An Effective MILP Model for Food Grain Inventory Transportation in India—A Heuristic Approach

Chakraborty, Sayan; Bhattacharjee, Kaushik; Sarmah, S. P.

doi:10.1007/978-981-13-9698-4_19

Sayan Chakraborty⁶,
Kaushik Bhattacharjee⁷ &
S. P. Sarmah⁶

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Abstract

In this work, we investigate a real-life inventory transportation problem faced by the Food Corporation of India (FCI). FCI is the central agency responsible for procurement, storage, and transportation of food grains over a large geographical area of India. Due to lopsided procurement and consumption of major food grains (i.e., rice & wheat) transportation of food grains across the warehouses becomes inevitable. FCI faces a significant challenge to find the optimal amount of food grains to be stored at each warehouse and transported among the warehouses to meet the demand during each period. In this study, we formulate an MILP model to determine the optimal inventory transportation decisions related to food grain transportation in India and demonstrate it via a case study. Commercial optimization packages can be used to solve the problem of this class. However, as we see, they fail to provide a solution for large size problem instances. Therefore, we propose a heuristic-based solution approach to solve the problem. It is seen that under a practical time limit, the proposed heuristic performs significantly well in terms of accuracy as compared to commercial optimizations packages. The nature of the study is generic in nature and can be also applied to various similar real-life problem scenarios.

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Authors and Affiliations

Department of Industrial and Systems Engineering, Indian Institute of Technology Kharagpur, Kharagpur, India
Sayan Chakraborty & S. P. Sarmah
School of Management Sciences, Indian Institute of Engineering Science and Technology, Shibpur, India
Kaushik Bhattacharjee

Authors

Sayan Chakraborty
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Kaushik Bhattacharjee
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S. P. Sarmah
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Corresponding author

Correspondence to Sayan Chakraborty .

Editor information

Editors and Affiliations

Department of Mathematics, Gujarat University, Ahmedabad, India
Nita H. Shah
Department of Mathematics, Amity Institute of Applied Sciences, Amity University, Noida, India
Mandeep Mittal

Appendices

Appendix 1

Results for scenario 1

Sl. No.	Instance size	Alpha	Number of source	Number of destination	Heuristic		CPLEX		Gap (%)
Sl. No.	Instance size	Alpha	Number of source	Number of destination	Value	Solution time	Value	Time limit (sec)	Gap (%)
1	50	0.2821	39	11	1651450	0.0312	1616545	3600	2.1592
2	50	0.3158	38	12	1612530	0.0312	1596100	3600	1.0294
3	50	0.3158	38	12	1479995	0.0156	1451435	3600	1.9677
4	50	0.1905	42	8	2181265	0.0156	2146540	3600	1.6177
5	50	0.2500	40	10	1530045	0.0468	1513665	3600	1.0821
6	100	0.2658	79	21	3302700	0.0468	3243850	3600	1.8142
7	100	0.1494	87	13	4535025	0.0624	4469196	3600	1.4729
8	100	0.2821	78	22	3378030	0.0468	3309245	3600	2.0786
9	100	0.2658	79	21	2885435	0.0624	2846836	3600	1.3559
10	100	0.2346	81	19	2803930	0.0312	2746175	3600	2.1031
11	200	0.1628	172	28	7232030	0.1092	7106100	3600	1.7721
12	200	0.2346	162	38	7839570	0.156	7642490	3600	2.5787
13	200	0.1765	170	30	7725335	0.1248	7607955	3600	1.5429
14	200	0.2422	161	39	7247205	0.0936	7118755	3600	1.8044
15	200	0.2195	164	36	8172980	0.1248	7914580	3600	3.2649
16	300	0.2245	245	55	9210160	0.2496	9059235	3600	1.6660
17	300	0.2000	250	50	10485170	0.2028	10292360	3600	1.8733
18	300	0.2712	236	64	11873735	0.2652	11475055	3600	3.4743
19	300	0.2195	246	54	9526675	0.2184	9306545	3600	2.3653
20	300	0.1811	254	46	11082185	0.1872	10763540	3600	2.9604
21	500	0.2225	409	91	16181110	0.9516	15718415	3600	2.9436
22	500	0.2225	409	91	20159315	0.78	19193905	3600	5.0298
23	500	0.2658	395	105	16636445	0.8736	16274570	3600	2.2236
24	500	0.2107	413	87	13790340	0.8424	13522505	3600	1.9807
25	500	0.2563	398	102	18860395	0.8892	18210625	3600	3.5681
26	800	0.2289	651	149	29411205	2.7456	28235380	3600	4.1644
27	800	0.2214	655	145	31008890	3.1668	29714055	3600	4.3577
28	800	0.2289	651	149	25387080	3.042	24376880	3600	4.1441
29	800	0.2140	659	141	31594345	3.1668	29911875	3600	5.6248
30	800	0.2422	644	156	32154915	2.8704	30253295	3600	6.2857
31	1200	0.2371	970	230	41726305	13.96	39525370	3600	5.5684
32	1200	0.2500	960	240	51643170	11.62	48340740	3600	6.8316
33	1200	0.2513	959	241	44470050	14.6644	41633685	3600	6.8127
34	1200	0.2295	976	224	41368565	12.3548	39685200	3600	4.2418
35	1200	0.2346	972	228	37756320	10.3274	36494555	3600	3.4574

Appendix 2

Results for scenario 2

Sl. No.	Instance size	Alpha	Number of source	Number of destination	Heuristic		CPLEX		Gap (%)
Sl. No.	Instance size	Alpha	Number of source	Number of destination	Value	Solution time	Value	Time limit (sec)	Gap (%)
1	50	0.5625	32	18	812325	0.3120	798040	3600	1.7900
2	50	0.5152	33	17	1042685	0.0156	1020880	3600	2.1359
3	50	0.5152	33	17	1217230	0.0468	1203455	3600	1.1446
4	50	0.3514	37	13	1475270	0.3900	1457215	3600	1.2390
5	50	0.5152	33	17	1659900	0.3744	1634145	3600	1.5761
6	100	0.7857	56	44	1746685	0.2496	1734845	3600	0.6825
7	100	0.3889	72	28	3219010	0.2184	3179825	3600	1.2323
8	100	0.6949	59	41	1979970	0.5148	1924935	3600	2.8591
9	100	0.6667	60	40	1952025	0.2028	1926705	3600	1.3142
10	100	0.4706	68	32	2713960	0.1404	2641405	3600	2.7468
11	200	0.5625	128	72	4079020	0.3432	4035880	3600	1.0689
12	200	0.4697	132	62	4695785	0.3432	4646840	3600	1.0533
13	200	0.3514	148	52	6683790	0.1872	6561325	3600	1.8665
14	200	0.3986	143	57	6245100	0.2340	6127485	3600	1.9195
15	200	0.4815	135	65	4476170	0.1716	4391710	3600	1.9232
16	300	0.5306	196	104	7042970	1.0452	6821860	3600	3.2412
17	300	0.5873	189	111	6664130	0.5148	6352040	3600	4.9132
18	300	0.4634	205	95	6981260	0.5772	6783870	3600	2.9097
19	300	0.5385	195	105	7646975	0.4212	7434005	3600	2.8648
20	300	0.5789	190	110	5799355	0.4056	5686215	3600	1.9897
21	500	0.5106	331	169	11217725	2.5272	10825845	3600	3.6199
22	500	0.4620	342	158	15632570	1.6068	14790680	3600	5.6920
23	500	0.5291	327	173	12132230	1.4196	11658955	3600	4.0593
24	500	0.6393	305	195	10457775	1.5444	10070425	3600	3.8464
25	500	0.4837	337	163	11598800	1.2636	11238320	3600	3.2076
26	800	0.5326	522	278	20317015	7.1136	18580980	3600	9.3431
27	800	0.5748	508	292	23043050	7.0900	21287010	3600	8.2494
28	800	0.4981	534	266	20013165	6.8900	18659160	3600	7.2565
29	800	0.5355	521	279	18633300	6.3000	17779830	3600	4.8002
30	800	0.6097	497	303	19422815	8.0300	17808285	3600	9.0662
31	1200	0.4634	820	380	30810930	23.0200	28035140	3600	9.9011
32	1200	0.5748	762	438	28919055	24.6600	26148415	3600	10.5958
33	1200	0.5228	788	412	28866420	19.9200	26852685	3600	7.4992
34	1200	0.5464	776	424	31690120	24.7700	27829950	3600	13.8706
35	1200	0.5564	771	429	33647415	23.6100	28825775	3600	16.7268

Appendix 3

Results for scenario 3

Sl. No.	Instance size	Alpha	Number of source	Number of destination	Heuristic		CPLEX		Gap (%)
Sl. No.	Instance size	Alpha	Number of source	Number of destination	Value	Solution Time	Value	Time limit (sec)	Gap (%)
1	50	6.1429	7	43	4981685	0.0398	4921825	3600	1.2162
2	50	6.1429	7	43	3223425	0.0778	3187710	3600	1.1204
3	50	7.3333	6	44	2079975	0.0381	2036070	3600	2.1564
4	50	3.5455	11	39	1494890	0.0627	1464555	3600	2.0713
5	50	2.3333	15	35	1328165	0.0498	1306285	3600	1.6750
6	100	3.3478	23	77	3299650	0.2451	3181875	3600	3.7014
7	100	3.3478	23	77	3690860	0.0727	3556420	3600	3.7802
8	100	4.2632	19	81	3642470	0.0679	3521515	3600	3.4347
9	100	3.1667	24	76	2711575	0.0668	2602320	3600	4.1984
10	100	3.1667	24	76	3641430	0.0738	3536805	3600	2.9582
11	200	5.0606	33	167	7072930	0.12	6822750	3600	3.6668
12	200	3.4444	45	155	8074245	0.1248	7733115	3600	4.4113
13	200	4.5556	36	164	7490365	0.1248	7181364	3600	4.3028
14	200	3.6512	43	157	6645620	0.1092	6394775	3600	3.9227
15	200	3.5455	44	156	7642950	0.1404	7289610	3600	4.8472
16	300	4.5556	54	246	12233600	0.234	11416165	3600	7.1603
17	300	3.9180	61	239	9274165	0.234	8949305	3600	3.6300
18	300	3.6875	64	236	8131880	0.2496	7869360	3600	3.3360
19	300	4.4545	55	245	13339635	0.2496	13402075	3600^a	−0.4659
20	300	4.8824	51	249	11978365	0.3276	11336165	3600	5.6651
21	500	4.2083	96	404	17876425	0.78	16801105	3600	6.4003
22	500	3.5872	109	391	15447495	0.9204	14839285	3600	4.0986
23	500	4.2083	96	404	18047305	1.014	18872055	3600^a	−4.3702
24	500	3.5872	109	391	16618755	1.2168	17630594	3600^a	−5.7391
25	500	4.0000	100	400	18938390	0.8736	17745595	3600	6.7216
26	800	4.3691	149	651	35611425	3.6036	34186968	3600	4.1667
27	800	7.2474	97	703	35365390	3.3852	33080785	3600	6.9061
28	800	3.6784	171	629	23279945	3.744	22551970	3600	3.2280
29	800	3.5977	174	626	24362435	4.47	23197980	3600	5.0196
30	800	4.2632	152	648	31086625	4.0092	29056840	3600	6.9856
31	1200	3.7431	253	947	46173110	13.6498	45190590	3600	2.1742
32	1200	4.3333	225	975	51691665	11.2478	46962155	3600	10.0709
33	1200	4.5046	218	982	40734345	9.3758	37940585	3600	7.3635
34	1200	4.0633	237	963	44112455	13.2444	39902870	3600	10.5496
35	1200	3.7244	254	946	40565095	12.4648	37375475	3600	8.5340

^aExceeded CPLEX time limit

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Chakraborty, S., Bhattacharjee, K., Sarmah, S.P. (2020). An Effective MILP Model for Food Grain Inventory Transportation in India—A Heuristic Approach. In: Shah, N., Mittal, M. (eds) Optimization and Inventory Management. Asset Analytics. Springer, Singapore. https://doi.org/10.1007/978-981-13-9698-4_19

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DOI: https://doi.org/10.1007/978-981-13-9698-4_19
Published: 01 September 2019
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-9697-7
Online ISBN: 978-981-13-9698-4
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