Improving delivery planning via an optimization technique for a case study of a construction material store

Figures & data

Table 1. The solution method of each study in the literature

Reference	Problem characteristics					Solution method
	Single depot	Split delivery	Multi-product	Heterogeneous fleet	Capacitated vehicle routing
Aganis and Sirawadee (2019)	✓	✓		✓		Branch-and-reduce
Ibrahim et al. (2019)	✓				✓	LP
Ozbaygin et al. (2018)		✓				Exact algorithm
Munari and Savelsbergh (2022)		✓				Branch-and-cut
Tavakkoli et al. (2015)			✓	✓		MILP
Ayyildiz et al. (2022)		✓	✓			MIP
Siriruk and Tangmo (2017)				✓		Cluster-First Route-Second
Setiawan et al. (2019)			✓	✓		MILP
Basuki et al. (2019)			✓	✓		Saving Matrix
Dellaert et al. (2021)					✓	Exact algorithm
This study	✓	✓	✓	✓	✓	MILP

Table 2. Distance matrix (km)

$\mathit{Dis}{\mathit{t}}_{\mathit{ij}}$	1	2	3	4	5	6	7	8	9	10	11	12
1	0	10	53	18	13	11	5	70	59	62	26	61
2	10	0	35	29	14	18	10	71	56	47	30	11
3	53	34	0	16	36	29	33	61	50	37	53	40
4	18	24	16	0	29	17	16	60	41	35	46	33
5	12	10	34	27	0	23	14	69	61	45	25	17
6	14	19	29	19	28	0	11	79	32	55	44	27
7	2	10	35	21	17	10	0	70	47	46	34	18
8	69	71	57	60	73	79	70	0	100	56	72	77
9	63	56	50	41	65	32	48	91	0	49	81	64
10	65	46	32	36	48	54	45	55	49	0	65	53
11	26	30	53	47	24	43	34	72	81	65	0	20
12	60	11	41	35	20	31	22	76	69	53	20	0

Table 3. Load weight and cost of each type of transport vehicle

${\mathit{k}}_{\mathit{\hspace{0.17em}}}$	Truck Type	$\mathit{Ca}{\mathit{p}}_{\mathit{k}}$	$\mathit{F}{\mathit{C}}_{\mathit{k}}$	$\mathit{V}{\mathit{C}}_{\mathit{k}}$	$\mathit{D}{\mathit{C}}_{\mathit{k}}$
1	Pickup	1,000	275	13	30
2	Box	1,500	300	14	30
3	6W Crane	5,000	3,600	29	50

Table 4. Product weight (kg) and limitations of each product

$\mathit{l}$	Product Type	${\mathit{W}}_{\mathit{l}}$	Pickup	Box	6W Crane
1	Steel	3.95	X	X	Y
2	Wood Planks	7	X	X	Y
3	Cement Bags	50	Y	Y	Y
4	Tiles	25	Y	Y	Y
5	Lightweight Brick	6.5	Y	Y	Y

Table 5. Demand for each type of each order (units)

$\mathit{D}{\mathit{M}}_{\mathit{il}}$	1	2	3	4	5
1	0	0	0	0	0
2	200	0	0	0	0
3	0	50	0	10	0
4	0	0	20	0	0
5	0	0	0	40	100
6	0	0	0	15	0
7	200	50	5	5	20
8	0	0	0	5	200

Table 6. All objective function value and delivery planning results

${\mathit{x}}_{\mathit{ijk}}$	Distance (km)	$\mathit{F}{\mathit{C}}_{\mathit{k}}$	$\mathit{V}{\mathit{C}}_{\mathit{k}}$	$\mathit{D}{\mathit{C}}_{\mathit{k}}$	Total cost (THB)
1,4,1	18	275	234		509
4,1,1	18		234		234
1,8,2	70	300	980		1,280
8,7,2	70		980		980
7,1,2	2		28	30	58
1, 6, 3	11	3,600	319		3,919
6, 3, 3	29		841		841
3, 5, 3	36		1,044	50	1,094
5, 2, 3	10		290	50	340
2, 7, 3	10		290	50	340
7, 1, 3	2		58	50	108

Figure 1. Delivery routes of the different vehicles, where node 1 represents the construction material store and nodes 2–8 are customer locations.

Table 7. The number of products for each vehicle loading

${\mathit{k}}_{\mathit{\hspace{0.17em}}}$	${\mathit{D}}_{\mathit{ikl}}$	${\mathit{D}}_{\mathit{ikl}}\mathit{\hspace{0.17em}}\left(\mathit{units}\right)$	${\mathit{W}}_{\mathit{l}}$	${\mathit{D}}_{\mathit{ikl}}{\mathit{W}}_{\mathit{l}}$	${\displaystyle \sum _{\mathit{i}=1}^8\mathit{ }}{\displaystyle \sum _{\mathit{l}=1}^5{D}_{\mathit{ikl}}}{W}_l$	$\mathit{Ca}{\mathit{p}}_{\mathit{k}}$	$\mathbf{\%}\mathit{Capacityutilizatio}{\mathit{n}}_{\mathit{\hspace{0.17em}}}$
1	4,1,3	20	50.00	1,000.00	1,000.00	1,000	100.00
2	7,2,4	2	25.00	50.00	1,488.00	1,500	99.20
	8,2,4	5	25.00	125.00
	7,2,5	2	6.50	13.00
	8,2,5	200	6.50	1,300.00
3	2,3,1	200	3.95	790.00	4,997.00	5,000	99.94
	7,3,1	200	3.95	790.00
	3,3,2	50	7.00	350.00
	7,3,2	50	7.00	350.00
	7,3,3	5	50.00	250.00
	3,3,4	10	25.00	250.00
	5,3,4	40	25.00	1,000.00
	6,3,4	15	25.00	375.00
	7,3,4	3	25.00	75.00
	5,3,5	100	6.50	650.00
	7,3,5	18	6.50	117.00

Figure 2. Vehicle loading for different vehicle types.

Table 8. The results of 20 scenarios

Scenario	# Customer	# Vehicle	# Product	Runtime (hh:mm:ss)
1	5	3	10	0:00:04
2	6	3	10	0:00:07
3	7	3	5	0:01:22
4	8	3	10	0:00:51
5	9	7	10	0:07:46
6	10	3	10	0:04:42
7	11	3	10	0:27:15
8	12	3	10	0:43:22
9	13	3	5	0:01:28
10	14	6	5	0:00:05
11	16	1	1	0:00:02
12	20	1	1	0:00:04
13	25	1	1	0:00:02
14	31	1	1	3:45:40
15	32	1	1	3:38:26
16	33	1	1	3:35:06
17	34	1	1	2:02:10
18	35	1	1	8:09:02
19	9	20	10	8:49:43
20	9	10	20	2:48:27

Aganis, S., & Sirawadee, A. (2019). Vehicle routing problem with split delivery and heterogeneous fleet using differential evolution method: A case study of beverage logistics company. KMUTT Research and Development Journal, 42, 142–159.

 Google Scholar

Ibrahim, A. A., Lo, N., Abdulaziz, R. O., & Ishaya, J. A. (2019). Capacitated vehicle routing problem. International Journal of Research - Granthaalayah, 7(3), 310–327. https://doi.org/10.29121/granthaalayah.v7.i3.2019.976

 Google Scholar

Ozbaygin, G., Karasan, O., & Yaman, H. (2018). New exact solution approaches for the split delivery vehicle routing problem. EURO Journal on Computational Optimization, 6(1), 85–115. https://doi.org/10.1007/s13675-017-0089-z

 Web of Science ®Google Scholar

Munari, P., & Savelsbergh, M. (2022). Compact formulations for split delivery routing problems. Transportation Science, 56(4), 1022–1043. https://doi.org/10.1287/trsc.2021.1106

 Web of Science ®Google Scholar

Tavakkoli, M. R., Raziei, Z., & Tabrizian, S. (2015). Solving a bi-objective multi-product vehicle routing problem with heterogeneous fleets under an uncertainty condition. International Journal of Transportation Engineering, 3(3), 207–225.

 Google Scholar

Ayyildiz, E., Şahin, M. C., & Taşkin, A. (2022). A multi depot multi product split delivery vehicle routing problem with time windows: A real cash in transit problem application in Istanbul, Turkey. Journal of Transportation and Logistics, 7(2), 213–232. https://doi.org/10.26650/JTL.2022.1113726

 Google Scholar

Siriruk, P., & Tangmo, Y. (2017, April). Heterogeneous fleet vehicle routing problem for retail construction material stores. In 2017 4th International Conference on Industrial Engineering and Applications (ICIEA) (pp. 234–238). IEEE. https://doi.org/10.1109/IEA.2017.7939213

 Google Scholar

Setiawan, F., Masruroh, N. A., & Pramuditha, Z. I. (2019). On modelling and solving heterogeneous vehicle routing problem with multi-trips and multi-products. Jurnal Teknik Industri, 21(2), 91–104. https://doi.org/10.9744/jti.21.2.91-104

 Google Scholar

Basuki, M., Hidayat, M. J., Aji, F. B., & Aji, F. B. Application of saving matrix methods and cross entropy for capacitated vehicle routing problem (CVRP) resolving. (2019). IOP Conference Series: Materials Science & Engineering, 462(1), 012025. IOP Publishing. https://doi.org/10.1088/1757-899X/462/1/012025

 Google Scholar

Dellaert, N., Van Woensel, T., Crainic, T. G., & Saridarq, F. D. (2021). A multi-commodity two-Echelon capacitated vehicle routing problem with time windows: Model formulations and solution approach. Computers & Operations Research, 127, 105154. https://doi.org/10.1016/j.cor.2020.105154

 Web of Science ®Google Scholar