1 Introduction
2 Literature review
2.1 Picture fuzzy set based multi-criteria decision-making models
Author(s) and year | Research focus | Method | MCGDM | Application type |
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Wei [68] | Emerging technology commercialization | PF Cross-entropy | No | Illustrative example |
Liang et al. [35] | Gold mines | PF EDAS + ELECTRE III | Yes | Illustrative example |
Wang et al. [64] | Energy performance contracting | PF MABAC | Yes | Real-life |
Wang et al. [66] | Risk evaluation of construction project | PF Entropy + VIKOR | Yes | Real-life |
Wei [69] | Emerging technology commercialization | PF TODIM | No | Illustrative example |
Wei et al. [70] | Emerging technology commercialization | PF Projection | No | Illustrative example |
Zhang et al. [78] | Offshore wind power station location | PF RP + TOPSIS | Yes | Real-life |
Ashraf et al. [2] | Air quality | PF TOPSIS | Yes | Illustrative example |
Ju et al. [27] | Electric vehicle charging station location | Fuzzy AHP + PF GRP | Yes | Real-life |
Liang et al. [34] | Gold mines | PF TODIM + ELECTRE | Yes | Real-life |
Liu et al. [36] | Emerging technology commercialization | PF GRA | No | Illustrative example |
Meksavang et al. [38] | Beef supply chain | PF VIKOR | Yes | Illustrative example |
Sindhu et al. [51] | – | LP + PF TOPSIS | No | Illustrative example |
Torun and Gördebil [60] | Satisfaction level | PF TOPSIS | No | Real-life |
Zhang et al. [77] | Green supplier selection | PF EDAS | Yes | Illustrative example |
Joshi [25] | Personnel and investment selection | PF Entropy + VIKOR | Yes | Illustrative examples |
Tian and Peng [57] | Tourism attraction recommendation | PF ANP + TODIM | Yes | Illustrative example |
Tian et al. [58] | Tourism attraction recommendation | PF AHP + PROMETHEE II | Yes | Illustrative example |
Wang et al. [65] | Hotel selection | PF TODIM | Yes | Real-life |
Yue [73] | Software reliability | PF VIKOR | Yes | Illustrative example |
Our study | Last-mile delivery mode selection | PF WASPAS | Yes | Real-life |
2.2 Applications of the WASPAS method
Author(s) and year | Research focus | Application type | Parameter type |
---|---|---|---|
Zavadskas et al. [75] | Waste incineration plant location | Real-life | Single-valued neutrosophic |
Zolfani et al. [80] | Supplier selection | Real-life | Deterministic |
Ghorabaee et al. [19] | Green supplier selection | Illustrative example | Interval type-2 fuzzy |
Petrović et al. [42] | Waste collection | Real-life | Deterministic |
Yazdani et al. [72] | Green supplier selection | Real-life | Deterministic |
Ghorabaee et al. [18] | 3PL provider selection | Illustrative example | Interval type-2 fuzzy |
Khodadadi et al. [29] | Wastewater purification | From literature | Deterministic |
Deveci et al. [11] | Car sharing site selection | Real-life | Interval type-2 fuzzy |
Sremac et al. [53] | 3PL provider selection | Real-life | Rough |
Stević et al. [55] | Roundabout location | Real-life | Rough |
Dimitrova Stoilova [13] | Rail transportation | Real-life | Deterministic |
Gupta et al. [21] | Green supplier selection | Real-life | Fuzzy |
Krishankumar et al. [30] | Green supplier selection | From literature | Probabilistic linguistic term |
Mishra et al. [39] | Green supplier selection | Illustrative example | Hesitant fuzzy |
Pamučar et al. [41] | 3PL provider selection | Real-life | Interval rough |
Prajapati et al. [43] | Reverse logistics barriers | Real-life | Deterministic |
Ren et al. [46] | Electric car charging station | Real-life | Hesitant fuzzy linguistic term |
Davoudabadi et al. [10] | Supplier selection | From literature | Interval-valued intuitionistic fuzzy |
Dorfeshan and Mousavi [15] | Aircraft maintenance | From literature | Interval type-2 fuzzy |
Eghtesadifard et al. [16] | Solid waste landfill location | Real-life | Deterministic |
Rani and Mishra [45] | Fuel technology selection | From literature | Q-rung orthopair fuzzy |
Our study | Last-mile delivery mode selection | Real-life | Picture fuzzy |
2.3 Research gaps
3 Methodology
3.1 Picture fuzzy sets
3.2 Picture fuzzy WASPAS method
4 Case study
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(A1) Traditional. Postal companies mainly use the traditional LMD mode. In Belgrade, the couriers perform LMD most often by using a vehicle with a diesel engine (e.g., Peugeot Boxer and Partner). This delivery process involves several activities, such as loading shipments into a vehicle, driving to the LMD locations, and handing over a package.
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(A2) Autonomous vehicle. This is a very attractive LMD mode for delivery companies because it requires minor infrastructure adaptation and reduces courier engagement. The autonomous vehicle and drone LMD modes are similar. The main difference is the fact that autonomous vehicles move on the ground, especially on sidewalks or specially designed paths. The shipments are loaded in the storage space of an autonomous vehicle, and then it visits users’ locations.
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(A3) Bicycle. This LMD mode involves the use of cargo bicycles by a courier. It is particularly convenient from an environmental standpoint because it does not use any artificial energy source.
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(A4) Drone. The delivery process requires strong technological support. First, a drone with a shipment departs from a suitable station, which may be a fixed infrastructure object or a moving station within a suitable means of transport, located on the ground near a delivery location. Then, it is flying to the delivery location. Finally, the drone lands, recognizing the appropriate landing tag or by predefined coordinates, and leaves the shipment.
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(A5) Postomate. This LMD mode includes vending machines accessible to users 24/7, which are set up in typical locations such as gas stations, shopping malls, etc. They provide easy access authorization and fast picking up a shipment.
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(A6) Tube transport. This external transportation system for the delivery of shipments relies on an infrastructure made of pipes and specialized packaging for shipments. The shipments are transported through tubes to appropriate stations from which users take them.
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(C11) Company value. The impact on the value of a company through infrastructure and technical improvements, public acceptance, and brand strengthening.
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(C12) Exploitation cost. The cost incurred in exploiting the delivery concept; e.g., labor expenses, cost of fuel, and other consumables.
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(C13) Maintenance cost. The cost of maintaining an entire LMD mode so that all activities can be completed successfully.
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(C14) Savings. The savings that can be made by applying a particular LMD mode.
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(C15) Total investment cost. The necessary costs for implementing an LMD mode; e.g., construction of infrastructure, leasing space, procurement of technical equipment and software, etc.
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(C21) Air emission. The environmental impact of an LMD mode through the level of air emissions exhausted during delivery.
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(C22) Legislation. The compliance of a delivery mode with available directives and environmental plans.
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(C23) Noise pollution. The impact on noise production is significant since delivery is realized in populated places in different parts of the day.
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(C24) Resources consumption. Raw materials and energy consumption of an LMD mode to provide services.
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(C31) Job opportunities. The number, type (e.g., postal traffic, logistics, software engineering, etc.), and quality of jobs to implement an LMD mode.
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(C32) Occupational health. The impact of an LMD mode on workers’ health through direct contact.
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(C33) Public health. The expected and abrupt (e.g., explosions, fires, and other hazards) impacts on public health of an LMD mode.
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(C34) Public space usage. The occupation of public space by resources that are part of an LMD mode; e.g., usage of sidewalks and parking spaces.
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(C35) Workforce availability. A sufficient number of workers with proficiencies to implement and operate an LMD mode.
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(C41) Availability of services. The impact of an LMD mode on the spatial, temporal, and financial availability of services.
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(C42) Flexibility. The possibility of permanent adaptation to market changes.
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(C43) Infrastructure adequacy. The existence of adequate infrastructure (e.g., bicycle paths, drone stations, etc.) for an LMD mode.
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(C44) Technical accessibility. The existence of necessary technical equipment and means to implement an LMD mode.
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(C45) Urban planning and relief. Changes in urban planning and relief to implement and exploit an LMD mode.
5 Results and discussion
5.1 Experimental results
Alternative | Additive relative importance | Multiplicative relative importance | Joint generalized criterion | Rank | |
---|---|---|---|---|---|
Picture fuzzy | Crisp | ||||
A1 | < 0.303, 0.204, 0.392> | < 0.232, 0.204, 0.453> | < 0.268, 0.204, 0.422> | 0.415 | 4 |
A2 | < 0.183, 0.318, 0.374> | < 0.151, 0.318, 0.40> | < 0.167, 0.318, 0.387> | 0.376 | 5 |
A3 | < 0.439, 0.309, 0.159> | < 0.420, 0.309, 0.192> | < 0.430, 0.309, 0.175> | 0.638 | 2 |
A4 | < 0.304, 0.424, 0.185> | < 0.295, 0.424, 0.188> | < 0.30, 0.424, 0.187> | 0.562 | 3 |
A5 | < 0.506, 0.314, 0.125> | < 0.492, 0.314, 0.131> | < 0.499, 0.314, 0.128> | 0.696 | 1 |
A6 | < 0.171, 0.276, 0.459> | < 0.153, 0.276, 0.482> | < 0.162, 0.276, 0.470> | 0.332 | 6 |
5.2 Ranking discussion
5.3 Sensitivity analyses
5.4 Comparative analysis
Picture fuzzy MCDM method | Ordering |
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WASPAS (our study) | A5 ≻ A3 ≻ A4 ≻ A1 ≻ A2 ≻ A6 |
A5 ≻ A3 ≻ A1 ≻ A4 ≻ A2 ≻ A6 | |
A5 ≻ A3 ≻ A4 ≻ A1 ≻ A6 ≻ A2 | |
A5 ≻ A3 ≻ A4 ≻ A2 ≻ A1 ≻ A6 | |
VIKOR [66] | A5 ≻ A4 ≻ A3 ≻ A2 ≻ A6 ≻ A1 |
MABAC [64] | A5 ≻ A3 ≻ A4 ≻ A1 ≻ A2 ≻ A6 |
Cross-entropy [68] | A5 ≻ A3 ≻ A4 ≻ A1 ≻ A2 ≻ A6 |
Projection [70] | A5 ≻ A3 ≻ A4 ≻ A1 ≻ A2 ≻ A6 |
Grey relational projection [27] | A5 ≻ A3 ≻ A4 ≻ A2 ≻ A1 ≻ A6 |
Grey relational analysis [36] | A5 ≻ A3 ≻ A1 ≻ A4 ≻ A2 ≻ A6 |
PROMETHEE II [58] | A5 ≻ A3 ≻ A4 ≻ A1 ≻ A2 ≻ A6 |