Asymmetric vehicle routing problem with heterogeneous limited fleet: a case study in a beverage industry

Kramer, Raphael Harry Frederico Ribeiro; Subramanian, Anand; Penna, Puca Huachi Vaz

doi:10.1590/0104-530X1442-14

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Articles • Gest. Prod. 23 (1) • Jan-Mar 2016 • https://doi.org/10.1590/0104-530X1442-14 copy

Asymmetric vehicle routing problem with heterogeneous limited fleet: a case study in a beverage industry

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

This article deals with a case study in a beverage industry concerning the Asymmetric Vehicle Routing Problem with Heterogeneous Limited Fleet (AVRPHLF). The objective of the present paper is to define the vehicle routes so as to reduce distribution costs. The AVRPHLF belongs to the NP-hard class, that is, its resolution through exact methods is an extremely hard task. In practice, problems of this nature are generally treated via heuristics. Among the various solution approaches, we decided to perform an adaptation of a heuristic from the literature that has proved to be efficient, capable of generating high-quality solutions in a reasonable execution time. Computational experiments were conducted in a set of seven instances obtained from the company in question. The results obtained show that there was a considerable reduction in the number of vehicles used and in the total distance traveled with respect to the solutions adopted by the company.

Keywords:
Optimization; Beverage industry; Iterated Local Search; Logistics

Vehicle	Quantity	Capacity (Kg)
3/4	14	4000
Toco	7	8000
Truck A	9	12000
Truck B	6	13000
Cart	1	25000

1:	Procedure GetMatrices()
2:	i = 1;
3:	j = 1;
4:	while i ≤ n do
5:	while j ≤ n do
6:	add address of i to the path;
7:	add address of j to the path;
8:	if size of the path = 24 or j = n then
9:	add address of i to the path;
10:	sends path as a route requisition;
11:	empty path;
12:	end if
13:	j = j + 1;
14:	end while
15:	i = i + 1;
16:	j = 1;
17:	end while
18:	end GetMatrices.

1:	Procedure ILS-RVND(MaxIter, MaxIterILS, v)
2:	LoadData();
3:	f* ← ∞;
4:	fori = 1, ..., MaxIterdo
5:	s ← GenerateInitialSolution (v, MaxIter, seed);
6:	s' ← s;
7:	iterILS ← 0;
8:	whileiterILS ≤ MaxIterILSdo
9:	s ← RVND(s);
10:	iff(s) <f(s') then
11:	s' ← s;
12:	iterILS← 0;
13:	end if
14:	s' ← Perturb(s', seed);
15:	iterILS ← iterILS + 1;
16:	end while
17:	iff(s') < f*then
18:	s* ← s';
19:	f* ← f(s');
20:	end if
21:	end for
22:	returns*;
23:	end ILS-RVND.

1:	Procedure GenerateInitialSolution(v, MaxIter, seed)
2:	ConsecutiveTrials ← 0;
3:	Initialize CL;
4:	Let s = {s¹, ..., s^v} the set composed of v empty routes, sorted in descending order according to the capacity;
5:	forv’ = 1, ..., v-1 do
6:	s^v' ← k associated with max_{k $\in$}CL{q_k};
7:	Update CL; {CL ← CL – {k}}.
8:	end for
9:	InsertionCriterion ← MCFIC or NFIC (selected at random);
10:	InsertionStrategy ← SIS or PIS (selected at random);
11:	if InsertionStrategy = SIS then
12:	s ← SequentialInsertion(s, v, CL, InsertionCriterion);
13:	else
14:	s ← ParallelInsertion(s, v, CL, InsertionCriterion);
15:	end if
16:	ifs is infeasible then
17:	ConsecutiveTrials ← ConsecutiveTrials + 1;
18:	ifConsecutiveTrials = MaxIter then
19:	v ← v + 1;
20:	ConsecutiveTrials ← 0;
21:	end if
22:	Go to line 3;
23:	else
24:	return s;
25:	end if
26:	end GenerateInitialSolution.

1:	Procedure RVND(s)
2:	Initialize the inter-route Neighborhood List NL;
3:	whileNL ≠ 0 do
4:	Select a neighborhood N^(η) $\in$ NL at random;
5:	Find the best neighbor s' of s $\in$ N^(η);
6:	if f(s') < f(s) then
7:	s ← s';
8:	s ← IntraRouteSearch(s);
9:	Update NL;
10:	else
11:	Remove N^(η) from NL;
12:	end if
13:	end while
14:	returns;
15:	end RVND.

Instance	n	Total Demand (Kg)	Vehicles
Instance	n	Total Demand (Kg)	v	Types	Quantity (by type)	Capacities (by type - Kg)	Total Capacity (Kg)
KSP1	299	96736.81	17	4	13, 2, 1, 1	4000, 8000, 8564, 24123	100687
KSP2	313	52520.43	14	4	11, 1, 1, 1	4000, 4390, 4621, 8000	61011
KSP3	294	62624.06	14	2	13, 1	4000, 14206	66206
KSP4	341	49381.47	12	3	10, 1, 1	4000, 8320, 8696	57016
KSP5	318	46827.40	11	3	9, 1, 1	4000, 8320, 8626	53016
KSP6	291	46142.22	11	3	9, 1, 1	4000, 8320, 8626	53016
KSP7	108	23486.33	6	2	5, 1	4000, 4093	24093

Instance	Total Distance (Km)			CPU Time (s)
Instance	Best Solution	Average Solution	Std. Dev.	Best Solution	Average Solution	Std. Dev.
KSP1	1394.48	1417.3	12.10	293.80	285.39	40.90
KSP2	1049.56	1054.01	2.24	360.86	335.46	31.04
KSP3	1157.02	1165.06	4.74	274.21	288.42	31.89
KSP4	1158.30	1168.89	6.79	637.06	599.74	84.05
KSP5	877.46	889.54	8.72	465.71	536.37	48.41
KSP6	856.12	861.17	3.40	277.40	318.95	33.37
KSP7	509.33	514.16	2.18	7.32	7.64	1.37

Instance	Distance (Km)			Average Gap (%)
Instance	Company	ILS-RVND Best Solution	ILS-RVND Average Solution	Average Gap (%)
KSP1	1519.30	1394.48	1417.30	-6.71
KSP2	1342.70	1049.56	1054.01	-21.50
KSP3	1318.90	1157.02	1165.06	-11.66
KSP4	1288.90	1158.30	1168.89	-9.31
KSP5	1082.80	856.12	861.17	-20.47
KSP6	600.20	509.33	514.16	-14.34
KSP7	1519.30	1394.48	1417.30	-6.71
			Average	-14.00%

Instance	No. of vehicles used		Reduction
Instance	Company	ILS-RVND	Reduction
KSP1	17	17	0
KSP2	14	12	2
KSP3	14	14	0
KSP4	12	11	1
KSP6	11	10	1
KSP7	6	6	0

Universidade Federal de São Carlos Departamento de Engenharia de Produção , Caixa Postal 676 , 13.565-905 São Carlos SP Brazil, Tel.: +55 16 3351 8471 - São Carlos - SP - Brazil
E-mail: gp@dep.ufscar.br

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