Pricing strategy in an interval-valued production inventory model for high-tech products under demand disruption and price revision

Subhendu Ruidas; Mijanur Rahaman Seikh; Prasun Kumar Nayak

doi:10.3934/jimo.2022222

Article Contents

2023, Volume 19, Issue 9: 6451-6477. Doi: 10.3934/jimo.2022222

This issue Previous Article Two-stage distributionally robust noncooperative games: Existence of Nash equilibrium and its application to Cournot–Nash competition Next Article Deep learning-based recommendation method for top-K tasks in software crowdsourcing systems

Pricing strategy in an interval-valued production inventory model for high-tech products under demand disruption and price revision

1.
Department of Mathematics, Sonamukhi College, Bankura-722 207, India
2.
Department of Mathematics, Kazi Nazrul University, Asansol-713 340, India
3.
Department of Mathematics, Midnapore College (Autonomous) Midnapore-721 101, India

^*Corresponding author: Mijanur Rahaman Seikh
^*Corresponding author: Mijanur Rahaman Seikh

Received: June 2022

Revised: October 2022

Early access: November 2022

Published: September 2023

Abstract / Introduction Full Text(HTML) Figure(7) / Table(2) Related Papers Cited by

Abstract

Due to continuous development in technology, new and updated products are launching in the market more frequently in the area of some high-tech products such as smartphones, laptops, etc. It is noticed that after a certain period of releasing a new product by a particular company some other company develops a similar type of product at a lesser selling price. Customers generally become attracted to buy that updated product causing a sudden disruption in the demand for the first product. The demand for a normal product may also suddenly vanish as we have experienced during the COVID-19 lockdown period. The manufacturer is then compelled to reduce the selling price to sell the remaining products. This paper aims at developing a single period production inventory model addressing this particular market condition. This paper also considers carbon emissions from different inventory processes and examines the optimal inventory policies under the cap and trade regulatory policy. Again, in a real-life production system, the various inventory cost components and the carbon emission rates from different inventory processes are not fixed always. To incorporate this issue, the proposed model considers these quantities as interval numbers. The resulting optimization problem is thus also interval-valued and has been solved by using the quantum-behaved particle swarm optimization technique. A numerical illustration is provided to validate the proposed model. Finally, a sensitivity analysis with respect to key inventory parameters is performed to derive some key managerial implications. It is found that the frequency of launching new products is inversely proportional to the optimum profit of the manufacturer. Also, a higher carbon tax rate is found to be beneficial from an environmental point of view.

Keywords:

Single period production inventory model,
high-tech products,
carbon emission,
cap and trade mechanism,
interval number,
quantum-behaved particle swarm optimization technique.

Mathematics Subject Classification: Primary: 90B05, 90B30; Secondary: 49N30, 90C59.

Citation:

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Figure 1. Research scheme of our paper

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Figure 2. Behaviour of the inventory level with respect to time

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Figure 3. Concavity of the profit function w.r.t. $ t_1 $ and $ m $

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Figure 4. Impact on the optimal profit and optimal carbon emission due to changes in $ \alpha $

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Figure 5. Impact on the optimal profit and optimal cycle length due to changes in $ \beta $

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Figure 6. Impact on the optimal profit and optimal cycle length due to changes in $ t_3 $

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Figure 7. Impact on the optimal profit and optimal carbon emission due to changes in $ \bar{c_1} $

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Table 1. Summary of literature survey

References	Demand depends on	Demand disruption	Pricing strategy	Imprecise cost parameter	Carbon emission	Imprecise emission rate	Cap and trade policy
Rana et al. [37]	time	$ \checkmark $
Ali et al. [1]	price & service level	$ \checkmark $	$ \checkmark $
Wu et al. [61]	price	$ \checkmark $	$ \checkmark $
Cao [5]	price	$ \checkmark $	$ \checkmark $
Bhunia et. al [4]	price, time & advertisement		$ \checkmark $
San-Jos$ \acute{e} $ et al. [45]	price, time & advertisement		$ \checkmark $
Sepehri and Gholamian [46]	price		$ \checkmark $		$ \checkmark $		$ \checkmark $
Qu et al. [35]	price & warranty period		$ \checkmark $		$ \checkmark $		$ \checkmark $
Ruidas et al. [39]	price		$ \checkmark $	$ \checkmark $	$ \checkmark $	$ \checkmark $	$ \checkmark $
Gupta et al. [19]	price, advertisement & stock level			$ \checkmark $
Ruidas et al. [43]	price, time & advertisement	$ \checkmark $		$ \checkmark $
Proposed model	price, time & advertisement	$ \checkmark $	$ \checkmark $	$ \checkmark $	$ \checkmark $	$ \checkmark $	$ \checkmark $

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Table 2. Sensitivity analysis

Para meter	Changes	$ t_1^* $	$ m^* $	$ p^* $	Optimal profit	$ T^* $	Lot size	Carbon emission
$ \alpha $	355	0.17270	1.45493	104.03	[114.67, 287.68]	2.39599	120.89	[1477.52, 1643.34]
	360	0.17187	1.45506	104.04	[195.52, 383.80]	2.09882	120.31	[1651.05, 1831.13]
	365	0.16861	1.45521	104.05	[285.23, 500.86]	1.72357	118.03	[1946.66, 2152.35]
$ \beta $	2.9	0.17100	1.46419	104.69	[410.73, 643.00]	1.62241	119.70	[2109.67, 2331.19]
	3.0	0.17187	1.45506	104.04	[195.52, 383.80]	2.09882	120.31	[1651.05, 1831.13]
	3.1	0.17291	1.44652	103.42	[34.62, 199.66]	2.60076	121.04	[1381.65, 1540.06]
$ t_3 $	1.4	0.17171	1.46581	104.81	[178.32, 356.10]	2.27236	120.20	[1537.92, 1708.13]
	1.5	0.17187	1.45506	104.04	[195.52, 383.80]	2.09882	120.31	[1651.05, 1831.13]
	1.6	0.17219	1.44637	103.40	[213.47, 414.15]	1.93925	120.53	[1777.45, 1969.25]
$ X $	680	0.17707	1.45472	104.01	[196.64, 385.00]	2.09719	120.41	[1652.65, 1832.80]
	700	0.17187	1.45506	104.04	[195.52, 383.80]	2.09882	120.31	[1651.05, 1831.13]
	720	0.16697	1.45542	104.06	[194.48, 382.66]	2.10102	120.22	[1649.15, 1829.14]
$ C $	35	0.16796	1.45036	103.70	[190.90, 379.31]	2.02636	117.57	[1670.54, 1850.51]
	40	0.17187	1.45506	104.04	[195.52, 383.80]	2.09882	120.31	[1651.05, 1831.13]
	45	0.17633	1.46035	104.43	[200.25, 389.50]	2.17013	123.43	[1639.34, 1820.61]
$ A $	7	0.17060	1.45949	104.35	[182.14, 363.09]	2.19535	119.42	[1578.43, 1752.02]
	8	0.17187	1.45506	104.04	[195.52, 383.80]	2.09882	120.31	[1651.05, 1831.13]
	9	0.17309	1.45125	103.95	[207.52, 403.22]	2.01279	121.16	[1722.83, 1909.47]
$ \lambda $	0.45	0.16777	1.43493	102.60	[262.57, 461.62]	1.78169	117.44	[1880.62, 2080.04]
	0.50	0.17187	1.45506	104.04	[195.52, 383.80]	2.09882	120.31	[1651.05, 1831.13]
	0.55	0.17371	1.47242	105.28	[134.10, 318.82]	2.34277	121.60	[1512.42, 1681.33]
$ l $	0.93	0.16039	1.44121	103.05	[173.02, 379.07]	1.72905	112.27	[1869.26, 2065.62]
	0.95	0.17187	1.45506	104.04	[195.52, 383.80]	2.09882	120.31	[1651.05, 1831.13]
	0.97	0.18164	1.46798	104.96	[224.87, 403.38]	2.42734	127.15	[1516.83, 1688.15]
$ \bar{c_0} $	[1090,1110]	0.17109	1.45410	103.97	[199.84, 389.07]	2.07352	119.76	[1663.27, 1844.20]
	[1100,1120]	0.17187	1.45506	104.04	[195.52, 383.80]	2.09882	120.31	[1651.05, 1831.13]
	[1110,1130]	0.17270	1.45596	104.10	[191.22, 378.63]	2.12447	120.89	[1639.34, 1818.63]
$ \bar{c_1} $	[68.5, 69.5]	0.16815	1.46492	101.81	[305.21, 527.76]	1.65435	117.70	[2018.39, 2230.60]
	[70.5, 71.5]	0.17187	1.45506	104.04	[195.52, 383.80]	2.09882	120.31	[1651.05, 1831.13]
	[72.5, 73.5]	0.17219	1.44174	105.97	[97.90, 268.87]	2.43368	120.53	[1455.07, 1618.96]

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