Supply chain network optimization using a Tabu Search based heuristic

Braido, Gabriel Machado; Borenstein, Denis; Casalinho, Gilmar D’Agostini Oliveira

doi:10.1590/0104-530X1288-14

Gabriel Machado Braido

Programa de Pós-graduação em Administração – PPGAdm, Universidade do Vale do Rio dos Sinos – UNISINOS, Avenida Unisinos, 950, Cristo Rei, CEP 93022-750, São Leopoldo, RS, Brasil, e-mail: gabrielb@univates.br

Centro Universitário Univates – UNIVATES, Rua Avelino Tallini, 171, Bairro Universitário, CEP 95900-000, Lajeado, RS, Brasil

Denis Borenstein

Faculdad de Ciências Económicas y Administratívas, Universidad de Cuenca, Av. 12 de Abril, s/n, Agustín Cueva, Cuenca, Ecuador, e-mail: denisb@ea.ufrgs.br

Universidade Federal do Rio Grande do Sul – UFRGS, Rua Washington Luis, 855, Centro, CEP 90010-460, Porto Alegre, RS, Brasil

Gilmar D’Agostini Oliveira Casalinho

Programa de Pós-graduação em Administração – PPGA, Escola de Administração – EA, Universidade Federal do Rio Grande do Sul – UFRGS, Rua Washington Luis, 855, Centro, CEP 90010-460, Porto Alegre, RS, Brasil, e-mail: gilmarcasalinho@gmail.com

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10	Hsu & Li (2009)Hsu, C. I., & Li, H. C. (2009). An integrated plant capacity and production planning model for high-tech manufacturing firms with economies of scale. International Journal of Production Economics, 118(2), 486-500. http://dx.doi.org/10.1016/j.ijpe.2008.09.015. http://dx.doi.org/10.1016/j.ijpe.2008.09...	Design a company's supply network, seeking to exploit the economies of scale of impacts arising from the use of optimal capacity and the amount of production of each facility	Heuristic based in Simulated Annealing
11	Javid & Azad (2010)Javid, A. A., & Azad, N. (2010). Incorporating location, routing and inventory decisions in supply chain network design. Transportation Research Part E, Logistics and Transportation Review, 46(5), 582-597. http://dx.doi.org/10.1016/j.tre.2009.06.005. http://dx.doi.org/10.1016/j.tre.2009.06....	Simultaneous optimization of location, allocation, capacities, inventory and routing in a chain of stochastic supplies, where each client has an uncertain demand, and each CD has certain amount of safety stock	Tabu Search and Simulated Annealing
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13	Shimizu & Fujikura (2010)Shimizu, Y., & Fujikura, T. (2010). A hybrid meta-heuristic approach for integrated capacitated multi-commodity logistics optimization over planning horizon. Journal of Advanced Mechanical Design, Systems and Manufacturing, 4(3), 716-727. http://dx.doi.org/10.1299/jamdsm.4.716. http://dx.doi.org/10.1299/jamdsm.4.716...	Strategic optimization of a logistics network design to improve the efficiency of a supply chain	Hibrid Tabu Search
14	Lee & Kwon (2010)Lee, Y. H., & Kwon, S. G. (2010). The hybrid planning algorithm for the distribution center operation using tabu search and decomposed optimization. Expert Systems with Applications, 37(4), 3094-3103. http://dx.doi.org/10.1016/j.eswa.2009.09.020. http://dx.doi.org/10.1016/j.eswa.2009.09...	Facilities location problem and a distribution plan in a single-source network	Tabu Search
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17	Sun (2012)Sun, M. (2012). A tabu search heuristic procedure for the capacitated facility location problem. Journal of Heuristics, 18(1), 97-118. http://dx.doi.org/10.1007/s10732-011-9157-3. http://dx.doi.org/10.1007/s10732-011-915...	Capacited facility location	Tabu Search
18	Badri et al. (2013)Badri, H., Bashiri, M., & Hejazi, T. (2013). Integrated strategic and tactical planning in a supply chain network design with a heuristc solution method. Computers & Operations Research, 40(4), 1143-1154. http://dx.doi.org/10.1016/j.cor.2012.11.005. http://dx.doi.org/10.1016/j.cor.2012.11....	Design and strategic and tactical planning of a network of supply chains	Lagrangean relaxation
19	Addis et al. (2013)Addis, B., Carello, G., & Ceselli, A. (2013). Combining very large scale and ILP based neighborhoods for a two-level location problem. European Journal of Operational Research, 231(3), 535-546. http://dx.doi.org/10.1016/j.ejor.2013.06.010. http://dx.doi.org/10.1016/j.ejor.2013.06...	Solve a generalization of the facility location problem in which two levels of facilities should be located	Neighborhood search
20	Rahmani & Mirhassani (2014)Rahmani, A., & Mirhassani, S. A. (2014). A hybrid firefly-genetic Algotithm for the capacitated facility location problem. Information Sciences, 283, 70-78. http://dx.doi.org/10.1016/j.ins.2014.06.002. http://dx.doi.org/10.1016/j.ins.2014.06....	Where to locate the facilities and how to move commodities to minimize costs	Genetic algorithm
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23	Ho (2015)Ho, S. (2015). An iterated tabu search heuristic for the single source capacitated facility location problem. Applied Soft Computing, 27, 169-178. http://dx.doi.org/10.1016/j.asoc.2014.11.004. http://dx.doi.org/10.1016/j.asoc.2014.11...	Determine a subset of enabled facilities to be opened in order to meet the demands of customers so that the costs are minimized.	Tabu Search

$x_{f w s}$	quantity of product $s \in S$ shipped from factory $f \in F$ to DC $w \in W$
$y_{v f r}$	quantity of raw material $r \in R$ shipped from vendor $v \in V$ to factory $f \in F$
$z_{w}$	binary variable, where: 1 if the DC $w \in W$ is selected; and 0 otherwise
$g_{w c}$	binary variable, where: 1 if the DC $w \in W$ meets the demand of the consumer area $c \in C$ ; and 0 otherwise

$d_{s c}$	demand of products $s \in S$ by the customer $c \in C$ ;
$U_{w}$	maximum of DCs that can be opened;
$u_{r s}$	utilization rate of raw material $r \in R$ per unit of product $s \in S$ ;
$u_{s}$	utilization rate of production capacity per unit of product $s \in S$ ;
$C A P_{w}$	transfer capability of DC $w \in W$ ;
$C A P_{v r}$	supply capacity of raw material $r \in R$ by supplier $v \in V$ ;
$C A P_{f}$	production capacity of factory $f \in F$ ;
$C T_{w}^{o}$	annual fixed cost of operation of DC $w \in W$ ;
$C T_{w}^{g}$	unit cost transfer of DC $w \in W$ ;
$C T_{f s}^{p}$	unit cost of production of product $s \in S$ at the factory $f \in F$ ;
$C T_{f v r}^{t}$	unit cost of transportation of raw material $r \in R$ from supplier $v \in V$ to factory $f \in F$ ;
$C T_{f w s}^{t}$	unit cost of transportation of product $s \in S$ from factory $f \in F$ to DC $w \in W$ ;
$C T_{w c s}^{t}$	unit cost of transportation of product $s \in S$ from DC $w \in W$ to customer $c \in C$ ;
$u_{\min}$	minimum demand for opening DC $w \in W$ .

Instance	DC	Arc	Instance	DC	Arc
1	5	9	12	7	20
2	6	18	13	7	50
3	7	25	14	7	100
4	8	26	15	8	25
5	9	50	16	8	50
6	5	9	17	8	120
7	5	25	18	9	24
8	5	40	19	9	44
9	6	20	20	9	150
10	6	50	21	6	20
11	6	110	22	6	100

Instance	Vendors	Raw Materials	Factories	DCs	Group of Products	Customers
1	5	5	3	10	5	150
2	5	5	3	20	5	150
3	5	5	3	30	5	150
4	5	5	3	40	5	150
5	5	5	3	50	5	150
6	5	5	3	10	10	150
7	5	5	3	10	50	150
8	5	5	3	10	100	150
9	5	5	3	20	10	150
10	5	5	3	20	50	150
11	5	5	3	20	100	150
12	5	5	3	30	10	150
13	5	5	3	30	50	150
14	5	5	3	30	100	150
15	5	5	3	40	10	150
16	5	5	3	40	50	150
17	5	5	3	40	100	150
18	5	5	3	50	10	150
19	5	5	3	50	50	150
20	5	5	3	50	100	150
21	5	5	3	20	10	150
22	5	5	3	20	50	150

	Solution ($)			CPU Time (s)
Instance	CPLEX	TS	gap (%)	CPLEX	TS	Reduction (%)
1	16,970,300	17,796,420	4.87%	2.07	0.66	–68.12%
2	16,541,500	16,750,500	1.26%	2.42	0.25	–89.59%
3	17,484,800	18,605,000	6.41%	4.06	0.45	–88.87%
4	15,453,300	16,568,600	7.22%	7.65	0.16	–97.87%
5	15,051,100	15,857,900	5.36%	4.86	0.44	–90.86%
6	31,098,000	31,224,000	0.41%	2.45	0.53	–78.53%
7	30,755,440	30,811,316	0.18%	3.97	1.46	–63.17%
8	29,169,246	29,661,682	1.69%	9.61	5.63	–41.47%
9	28,816,500	30,275,000	5.06%	3.93	1.09	–72.26%
10	30,880,456	32,487,848	5.21%	10.97	2.16	–80.29%
11	31,226,678	33,249,280	6.48%	39.62	4.82	–87.84%
12	27,681,500	29,284,500	5.79%	4.39	1.95	–55.69%
13	29,728,252	32,029,352	7.74%	13.54	2.53	–81.32%
14	27,813,526	29,738,192	6.92%	36.44	3.42	–90.62%
15	28,525,950	29,899,900	4.82%	10.74	0.32	–97.00%
16	29,947,862	31,839,320	6.32%	15.03	2.71	–81.99%
17	28,943,138	29,780,336	2.89%	54.42	3.99	–92.67%
18	27,532,500	29,234,500	6.18%	4.96	0.56	–88.77%
19	27,763,300	29,810,824	7.37%	17.45	3.64	–79.13%
20	27,935,264	29,855,046	6.87%	38.47	4.82	–87.48%
21	60,940,660	63,570,312	4.32%	7.12	0.67	–90.60%
22	63,771,168	67,760,184	6.26%	13.23	2.84	–78.53%
Average			4.98%	13.97	2.05	–81.03%

Instance	Vendors	Raw Materials	Factories	DCs	Group of Products	Customers
A	5	5	2	10	132	261
B	5	5	2	20	132	261
C	5	5	5	40	130	200
D	5	5	5	100	130	1000

\begin{array}{l} \min \sum_{w \in W} C T_{w}^{o} z_{w} + \sum_{w \in W} \sum_{c \in C} \sum_{s \in S} C T_{w}^{g} d_{s c} g_{w c} + \sum_{f \in F} \sum_{w \in W} \sum_{s \in S} C T_{f s}^{p} x_{f w s} + \\ \sum_{v \in V} \sum_{f \in F} \sum_{r \in R} C T_{f v r}^{t} y_{v f r} + \sum_{f \in F} \sum_{w \in W} \sum_{s \in S} C T_{f w s}^{t} x_{f w s} + \sum_{w \in W} \sum_{c \in C} \sum_{s \in S} C T_{w c s}^{t} d_{s c} g_{w c} \end{array}

[1] Source: elaborated by the authors.

Instance	DC	Arc	Instance	DC	Arc
1	5	9	12	7	20
2	6	18	13	7	50
3	7	25	14	7	100
4	8	26	15	8	25
5	9	50	16	8	50
6	5	9	17	8	120
7	5	25	18	9	24
8	5	40	19	9	44
9	6	20	20	9	150
10	6	50	21	6	20
11	6	110	22	6	100

Instance	Vendors	Raw Materials	Factories	DCs	Group of Products	Customers
1	5	5	3	10	5	150
2	5	5	3	20	5	150
3	5	5	3	30	5	150
4	5	5	3	40	5	150
5	5	5	3	50	5	150
6	5	5	3	10	10	150
7	5	5	3	10	50	150
8	5	5	3	10	100	150
9	5	5	3	20	10	150
10	5	5	3	20	50	150
11	5	5	3	20	100	150
12	5	5	3	30	10	150
13	5	5	3	30	50	150
14	5	5	3	30	100	150
15	5	5	3	40	10	150
16	5	5	3	40	50	150
17	5	5	3	40	100	150
18	5	5	3	50	10	150
19	5	5	3	50	50	150
20	5	5	3	50	100	150
21	5	5	3	20	10	150
22	5	5	3	20	50	150

Instance	DC	Arc	Instance	DC	Arc
1	5	9	12	7	20
2	6	18	13	7	50
3	7	25	14	7	100
4	8	26	15	8	25
5	9	50	16	8	50
6	5	9	17	8	120
7	5	25	18	9	24
8	5	40	19	9	44
9	6	20	20	9	150
10	6	50	21	6	20
11	6	110	22	6	100

Instance	Vendors	Raw Materials	Factories	DCs	Group of Products	Customers
1	5	5	3	10	5	150
2	5	5	3	20	5	150
3	5	5	3	30	5	150
4	5	5	3	40	5	150
5	5	5	3	50	5	150
6	5	5	3	10	10	150
7	5	5	3	10	50	150
8	5	5	3	10	100	150
9	5	5	3	20	10	150
10	5	5	3	20	50	150
11	5	5	3	20	100	150
12	5	5	3	30	10	150
13	5	5	3	30	50	150
14	5	5	3	30	100	150
15	5	5	3	40	10	150
16	5	5	3	40	50	150
17	5	5	3	40	100	150
18	5	5	3	50	10	150
19	5	5	3	50	50	150
20	5	5	3	50	100	150
21	5	5	3	20	10	150
22	5	5	3	20	50	150

Brasil

Brasil

Supply chain network optimization using a Tabu Search based heuristic

Abstract

Instance	DC	Arc	Instance	DC	Arc
1	5	9	12	7	20
2	6	18	13	7	50
3	7	25	14	7	100
4	8	26	15	8	25
5	9	50	16	8	50
6	5	9	17	8	120
7	5	25	18	9	24
8	5	40	19	9	44
9	6	20	20	9	150
10	6	50	21	6	20
11	6	110	22	6	100

Instance	Vendors	Raw Materials	Factories	DCs	Group of Products	Customers
1	5	5	3	10	5	150
2	5	5	3	20	5	150
3	5	5	3	30	5	150
4	5	5	3	40	5	150
5	5	5	3	50	5	150
6	5	5	3	10	10	150
7	5	5	3	10	50	150
8	5	5	3	10	100	150
9	5	5	3	20	10	150
10	5	5	3	20	50	150
11	5	5	3	20	100	150
12	5	5	3	30	10	150
13	5	5	3	30	50	150
14	5	5	3	30	100	150
15	5	5	3	40	10	150
16	5	5	3	40	50	150
17	5	5	3	40	100	150
18	5	5	3	50	10	150
19	5	5	3	50	50	150
20	5	5	3	50	100	150
21	5	5	3	20	10	150
22	5	5	3	20	50	150