The electric boat charging problem

Villa, Daniel; Montoya, Alejandro; Ciro, Juan M.

doi:10.1590/0103-6513.20190067

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Sumário

Thematic Section - Sustainability in Transportation and Logistics • Prod. 29 • 2019 • https://doi.org/10.1590/0103-6513.20190067 copy

The electric boat charging problem

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Paper aims

This paper studies a new optimization problem called the Electric Boat Charging Problem (EBCP), which is based on the application of electric mobility in a river transport operation problem.

Originality

This work pioneers the studies of the electric mobility on the river operations, by proposing the EBCP. This problem includes real features of the electric mobility such as nonlinear charging functions, battery degradation costs, and speed variation.

Research method

For solving the EBCP, we propose a Mixed-Integer Linear Programming (MILP) formulation. For testing our MILP formulation, we use a set of instances based on a future transport operation. We also analyze the impact of some problem parameters on the objective function, and decision variables.

Main findings

Our MILP formulation is capable to optimally solve different type of instances in competitive CPU times. The battery capacity and a time limit constraint have and important impact on the objective function and the decision-making variables.

Implications for theory and practice

We model the EBCP as a MILP formulation. This model allows to optimally solve industrial scale instances. Moreover, using a sensitivity analysis, we unveil that both the battery capacity and the time limit constraint of the EB route are critical parameters.

Keywords
Electric boat; Charging decisions; Battery degradation; MILP formulation

Instance	# of segments	# of CS	Total length (km)	Objective Function	Optimality Gap	CPU time (s)	Cost with fuel ($)	Gap (%)	CO₂ emissions (Kg)	SCC ($)	Total cost ($)	Gap (%)
1	17	2	124.2	45.7	0.01%	0.4	38.9	14.8%	119.6	8.0	46.9	-2.7%
2	23	2	144.8	55.7	0.01%	0.5	47.8	14.2%	146.9	9.8	57.6	-3.5%
3	16	1	84.8	25.8	0.00%	0.1	30.2	-16.7%	92.7	6.2	36.4	-40.8%
4	32	3	174.1	96.8	0.01%	1.0	64.1	33.8%	197.0	13.2	77.3	20.2%
5	35	4	248.4	60.9	0.01%	0.6	51.1	16.1%	157.2	10.5	61.6	-1.2%
6	46	4	289.5	109.3	0.00%	1.8	65.5	40.1%	201.3	13.5	79.0	27.7%
7	32	2	169.7	33.4	0.00%	0.4	34.4	-3.1%	105.8	7.1	41.5	-24.3%
8	64	6	348.2	157.7	0.01%	82.5	84.1	46.7%	258.6	17.3	101.4	35.7%
9	23	2	73.2	24.1	0.01%	1.0	26.6	-10.2%	81.8	5.5	32.1	-32.9%
10	20	3	114.4	51.1	0.01%	0.4	45.3	11.4%	139.3	9.3	54.6	-6.9%
11	20	1	112.0	35.2	0.01%	0.2	40.5	-15.0%	124.4	8.3	48.8	-38.6%
12	20	2	134.6	65.2	0.00%	0.3	46.9	28.0%	144.3	9.7	56.6	13.1%
13	18	1	114.0	41.5	0.00%	0.3	41.3	0.5%	127.0	8.5	49.8	-20.0%
14	14	1	97.5	31.9	0.00%	0.1	34.8	-9.2%	107.2	7.2	42.0	-31.7%
15	46	4	146.3	13.9	0.00%	0.9	27.8	-99.2%	85.4	5.7	33.5	-140.3%
16	40	6	228.7	52.2	0.01%	2.9	49.9	4.4%	153.4	10.3	60.2	-15.3%
17	40	2	224.1	39.0	0.00%	0.3	42.7	-9.5%	131.4	8.8	51.5	-32.1%
18	40	4	269.2	64.0	0.01%	1.2	53.2	16.8%	163.7	11.0	64.2	-0.4%
19	36	2	228.0	47.0	0.01%	0.4	44.4	5.5%	136.5	9.1	53.5	-14.0%
20	28	2	195.0	33.8	0.00%	0.2	38.1	-12.7%	117.1	7.8	45.9	-35.9%
Average results		2.7	176.0	54.2	0.00%	4.8	45.4	2.8%	139.5	9.3	54.7	-17.2%

Parameter	Original	Δ 10%	Gap (%)	Δ 20%	Gap (%)
Feasible solutions	20/20	20/20	-	19/20	-
Avg. Obj. Function ($)	54.2	57.8	6.7%	59.5	9.7%
Avg. Charged energy cost ($)	24.6	27.5	11.7%	29.6	20.3%
Avg. degradation cost ($) (in charge)	8.3	9.4	13.7%	10.2	23.2%
Avg. degradation cost ($) (in discharge)	21.3	20.9	-1.9%	19.7	-7.8%
Avg. Charged energy (kWh) (Slow charge)	29.5	33.6	13.9%	31.0	4.9%
Avg. Charged energy (kWh) (Fast charger)	21.7	23.8	9.5%	30.9	42.2%
Avg. # of charges (Slow Charger)	1.5	1.6	6.7%	1.3	-12.3%
Avg. # of charges (Fast charger)	0.9	1.0	11.8%	1.2	36.2%
Average speed (Km/h)	12.4	12.7	2.2%	12.8	3.1%

Parameter	Base	Δ 10%	Gap (%)	Δ 20%	Gap (%)
Feasible solutions	20/20	20/20	-	18/20	-
Avg. Obj. Function ($)	54.2	63.2	16.5%	60.3	11.2%
Avg. Charged energy cost ($)	24.6	31.1	26.3%	29.9	21.7%
Avg. degradation cost ($) (in charge)	8.3	9.6	16.5%	8.8	6.8%
Avg. degradation cost ($) (in discharge)	21.3	22.5	5.3%	21.5	0.8%
Avg. Charged energy (kWh) (Slow charge)	29.5	18.8	-36.2%	7.8	-73.7%
Avg. Charged energy (kWh) (Fast charger)	21.7	39.5	81.8%	44.9	106.5%
Avg. # of charges (Slow Charger)	1.5	1.1	-30.0%	0.6	-59.3%
Avg. # of charges (Fast charger)	0.9	1.4	64.7%	1.6	83.0%
Average speed (Km/h)	12.4	13.5	9.0%	14.5	16.9%

	1 (Km/h)	0.5 (Km/h)	0.25 (Km/h)
Avg. Gap (%)		0.08%	0.10%
Max Gap (%)		0.17%	0.18%
CPU time (s)	4.77	5.62	7.03

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