NEW MULTI-OBJECTIVE VRP INSTANCES MODELLING MAIL DELIVERIES FOR RIO CLARO CITY, SÃO PAULO, BRAZIL

Azorli, Samuel L.; Meira, Luis A. A.

doi:10.1590/0101-7438.2022.042.00257140

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ARTICLES • Pesqui. Oper. 42 • 2022 • https://doi.org/10.1590/0101-7438.2022.042.00257140 copy

NEW MULTI-OBJECTIVE VRP INSTANCES MODELLING MAIL DELIVERIES FOR RIO CLARO CITY, SÃO PAULO, BRAZIL

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

Optimization benchmarks are tools for the validation and comparison of algorithms. Routing benchmarks are particularly relevant to industry. However, there are few available VRP benchmarks based on realistic situations. This research creates a set of multi-objective (three objectives) instances for a length- constrained variant of VRP. The instances model a realistic case of mail delivery performed by mail carriers on foot in the Brazilian city of Rio Claro. A new graph of the city road map was created, and mail carriers’ activities were estimated. Streets were assigned with distinct probability densities to receive deliveries. This research produces 80 mail delivery instances with up to 50,000 deliveries per instance. Finally, bounds for a set of instances were produced. The instances are publicly available for the community to test, compare and validate multi-objective optimization algorithms.

Keywords:
VRP instances; multi-objective; logistics

Attribute	Level 1_(pen)	Level 2_(pen)	Level 3_(pen)	Level 4_(pen)
Region(R)	central_(1.0)	peripheral_(0.75)	distant_(0.4)	isolated_(0.2)
Type(T)	avenue_(1.0)	street_(0.75)	path_(0.4)	highway₍₀₎
Zone(Z)	commercial_(1.0)	mixed_(0.75)	residential_(0.4)	-

Group	#Instances	#Deliveries	Max Len.(h)	#Vehicles(max)
Toy	30	3 to 5,000	6	3 to 45
Normal	15	10,000 to 14,000	6	90
OnStrike	15	15,000 to 19,000	8	90
Christmas	20	20,000 to 50,000	8	90 to 120

ID	#Deliveries	W/R max avg±std	#vehicles avg±std	time(s) avg±std
12	50	1.78±0.03	2.8±0.4	0.001±0.002
15	100	2.72±0.04	4.0±0.0	0.0±0.0
18	200	4.10±0.06	6.2±0.4	0.004±0.003
21	500	6.36±0.06	9.0±0.0	0.022±0.002
24	1000	8.91±0.05	13.0±0.0	0.14±0.01
27	5000	18.15±0.07	26.0±0.0	3.6±0.1
30	10000	24.75±0.08	35.4±0.5	18±3
45	15000	22.09±0.08	28.6±0.5	42±2
51	17000	23.15±0.06	29.8±0.4	65±4
60	20000	24.79±0.10	32.2±0.4	120±13
63	22000	25.66±0.03	33.0±0.0	174±14
66	24000	26.69±0.10	34.2±0.4	209±9
69	26000	27.73±0.08	35.8±0.4	281±19
72	28000	28.28±0.04	36.4±0.5	348±19
75	30000	29.32±0.07	38.0±0.0	445±32

ID	#Deliveries	W/R max avg±std	#vehicles avg±std	time(s) avg±std
72	28000	28.28±0.06	36.2±0.4	3054±203
75	30000	29.25±0.07	37.8±0.4	4256±599
78	40000	32.79±0.06	42.2±0.4	4566±266
79	50000	35.87±0.07	46.0±0.0	8055±630

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