Mathematical model for planning the distribution of locomotives to meet the demand for making up trains

Nascimento, Fabiano Cézar Gomes; Rosa, Rodrigo de Alvarenga

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Original Article • Gest. Prod. 26 (2) • 2019 • https://doi.org/10.1590/0104-530X-2557-19 copy

Mathematical model for planning the distribution of locomotives to meet the demand for making up trains

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

The cost for locomotive distribution over the rail yards to meet the locomotive demand for train formation is very high. Thus, this paper proposes a mathematical model based on the Locomotive Scheduling Problem for locomotive distribution planning to meet the demand of the rail yards seeking to minimize the distribution costs. The proposed model presents a new formulation for the LSP with Multiple Locomotives and considers the imbalance between offer and demand of locomotives, this situation was not addressed in the literature yet. Tests on instances based on real data from the Vitória a Minas Railroad (EFVM) were solved optimally using CPLEX 12.6. The model proved to be a good tool to analyze the locomotive distribution planning. When compared with the manual planning currently held by the railroad, the results showed several gains.

Keywords:
Locomotive distribution planning; Locomotive scheduling problem; Locomotive assignment problem; Railroad transport

Group	Instance	Variation of the Instances	Number of trains / week
A	1	Standard	156
	2	Maximum 4 locomotives per train	156
	3	Maximum 8 locomotives per train	156
	4	+10% interval between trains	148
	5	+10% interval between trains and at maximum 8 locomotives per train	148
	6	-10% interval between trains	174
	7	-10% interval between trains and at maximum 8 locomotives per train	174
B	8	1^st week of July/2015	162
	9	4^th week of July/2015	157
	10	4^th week of August/2015	132

Group	Instance	OF	GAP (%)	Execution Time (s)	Total Cost Light + Dead (US$)	Number of distributed locomotives
Group	Instance	OF	GAP (%)	Execution Time (s)	Total Cost Light + Dead (US$)	Dead	Light	Virtual
A	1	74,792.60	0.0	14.01	1,790.00	19	16	73
	2	74,792.60	0.0	18.17	1,790.00	19	16	73
	3	74,792.60	0.0	13.81	1,790.00	19	16	73
	4	75,492.40	0.0	16.33	1,490.00	9	14	74
	5	75,492.40	0.0	15.73	1,490.00	9	14	74
	6	82,812.85	0.0	23.65	1,810.00	21	16	81
	7	82,812.85	0.0	15.60	1,810.00	21	16	81
B	8	79,827.32	0.0	17.99	1,723.94	22	15	78
	9	80,034.81	0.0	17.13	1,997.69	29	17	72
	10	67,834.53	0.0	18.41	1,256.78	35	11	67

Group	Instance	Number of distributed locomotives						Difference between CPLEX × Real Case Number of distributed locomotive
		Real Case			CPLEX
		Dead	Light	Unmet	Dead	Light	Unmet	Dead	Light	Unmet
B	8	18	0	101	22	15	78	4	15	-23
	9	27	0	98	29	17	72	2	17	-26
	10	31	0	87	35	11	67	4	11	-20

Group	Instance	Number of distributed locomotives						Difference between CPLEX × Real Case Number of distributed locomotive
		Real Case			CPLEX
		Dead	Light	Unmet	Dead	Light	Unmet	Dead	Light	Unmet
B	8	18	0	98	22	0	91	4	0	-7
	9	27	0	96	29	0	90	2	0	-6
	10	31	0	85	35	0	81	4	0	-4

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E-mail: gp@dep.ufscar.br

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