Skip to main content
SpringerLink
Log in

An EPQ model with stock and selling price dependent demand and variable production rate in interval environment

  • Original Article
  • Published:
International Journal of System Assurance Engineering and Management Aims and scope Submit manuscript

Abstract

The motto of this paper is to develop a production inventory model in real life situation. In reality, demand of a certain product becomes highly effected by on-hand stock level in stores and the selling price of the product. In the proposed model, demand of the product is dependent on these two vital deceive factors. In real life production systems, always there are some defective products which requires reworking in order to make them useful. The possibility of producing some defective items in regular production process and their reworking has been taken into account in the model. In case of inventories of highly demandable products, it is observed that production rate is proportional to demand. The situation also arises in case of launching a new product or in a multi-stage production system. In this model, production rate is a variable and it varies with the demand rate. Shortages are allowed and it is backlogged fully. Based on these assumptions, several researchers worked on but they considered that the associated inventory cost parameters are fixed real numbers. However, these are not fixed in reality and may vary time to time depending upon some scenario. Main objective of the paper is to develop a production inventory model under those assumptions considering various cost parameters as interval numbers. As a result the corresponding optimization problem is also interval valued. Quantum behaved particle swarm optimization technique has been applied to find the maximum profit in a single cycle. Numerical example and sensitivity analysis are given to illustrate the proposed inventory model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Balkhi ZT, Benkherouf L (1998) A production lot size inventory model deteriorating items and arbitrary production and demand rates. Eur J Oper Res 92:302–309

    MATH  Google Scholar 

  • Bhunia AK, Maiti M (1998) Deterministic inventory model for deteriorating items with finite rate of replenishment dependent on inventory level. Comput Oper Res 25(11):997–1006

    MATH  Google Scholar 

  • Bhunia AK, Shaikh AA (2014) A deterministic inventory model for deteriorating items with selling price dependent demand and three-parameter Weibull distributed deterioration. Int J Ind Eng Comput 5:497–510

    Google Scholar 

  • Bhunia AK, Mahato SK, Shaikh AA, Jaggi CK (2015) A deteriorating inventory model with displayed stocklevel-dependent demand and partially backlogged shortages with all unit discount facilities via particle swarm optimisation. Int J Syst Sci Oper Logist 1(3):164–180

    Google Scholar 

  • Cárdenas-Bárron LE (2009) Economic production quantity with rework process at a single-stage manufacturing system with planned backorders. Comput Ind Eng 57(3):1105–1113

    Google Scholar 

  • Chakrabortty S, Pal M, Nayak PK (2010) Solution of interval-valued manufacturing inventory models with shortages. Int J Ind Manuf Eng 4(8):613–618

    Google Scholar 

  • Chang HC (2004) An application of fuzzy sets theory to the EOQ model with imperfect quality items. Comput Oper Res 31(12):2079–2092

    MathSciNet  MATH  Google Scholar 

  • Chang CT, Chen YJ, Tsai TR, Wu SJ (2010) Inventory models with stock-and price dependent demand for deteriorating items based on limited shelf space. Yugosl J Oper Res 20(1):55–69

    MathSciNet  MATH  Google Scholar 

  • Clerc M, Kennedy J (2002) The particle swarm: explosion, stability, and convergence in a multi-dimensional complex space. IEEE Trans Evolut Comput 6(1):58–73

    Google Scholar 

  • Datta TK, Pal AK (1988) Order-level inventory system with power demand pattern for items with variable rate of deterioration. Indian J Pure Appl Math 19(1):1043–1053

    MathSciNet  MATH  Google Scholar 

  • Datta TK, Pal AK (2001) An inventory system with stock-dependent, price-sensitive demand rate. Prod Plan Control 12(1):13–20

    Google Scholar 

  • De SK, Mahata GC (2017) Decision of a fuzzy inventory with fuzzy backorder model under cloudy fuzzy demand rate. Int J Appl Comput Math 3(3):2593–2609

    MathSciNet  MATH  Google Scholar 

  • Giri BC, Chaudhuri KS (1998) Deterministic models of perishable inventory with stock-dependent demand rate and nonlinear holding cost. Eur J Oper Res 105:467–474

    MATH  Google Scholar 

  • Goyal SK, Cardenas-Barron LE (2002) Note on: Economic production quantity model for items with imperfect quality—a practical approach. Int J Prod Econ 77(1):85–87

    Google Scholar 

  • Gupta RK, Bhunia AK, Goyal SK (2007) An application of genetic algorithm in a marketing oriented inventory model with interval valued inventory costs and three-component demand rate dependent on displayed stock-level. Appl Math Comput 192(2):466–478

    MathSciNet  MATH  Google Scholar 

  • Hu BQ, Wang S (2006) A novel approach in uncertain programming part I: new arithmetic and order relation for interval numbers. J Ind Manag Optim 2(4):351–371

    MathSciNet  MATH  Google Scholar 

  • Ishibuchi H, Tanaka H (1990) Multiobjective programming in optimization of the interval objective function. Eur J Oper Res 48:219–225

    MATH  Google Scholar 

  • Kang CW, Ullah M, Sarkar B, Hussain I, Akhtar R (2017) Impact of random defective rate on lot size focusing work-in-process inventory in manufacturing system. Int J Prod Res 55(6):1748–1766

    Google Scholar 

  • Kim M, Sarkar B (2017) Multi-stage cleaner production process with quality improvement and lead time dependent ordering cost. J Clean Prod 144:572–590

    Google Scholar 

  • Kim M, Kim J, Sarkar B, Sarkar M, Iqbal MW (2018) An improved way to calculate imperfect items during long-run production in an integrated model with backorders. J Manuf Syst 47:153–167

    Google Scholar 

  • Kotler P (1971) Marketing decision making: a model building approach. Holt, Rinehart and Winston, New York

    Google Scholar 

  • Krishnamoorthi C, Panayappan S (2012) An EPQ model with imperfect production systems with rework of regular production and sales return. Am J Oper Res 2:225–234

    Google Scholar 

  • Levin RI, McLaughin CP, Lemone RP, Kottas JF (1972) Production/operations management: contemporary policy for managing operating systems. McGraw-Hill, New York

    Google Scholar 

  • Mahapatra NK, Bera UK, Maiti M (2012) A production inventory model with shortages, fuzzy preparation time and variable production and demand. Am J Oper Res 2:183–192

    Google Scholar 

  • Maiti A, Maiti M, Maiti M (2009) Inventory model with stochastic lead-time and price dependent demand in corporating advance payment. Appl Math Model 33(5):2433–2443

    MathSciNet  MATH  Google Scholar 

  • Mandal M, Maiti M (1999) Inventory of damagable items with variable replenishment rate, stock-dependent demand and some units in hand. Appl Math Model 23:799–807

    MATH  Google Scholar 

  • Mandal BN, Phaujdar S (1989) An inventory model for deteriorating items and stock-dependent consumption rate. J Oper Res Soc 40(5):483–488

    MATH  Google Scholar 

  • Moore RE (1979) Method and application of interval analysis. SIAM, Philadelphia

    Google Scholar 

  • Palanivel M, Uthayakumar R (2014) A production-inventory model with variable production cost and probabilistic deterioration. Asia Pac J Math 1(2):197–212

    MATH  Google Scholar 

  • Porteus EL (1986) Optimal lot sizing, process quality improvement and setup cost reduction. Oper Res 34(1):137–144

    MathSciNet  MATH  Google Scholar 

  • Ritha W, Jeyakumari SR (2013) Fuzzy inventory model for imperfect quality items with shortages. Ann Pure Appl Math 4(2):127–137

    Google Scholar 

  • Rosenblatt MJ, Lee HL (1986) Economic production cycles with imperfect production process. IIE Trans 18(1):48–55

    Google Scholar 

  • Roy MD, Sana SS, Chaudhuri KS (2014) An economic production lot size model for defective items with stochastic demand backlogging and rework. IMA J Manag Math 25(2):159–183

    MathSciNet  MATH  Google Scholar 

  • Ruidas S, Seikh MR, Nayak PK, Pal M (2017) An interval valued EPQ model in imperfect production system with rework of regular production, shortages and sales return via particle swarm optimization. Int J Pure Appl Math 113(6):375–384

    Google Scholar 

  • Ruidas S, Seikh MR, Nayak PK, Pal M (2018) Interval valued EOQ model with two types of defective items. J Stat Manag Syst 21(6):1059–1082

    Google Scholar 

  • Ruidas S, Seikh MR, Nayak PK, Sarkar B (2019) A single period production inventory model in interval environment with price revision. Int J Appl Comput Math. https://doi.org/10.1007/s40819-018-0591-x

    Article  MathSciNet  MATH  Google Scholar 

  • Sahoo L, Bhunia AK, Kapur PK (2012) Genetic algorithm based multi-objective reliability optimization in interval environment. Comput Ind Eng 62:152–160

    Google Scholar 

  • Salameh M, Jaber M (2000) Economic production quantity model for items with imperfect quality. Int J Prod Econ 64(1–3):59–64

    Google Scholar 

  • Sarkar B (2012a) An EOQ model with delay in payments and stock dependent demand in the presence of imperfect production. Appl Math Comput 218:8295–8308

    MathSciNet  MATH  Google Scholar 

  • Sarkar B (2012b) An inventory model with reliability in an imperfect production process. Appl Math Comput 218:4881–4891

    MathSciNet  MATH  Google Scholar 

  • Sarkar B (2013) A production-inventory model with probabilistic deterioration in two-echelon supply chain management. Appl Math Model 37:3138–3151

    MathSciNet  MATH  Google Scholar 

  • Sarkar B (2019) Mathematical and analytical approach for the management of defective items in a multi-stage production system. J Clean Prod. https://doi.org/10.1016/j.jclepro.2019.01.078

    Article  Google Scholar 

  • Sarkar B, Moon I (2013) Improved quality, setup cost reduction, and variable backorder costs in an imperfect production process. Int J Prod Econ 155:204–213

    Google Scholar 

  • Sarkar B, Sarkar S (2013) An improved inventory model with partial backlogging, time varying deterioration and stock-dependent demand. Econ Model 30:924–932

    Google Scholar 

  • Sarkar B, Sana SS, Chaudhuri KS (2011) An economic production quantity model with stochastic demand in an imperfect production system. Int J Serv Oper Manag 9(3):259–283

    Google Scholar 

  • Sarkar B, Cárdenas-Bárron LE, Sarkar M, Singgih ML (2014) An economic production quantity model with random defective rate, rework process and backorders for a single stage production system. J Manuf Syst 33(3):423–435

    Google Scholar 

  • Sarkar B, Majumder A, Sarkar M, Kim N, Ullah M (2018) Effect of variable production rate on quality of products in a single-vendor multi-buyer supply chain management. Int J Adv Manuf Technol 99(1–4):567–581

    Google Scholar 

  • Sengupta A, Pal TK (2000) On comparing interval numbers. Eur J Oper Res 127:28–43

    MathSciNet  MATH  Google Scholar 

  • Sett BK, Sarkar S, Sarkar B (2017) Optimal buffer inventory and inspection errors in an imperfect production system with regular preventive maintenance. Int J Adv Manuf Technol 90(1–4):545–560

    Google Scholar 

  • Shah NH, Patel DG, Shah DB (2016) EPQ model for returned/reworked inventories during imperfect production process under price-sensitive stock-dependent demand. Int J Oper Res. https://doi.org/10.1007/s12351-016-0267-4

    Article  Google Scholar 

  • Sun J, Feng B, Xu WB (2004) Particle swam optimization with particles having quantum behavior. In Proceedings of the 2004 IEEE congress on evolutionary computation, Portland, OR, USA, pp 326–331

    Google Scholar 

  • Taleizadeh AA, Cardenas-Barron LE, Biabani J, Nikousokhan R (2012) Multiproducts single machine EPQ model with immediate rework process. Int J Ind Eng Comput 3(2):93–102

    Google Scholar 

  • Tayyab M, Sarkar B (2016) Optimal batch quantity in a cleaner multi-stage lean production system with random defective rate. J Clean Prod 139:922–934

    Google Scholar 

  • Teng J, Chang C (2005) Economic production quantity models for deteriorating items with price and stock-dependent demand. Comput Oper Res 32:297–308

    MathSciNet  MATH  Google Scholar 

  • Urban TL (1992) Deterministic inventory models incorporating marketing decisions. Comput Ind Eng 22(1):85–93

    Google Scholar 

  • Urban TL (2005) Inventory models with inventory-level-dependent demand: a comprehensive review and unifying theory. Eur J Oper Res 162:792–804

    MATH  Google Scholar 

  • Wang X, Tang W (2009) Fuzzy EPQ inventory models with backorder. J Syst Sci Complex 22:313–323

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Kazi Nazrul University, Asansol, 713 340, India

    Subhendu Ruidas & Mijanur Rahaman Seikh

  2. Department of Mathematics, Midnapore College (Autonomous), Midnapore, 721 101, India

    Prasun Kumar Nayak

Authors
  1. Subhendu Ruidas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mijanur Rahaman Seikh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Prasun Kumar Nayak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mijanur Rahaman Seikh.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ruidas, S., Seikh, M.R. & Nayak, P.K. An EPQ model with stock and selling price dependent demand and variable production rate in interval environment. Int J Syst Assur Eng Manag 11, 385–399 (2020). https://doi.org/10.1007/s13198-019-00867-w

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13198-019-00867-w

Keywords

Search

Navigation