Note on : Supply chain inventory model for deteriorating items with maximum lifetime and partial trade credit to credit risk customers

Prasenjit Pramanik; Sarama Malik Das; Manas Kumar Maiti

doi:10.3934/jimo.2018096

Article Contents

2019, Volume 15, Issue 3: 1289-1315. Doi: 10.3934/jimo.2018096

This issue Previous Article Bi-objective integrated supply chain design with transportation choices: A multi-objective particle swarm optimization Next Article An inventory model with imperfect item, inspection errors, preventive maintenance and partial backlogging in uncertainty environment

Note on : Supply chain inventory model for deteriorating items with maximum lifetime and partial trade credit to credit risk customers

1.
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, Paschim Medinipur, West Bengal 721102, India
2.
Department of Mathematics, Calcutta Institute of Technology, Uluberia, Howrah, West Bengal 711316, India
3.
Department of Mathematics, Mahishadal Raj College, Mahishadal, Purba Medinipur, West Bengal 721628, India

* Corresponding author
* Corresponding author

Received: July 31, 2017

Revised: January 31, 2018

Early access: June 2018

Published: April 2019

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Abstract

In the recently published paper [Gour Chandra Mahata and Sujit Kumar De, Supply chain inventory model for deteriorating items with maximum lifetime and partial trade credit to credit-risk customers, International Journal of Management Science and Engineering Management, 2017, DOI:10.1080/17509653.2015.1109482], a supplier-retailer supply chain model of a deteriorating item with maximum lifetime and partial trade credit to credit risk customers is studied. In their study, unfortunately the amount of the payable bank interest due to the deteriorated units is omitted in the retailer's profit function for making the marketing decision. Some other unrealistic studies are also found in the numerical section of the paper. In this study those non-trivial flaws are identified and technically corrected. After correction, the theoretical existence of the optimal solutions of different scenarios are established and the solutions are derived using a soft computing technique.

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Mathematics Subject Classification: Primary: 90B05; Secondary 91B60.

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Figure 1. Pictorial representation of situation 1.1

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Figure 2. Interest earn and paid situations for the sold units

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Figure 3. Interest paid situation due to deteriorated units

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Figure 4. Pictorial representation of situation 1.2

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Figure 5. Interest earn and paid situations for the sold units

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Figure 6. Interest paid situation due to deteriorated units

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Figure 7. Pictorial representation of situation 1.3

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Figure 8. Interest earn and paid situations for the sold units

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Figure 9. Interest paid situation due to deteriorated units

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Figure 10. Pictorial representation of situation 2.1

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Figure 11. Interest earn and paid situations for the sold units

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Figure 12. Interest paid situation due to deteriorated units

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Figure 13. Pictorial representation of situation 2.2

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Figure 14. Interest earn and paid situations for the sold units

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Figure 15. Interest paid situation due to deteriorated units

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Table 1. Innovation of this paper related to the exiting literature

Article	Deteriorating item	Level of trade credit	Pattern of trade credit	Deterioration rate	Item(s) has expiration time	Interest paid for deteriorated units
[8,11,15,37,38]	$\surd$	$\times$	NA	Constant	$\times$	NA
[35]	$\surd$	$\times$	NA	Constant	$\surd$	NA
[1]	$\surd$	Supplier-Retailer	Full credit	Constant	$\times$	$\times$
[2,14,26]	$\surd$	Supplier-Retailer	Ordered quantity based full/ partial credit	Constant	$\times$	$\times$
[3,6,13,21,25]	$\surd$	Supplier-Retailer	Full credit	Constant	$\times$	$\times$
		Retailer-Customers	Full credit
[20]	$\surd$	Supplier-Retailer	Full credit	Constant	$\times$	$\times$
		Retailer-Customers	Partial credit
[7,27,34]	$\surd$	$\times$	NA	Time dependent	$\times$	NA
[5]	$\surd$	Supplier-Retailer	Order quantity based full credit	Time dependent	$\times$	$\times$
[22]	$\surd$	Supplier-Retailer	Full credit	Time dependent	$\surd$	$\times$
		Retailer-Customers	Partial credit
This Paper	$\surd$	Supplier-Retailer	Full credit	Time dependent	$\surd$	$\surd$
		Retailer-Customers	Partial credit
NA stands for ‘Not Applicable’.

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Table 2. Results of the model

Example	Appropriate for	$T^*$	$Q^*$	$TP^(T^)$
5.1	Situation 1.1	$T_{11}=0.1346$	319.396	$TP_{11}(T_{11})=9824.71$
5.2	Situation 1.2	$T_{12}=0.1404$	291.159	$TP_{12}(T_{12})=8643.00$
5.3	Situation 1.3	$T_{13}=0.1365$	296.892	$TP_{13}(T_{13})=8942.34$
5.4	Situation 2.1	$T_{21}=0.1382$	273.311	$TP_{21}(T_{21})=8087.69$
5.5	Situation 2.2	$T_{22}=0.1374$	256.299	$TP_{22}(T_{22})=7716.36$

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Table 3. Sensitivity Analysis

Parameter		$T^*$	$Q^*$	$TP^(T^)$
	2000	0.1404	291.159	8643.00
D	2500	0.1259	325.220	10991.49
	3000	0.1151	355.645	13355.68
	0.16	0.1404	291.159	8643.00
M	0.20	0.1395	289.318	8664.18
	0.25	0.1392	288.595	8694.01
	50	0.1000	205.167	9058.72
A	100	0.1404	291.159	8643.00
	200	0.1958	412.145	8048.82
	1	0.1404	291.159	8643.00
m	2	0.1569	322.272	8780.27
	3	0.1670	341.100	8853.89
	0.02	0.1409	292.159	8637.78
$I_{e}$	0.03	0.1404	291.159	8643.00
	0.04	0.1398	289.933	8648.24
	0.05	0.1404	291.159	8643.00
$\alpha$	0.10	0.1402	290.779	8645.21
	0.20	0.1403	290.972	8649.619
	0.04	0.1396	289.443	8662.98
N	0.08	0.1404	291.159	8643.00
	0.12	0.1407	291.855	8626.29
	1	0.1894	398.066	16983.74
c	3	0.1595	332.370	12795.03
	5	0.1404	291.159	8643.00
	1	0.1569	326.853	8795.10
h	2	0.1404	291.159	8643.00
	4	0.1189	244.171	8380.12
	0.02	0.1410	292.351	8644.47
$I_{c}$	0.03	0.1404	291.159	8643.00
	0.04	0.1400	290.248	8641.556
	10	0.1404	291.159	8643.00
s	15	0.1396	289.442	18650.87
	20	0.1390	288.053	28658.77

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