It allows a decrease in transportation costs. On the other hand, this situation increases the inventory holding cost. This scenario is an excellent case to examine the relations among model variables like unit cost values.

Scenario 4: Eliminating inventory holding cost does not make any sense on the model and does not create any change on the other parts of objective function. The only outcome is that the total cost decreases as much as the amount of warehousing cost.

Scenario 5: The parameters such as customer demand and unit transportation cost cause some changes on the objective function. Increase in benzine prices negatively affects the unit transportation costs in the country. For this reason, when we increase the unit transportation costs for fuel vehicles, the results obviously suggest using electric vehicles instead of fuel vehicles. It also makes contribution to decrease air pollution in urban area.

5 Conclusions

Increasing the satisfaction of stakeholders in cities and understanding their perceptions are essential for transportation management to respond to customers’ growing demands for acceptable quality of logistics services. This paper proposes to design a multi-level and multi-product distribution network that includes five conflicting objectives. In the proposed model, the amount of spare part products that must be transported between facilities, the amount of delayed products and the inventory level for main warehouses in each time period are calculated. The study also makes a decision between fuel and electric vehicles in urban freight transport. Instead of considering the objective of only one stakeholder, different priorities of each stakeholder in the city are included in the model. The proposed model considers all the logistics costs incurred in the distribution network by considering the service quality level of logistics operations. In addition, electric vehicles are becoming the new reality, moving the supply chain and logistics world further into the future by offering various benefits, such as a significant contributing factor in reducing the emission level. As a result, a customer-based approach is obtained and presented for a real-world case as a pilot study.

In future studies, new decision variables can be added that will increase the model complexity. For instance, the proposed model can be integrated with a freight vehicle routing problem. It will provide a new framework to calculate the count of vehicles and the capacities of these carriers in the distribution network. These complex problems can be solved by using heuristics methods or a wide range of simulation methods, such as genetic algorithms, tabu search or simulated annealing, etc., to get a better optimal solution. It is also possible to add more specific customer preferences.

In this study, utilized data are obtained directly from a company in automotive industry and used in the model with their approximate forms. However, especially for long-term decisions, there may be changes in the parameters’ values and the vagueness about the parameters may be reflected using fuzzy numbers.

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