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An integrated imperfect production system with advertisement dependent demand using branch and bound technique

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Abstract

This paper develops an integrated imperfect production-inventory system consisting of a retailer and a manufacturer who produces breakable items. As breakable items are very sensitive to transport, in this paper, to stimulate the retailer, the manufacturer offers (1) free transportation subject to the condition that the retailer must have to order a minimum replenishment quantity specified by the manufacturer and (2) a credit period depending on the replenishment quantity. Moreover, malfunctioning of the production system increases due to several kinds of problem and consequently it produces a mixture of perfect and imperfect quality items. So, to maintain the reliability of the production system, development cost has been incorporated. Also to aware the customer about the reliability of the production system, the manufacturer has paid attention to give a constant amount of advertisement regularly during his/her production period. Henceforth, the advertisement dependent demand has been considered here. Under such circumstances, an integrated profit function has been developed and solved by branch and bound technique to obtain the optimum values of the system. From numerical studies, it is revealed that in case of incorporation of the advertisement, the retailer’s average profit, the manufacturer’s average profit and the average integrated profit are higher than that in the case without advertisement.

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References

  • Agarwal V, Chao X, Seshadri S (2004) Dynamic balancing of inventory in supply chains. Eur J Oper Res 159(2):296–317

    MathSciNet  MATH  Google Scholar 

  • Annadurai K (2013) Integrated inventory model for deteriorating items with price-dependent demand under quantity-dependent trade credit. Int J Manuf Eng. https://doi.org/10.1155/2013/439190

    Article  MATH  Google Scholar 

  • Banerjee A (1986) A joint echonomic lot-size-model for purchaser and vendor. Decis Sci 17(3):292–311

    Google Scholar 

  • Banu A, Mondal SK (2016) An analysis of credit linked demand in an inventory model with varying ordering cost. Springer Plus 5(1):926

    Google Scholar 

  • Ben-Daya M, Hariga M (2000) Economic lot scheduling problem with imperfect production processes. J Oper Res Soc 51(7):875–881

    MATH  Google Scholar 

  • Cachon GP, Zipkin PH (1999) Competitive and cooperative inventory policies in a two-stage supply chain. Manag Sci 45(7):936–953

    MATH  Google Scholar 

  • Cho ID (1996) Analysis of optimal production and advertising policies. Int J Syst Sci 27(12):1297–1305

    MATH  Google Scholar 

  • Das BC, Das B, Mondal SK (2013) An integrated supply chain for a deteriorating item with procurement cost dependent credit period. Comput Ind Eng 64(3):788–796

    Google Scholar 

  • Das BC, Das B, Mondal SK (2014) Optimal transportation and business cycles in an integrated production-inventory model with a discrete credit period. Transp Res E 68:1–13

    Google Scholar 

  • Das BC, Das B, Mondal SK (2015) An integrated production inventory model under interactive fuzzy credit period for deteriorating item with several markets. Appl Soft Comput 28:453–465

    Google Scholar 

  • Das BC, Das B, Mondal SK (2017) An integrated production-inventory model with defective item dependent stochastic credit period. Comput Ind Eng 110:255–263

    Google Scholar 

  • Farahani P, Grunow M, Gunther HO (2012) Integrated production and distribution planning for perishable food products. Flex Serv Manuf J 24:28–51

    Google Scholar 

  • Goyal SK (1976) An integrated inventory model for a single supplier-single customer problem. Int J Prod Res 15(1):107–111

    Google Scholar 

  • Goyal SK (1985) Economic order quantity under conditions of permissible delay in payments. J Oper Res Soc 36(4):335–338

    MATH  Google Scholar 

  • Goyal SK (1988) A joint echonomic-lot-size model for purchaser and vendor: a comment. Decis Sci 19(1):236–241

    Google Scholar 

  • Guchhait P, Maiti MK, Maiti M (2010a) Multi-item inventory model of breakable items with stock-dependent demand under stock and time dependent breakability rate. Comput Ind Eng 59(4):911–920

    Google Scholar 

  • Guchhait P, Maiti MK, Maiti M (2010b) Production-inventory models for a damageable item with variable demands and inventory costs in an imperfect production process. Int J Prod Econ 144:180–188

    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):263–271

    Google Scholar 

  • Khara B, Dey JK, Mondal SK (2017) An inventory model under development cost dependent imperfect production and reliability dependent demand. J Manag Anal 4(3):258–275

    Google Scholar 

  • Khouja M, Mehrez A (1994) An economic production lot size model with imperfect quality and variable production rate. J Oper Res Soc 45(12):1405–1417

    MATH  Google Scholar 

  • Kim M, Sarkar B (2017) Multi-stage cleaner production process with quality improvement and lead time dependent ordering cost. J Cleaner Prod 144(15):572–590

    Google Scholar 

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

    Google Scholar 

  • Lee S, Kim D (2014) An optimal policy for a single vendor single-buyer integrated productiondistribution model with both deteriorating and defective items. Int J Prod Econ 147:161–170

    Google Scholar 

  • Liang Y, Zhou F (2011) A two-warehouse inventory model for deteriorating items under conditionally permissible delay in payment. Appl Math Model 35(5):2221–2231

    MathSciNet  MATH  Google Scholar 

  • Majumder P, Bera UK, Maiti M (2016) A multi-item EPQ model with imperfect production process for time varying demand with shortages. Hacet J Math Stat 45(3):929–955

    MathSciNet  MATH  Google Scholar 

  • Majumder A, Guchhait R, Sarkar B (2017) Manufacturing quality improvement and setup cost reduction in a vendor-buyer supply chain model. Eur J Ind Eng 11(5):588–612

    Google Scholar 

  • Mandal M, Maiti M (2000) Inventory of damageable items with variable replenishment and stock dependent demand. Asia Pac J Oper Res 17:41–54

    MathSciNet  MATH  Google Scholar 

  • Manna AK, Dey JK, Mondal SK (2014) Three-layer supply chain in an imperfect production inventory model with two storage facilities under fuzzy rough environment. J Uncertainty Anal Appl 2:17

    Google Scholar 

  • Manna AK, Dey JK, Mondal SK (2017) Imperfect production inventory model with production rate dependent defective rate and advertisement dependent demand. Comput Ind Eng 104:9–22

    Google Scholar 

  • Maragatham M, Gnanvel G (2017) A purchasing inventory model for breakable items with permissible delay in payments and price discount. Ann Pure Appl Math 15(2):305–314

    Google Scholar 

  • Mondal B, Bhunia AK, Maiti M (2003) An inventory system of ameliorating items for price dependent demand rate. Comput Ind Eng 45(3):443–456

    Google Scholar 

  • Moon I, Shin E, Sarkar B (2014) Min-max distribution free continuous-review model with a service level constraint and variable lead time. Appl Math Comput 229:310–315

    MathSciNet  MATH  Google Scholar 

  • Rathore H (2019) An inventory model with advertisement dependent demand and reliability consideration. Int J Appl Comput Math 5:33

    MathSciNet  MATH  Google Scholar 

  • Rosenblatt MJ, Lee HL (1986) Economic production cycles with imperfect production processes. IIE Trans 18(1):48–54

    Google Scholar 

  • Saha A, Roy A, Kar S, Maiti M (2010) Inventory models for breakable items with stock dependent demand and imprecise constraints. Math Comput Model 52:1771–1782

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  • Sana SS (2011) A production-inventory model of imperfect quality products in a three-layer supply chain. Decis Supp Syst 50(2):539–547

    Google Scholar 

  • Sarkar B (2012a) An EOQ model with delay-in-payments and time-varying deterioration rate. Math Comput Model 55:367–377

    MathSciNet  MATH  Google Scholar 

  • Sarkar B (2012b) An inventory model with reliability in an imperfect production process. Appl Math Comput 218(9):4881–4891

    MathSciNet  MATH  Google Scholar 

  • Sarkar B (2012c) An EOQ model with delay in payments and stock dependent demand in the presence of imperfect production. Appl Math Comput 218(17):8295–8308

    MathSciNet  MATH  Google Scholar 

  • Sarkar B (2013) A production-inventory model with probabilistic deterioration in two-echelon supply chain management. Appl Math Model 37(5):3138–3151

    MathSciNet  MATH  Google Scholar 

  • Sarkar B (2016) Supply chain coordination with variable backorder, inspections, and discount policy for fixed lifetime products. Math Prob Eng 201:6318737

    MathSciNet  MATH  Google Scholar 

  • Sarkar B (2019) Mathematical and analytical approach for the management of defective items in a multi-stage production system. Int J Prod Econ 218:896–919

    Google Scholar 

  • Sarkar B, Majumder A (2013) Integrated vendorbuyer supply chain model with vendors setup cost reduction. Appl Math Comput 224:362–371

    MathSciNet  MATH  Google Scholar 

  • Sarkar B, Moon I (2011) An EPQ model with inflation in an imperfect production system. Appl Math Comput 217:6159–6167

    MathSciNet  MATH  Google Scholar 

  • Sarkar B, Moon I (2014) Improved quality, set up cost reduction, and variable backorder costs in an imperfect production process. Int J Prod Econ 155:204–213

    Google Scholar 

  • Sarkar B, Saren S (2016) Product inspection policy for an imperfect production system with inspection errors and warranty cost. Eur J Oper Res 248(1):263–271

    MATH  Google Scholar 

  • Sarkar B, Saren S (2017) Ordering and transfer policy and variable deterioration for a warehouse model. Hacet J Math Stat 46(5):985–1014

    MathSciNet  MATH  Google Scholar 

  • Sarkar M, Sarkar B (2013a) An economic manufacturing quantity model with probabilistic deterioration in a production system. Econ Model 31:245–252

    Google Scholar 

  • Sarkar B, Sarkar S (2013b) Variable deterioration and demand-An inventory model. Econ Model 31:548–556

    Google Scholar 

  • Sarkar B, Sana SS, Chaudhuri KS (2011) An imperfect production process for time varying demand with inflation and time value of money—an EMQ model. Expert Sys with Appl 38(11):13543–13548

    Google Scholar 

  • Sarkar B, Cardenas-Barron LE, Sarkar M, Singgih ML (2014a) 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, Gupta H, Chaudhuri KS, Goyal SK (2014b) An integrated inventory model with variable lead time, defective units and delay in payments. Appl Math Comput 237:650–658

    MathSciNet  MATH  Google Scholar 

  • Sarkar B, Mandal B, Sarkar S (2015a) Quality improvement and backorder price discount under controllable lead time in an inventory model. J Manuf Syst 35:26–36

    Google Scholar 

  • Sarkar B, Chaudhuri KS, Moon I (2015b) Manufacturing setup cost reduction and quality improvement for the distribution free continuous-review inventory model with a service level constraint. J Manuf Syst 34:74–82

    Google Scholar 

  • Sarkar B, Sett BK, Sarkar S (2018a) Optimal production run time and inspection errors in an imperfect production system with warranty. J Ind Manag Opt 14(1):267–282

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • Teng JT, Chang CT (2005) Economic production quantity models for deteriorating items with price- and stock-dependent demand. Comput Oper Res 32(2):297–308

    MathSciNet  MATH  Google Scholar 

  • Tiwari S, Cardenas-Barron LE, Goh M, Shaikh AA (2018) Joint pricing and inventory model for deteriorating items with expiration dates and partial backlogging under two-level partial trade credits in supply chain. Int J Prod Econ 200:16–36

    Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, W.B., 721102, India

    Barun Khara & Shyamal Kumar Mondal

  2. Department of Mathematics, Mahishadal Raj College, Purba Medinipur, W.B., India

    Jayanta Kumar Dey

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  1. Barun Khara
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  2. Jayanta Kumar Dey
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  3. Shyamal Kumar Mondal
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Correspondence to Barun Khara.

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Khara, B., Dey, J.K. & Mondal, S.K. An integrated imperfect production system with advertisement dependent demand using branch and bound technique. Flex Serv Manuf J 33, 508–546 (2021). https://doi.org/10.1007/s10696-020-09377-5

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