Application of preservation technology for lifetime dependent products in an integrated production system

Muhammad Waqas Iqbal; Biswajit Sarkar

doi:10.3934/jimo.2018144

Article Contents

2020, Volume 16, Issue 1: 141-167. Doi: 10.3934/jimo.2018144

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Application of preservation technology for lifetime dependent products in an integrated production system

Muhammad Waqas Iqbal^1, and
Biswajit Sarkar^2, ,

1.
Department of Industrial & Management Engineering , Hanyang University , Ansan Gyeonggi-do, 426 791, South Korea
2.
Department of Industrial Engineering, Yonsei University, 50 Yonsei-ro, Sinchon-dong, Seodaemun-gu, Seoul, 03722, South Korea

* Corresponding author: bsbiswajitsarkar@gmail.com(Biswajit Sarkar), Phone Number-+82-31-400-5260, Fax No +82-31-436-8146
* Corresponding author: bsbiswajitsarkar@gmail.com(Biswajit Sarkar), Phone Number-+82-31-400-5260, Fax No +82-31-436-8146

Received: May 1, 2017

Revised: April 1, 2018

Early access: September 17, 2018

Published online: September 17, 2018

Abstract / Introduction Full Text(HTML) Figure(8) / Table(5) Related Papers Cited by

Abstract

It is important to adopt precisely the optimum level of preservation technology for deteriorating products, as with every passing day, a larger number of items deteriorate and cause an economic loss. For earning more profit, industries have a tendency to add more preservatives for long lifetime of products. However, realizing the health issues, there is a boundary that no manufacturer can add huge amount of preservatives for infinite lifetime of products. The correlation between the long lifetime along with the price of the product is introduced in this model to show the benefit of the optimum level of investment in preservation technology. To maintain the environmental sustainability, the deteriorated items, which can no longer be preserved by adding preservatives anywhere, are disposed with proper protection. The objective of the study is to obtain profit to show the application through a non-linear mathematical. The model is solved through Kuhn-Tucker and an algorithm. Robustness of the model is verified through numerical experiments and sensitivity analysis. Some comparative analyses are provided, which support the adoption of preservation technology for deteriorating products. Numerical studies proved that the profit increases significantly with the application of proposed preservation technology. Some important managerial insights are provided to help the decision makers while implementing the proposed model in real-world situations.

Keywords:

Mathematics Subject Classification: Primary: 90B30, 90C30; Secondary: 03C40.

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Figure 1. Process flow

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Figure 2. Product's maximum lifetime versus rate of deterioration

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Figure 3. Inventory behavior during one cycle

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Figure 4. Improvement of profit with application of proposed preservation technology

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Figure 5. Variation in production time by varying the setup cost, material cost, manufacturing cost, inventory holding cost and disposal cost

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Figure 6. Variation in cycle time by varying the setup cost, material cost, manufacturing cost, inventory holding cost and disposal cost

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Figure 7. Variation in cost of preservation by varying the setup cost, material cost, manufacturing cost, inventory holding cost and disposal cost

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Figure 8. Variation in profit by varying the setup cost, material cost, manufacturing cost, inventory holding cost and disposal cost

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Table 1. Authors' contribution to the literature

Reference paper	Deterioration		Preservation technology	MLD selling-price
Reference paper	type	formulation	Preservation technology	MLD selling-price
Hsu et al. [13]	constant	$-$	$\surd$	$-$
Sarkar [24]	Time-varying	MLD	$-$	$-$
Sarkar and Sarkar [28]	Time-varying	Linear
Dye [8]	Time-varying	Linear	$\surd$	$-$
Qin et al. [21]	Time-and temperature	Exponential varying	$-$	$-$
Wee and Widyadana [37]	Constant	$-$	$-$	$-$
Chew et al. [7]	$-$	$-$	$-$	$\surd$
Sarkar [25]	Random	Uniform, triangular Beta	$-$	$-$
Wang et al. [36]	Time-varying	MLD	$-$	$-$
Priyan and Uthayakumar [19]	Fuzzy	Triangular	$-$	$-$
Shah et al. [29]	Time-varying	MLD	$\surd$	$-$
Tsao [34]	Constant	$-$	$\surd$
This paper	Time-varying	MLD	$\surd$	$\surd$

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Table 2. Values of the parameters for numerical experiment

$C_s$ = $500/setup	$h$ = $0.8/unit/month	$a$ = 1500 units/month	$L$ = 4 months
$δ$ = 0.05	$C_{mt}$ = $15/unit	$C_d$ = $0.5/unit	$b$ = 60 units/month
$k$ = 3.2	$C_m$ = $10/unit	$\varepsilon$ = $100/unit	$ M$ = $10/unit
$γ$ = 0.005

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Table 3. Optimal solution for the numerical experiment when preservation technology is applied

$t_1^*$ = 0.21 month

$T^*$ = 0.68 month

$C_p^*$ = $1.78 /unit/unit time

$\pi^*$ = $115955/month

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Table 4. Optimal solution for the numerical experiment when preservation technology is not applied

$t_1^*$= 0:18 month

$T^*$= 0.54 month

$\pi^*$= $ \$ $111106/month

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Table 5. Sensitivity analysis

Parameters	Changes of parameters (in %)	$t_1^*$(in %)	$T^*$	$C_p^*$	$\pi^*$
	-50%	-26.82	-22.62	-19.26	+10.72
	-25%	-11.73	-9.31	-10.00	+5.03
$C_s$	+25%	+9.50	+7.98	+8.15	-8.92
	+50%	+18.44	+14.86	+15.19	-8.92
	-50%	+50.84	+38.14	+39.63	+53.65
	-25%	+19.55	+15.52	+15.93	+26.11
$C_{mt}$	+25%	-13.41	-11.09	-11.85	-25.15
	+50%	-23.46	-19.29	-20.37	-49.63
	-50%	+12.29	+9.76	+10.00	+17.27
	-25%	+5.59	+4.66	+4.44	+8.58
$C_m$	+25%	-5.03	-3.99	-4.44	-8.47
	+50%	-9.50	-7.76	-8.15	-16.85
	-50%	+11.17	+9.09	+9.26	+3.30
	-25%	+5.03	+4.21	+4.07	+1.60
$h$	+25%	-5.03	-3.55	-4.07	-1.52
	+50%	-8.94	-6.87	-7.41	-2.95
	-50%	+0.56	+0.67	+0.37	+0.22
	-25%	+0.00	+0.22	+0.00	+0.10
$C_d$	+25%	-0.56	-0.22	-0.37	-0.10
	+50%	-0.56	-0.44	-0.74	-0.22

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