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An entropic order quantity inventory model for quality assessment considering price sensitive demand

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Abstract

In today’s technology-driven world, despite of efficient planning of manufacturing system and development of refined production technologies and control systems; the items produced in a manufacturing system may have some fraction of defectives. Thus inspection of a lot of the items is essential to differentiate perfect and imperfect products. Every business sector has some hidden costs involved in additional managerial cost which are also imperative to calculate for smooth running of the business sector. This work considers an entropic order quantity model with selling price dependent demand and screening to separate imperfect quality products. We find an important observation about effect of entropy cost on the maximization of profit which states that the entropy cost has similar behavior as the selling price of the product. Our findings enlighten the insights of the entropic order inventory model and enrich the advancement of the literature of inventory model. Finally, a hypothetical numerical example is set to validate the model and sensitivity analysis has also been performed to study the impact of various parameters on the optimal solution.

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References

  1. Abad, P.L.: Optimal pricing and lot-sizing under conditions of perishability and partial backordering. Manage. Sci. 42(8), 1093–1104 (1996)

    Google Scholar 

  2. Bernstein, F., Federgruen, A.: Dynamic inventory and pricing models for competing retailers. Naval Res. Logist. 51(2), 258–274 (2004)

    Google Scholar 

  3. Burwell, T.H., Dave, D.S., Fitzpatrick, K.E., Roy, M.R.: An inventory model with planned shortages and price dependent demand. Decis. Sci. 22(5), 1187–1191 (1991)

    Google Scholar 

  4. Cárdenas-Barrón, L.E.: Observation on:“Economic production quantity model for items with imperfect quality” [Int. J. Production Economics 64 (2000) 59–64]. Int. J. Prod. Econ. 67(2), 201 (2000)

    Google Scholar 

  5. Chan, W.M., Ibrahim, R.N., Lochert, P.B.: A new EPQ model: integrating lower pricing, rework and reject situations. Prod. Plan. Control 14(7), 588–595 (2003)

    Google Scholar 

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

    Google Scholar 

  7. Chang, H.J., Teng, J.T., Ouyang, L.Y., Dye, C.Y.: Retailer’s optimal pricing and lot-sizing policies for deteriorating items with partial backlogging. Eur. J. Oper. Res. 168(1), 51–64 (2006)

    Google Scholar 

  8. De, M., Das, B., Maiti, M.: EPL models for complementary and substitute items under imperfect production process with promotional cost and selling price dependent demands. Opsearch 53(2), 259–277 (2015)

    Google Scholar 

  9. Dye, C.Y., Hsieh, T.P., Ouyang, L.Y.: Determining optimal selling price and lot size with a varying rate of deterioration and exponential partial backlogging. Eur. J. Oper. Res. 181(2), 668–678 (2007)

    Google Scholar 

  10. Eroglu, A., Ozdemir, G.: An economic order quantity model with defective items and shortages. Int. J. Prod. Econ. 106(2), 544–549 (2007)

    Google Scholar 

  11. Gerchak, Y.: Order point/order quantity models with random yield. Int. J. Prod. Econ. 26(1–3), 297–298 (1992)

    Google Scholar 

  12. Hesham, K.A., Ahmed, M.G.: Inventory and pricing model with price dependent demand, time- varying holding cost, and quantity discounts. Comput. Ind. Eng. 94(C), 170–177 (2016)

    Google Scholar 

  13. Jaber, M.Y., Goyal, S.K., Imran, M.: Economic production quantity model for items with imperfect quality subject to learning effects. Int. J. Prod. Econ. 115(1), 143–150 (2008)

    Google Scholar 

  14. Jaber, M.Y., Bonney, M., Rosen, M.A., Moualek, I.: Entropic order quantity (EnOQ) model for deteriorating items. Appl. Math. Model. 33(1), 564–578 (2009)

    Google Scholar 

  15. Jaggi, C.K., Khanna, A., Mittal, M.: Credit financing for deteriorating imperfect-quality items under inflationary conditions. Int. J. Serv. Oper. Inf. 6(4), 292–309 (2011)

    Google Scholar 

  16. Jaggi, C.K., Goel, S.K., Mittal, M.: Credit financing in economic ordering policies for defective items with allowable shortages. Appl. Math. Comput. 219(10), 5268–5282 (2013)

    Google Scholar 

  17. Jaggi, C.K., Mittal, M., Khanna, A.: Effects of inspection on retailer’s ordering policy for deteriorating items with time-dependent demand under inflationary conditions. Int. J. Syst. Sci. 44(9), 1774–1782 (2013)

    Google Scholar 

  18. Jaggi, C.K., Tiwari, S., Shafi, A.: Effect of deterioration on two-warehouse inventory model with imperfect quality. Comput. Ind. Eng. 88, 378–385 (2015)

    Google Scholar 

  19. Kar, S., Roy, T., Maiti, M.: Multi-item inventory model with probabilistic price dependent demand and imprecise goal and constraints. Yugosl. J. Oper. Res. 11(1), 93–103 (2001)

    Google Scholar 

  20. Kim, J., Hwang, H., Shinn, S.: An optimal credit policy to increase supplier’s profits with price-dependent demand functions. Prod. Plan. Control 6(1), 45–50 (1995)

    Google Scholar 

  21. Kohli, A.K.: Market Orientation in a Digital World. Glob. Bus. Rev. 18(3_suppl), S203–S205 (2017)

    Google Scholar 

  22. Lin, T.Y.: Optimal policy for a simple supply chain system with defective items and returned cost under screening errors. J. Oper. Res. Soc. Jpn. 52(3), 307–320 (2009)

    Google Scholar 

  23. Maddah, B., Jaber, M.Y.: Economic order quantity for items with imperfect quality: revisited. Int. J. Prod. Econ. 112(2), 808–815 (2008)

    Google Scholar 

  24. Modak, N.M., Panda, S., Sana, S.S.: Three-echelon supply chain coordinationconsidering duopolistic retailers with perfect quality products. Int. J. Prod. Econ. 182, 564–578 (2016)

    Google Scholar 

  25. Modak, N.M., Panda, S., Sana, S.S.: Two-echelon supply chain coordination among manufacturer and duopolies retailers with recycling facility. Int. J. Adv. Manuf. Technol. 87(5–8), 1531–1546 (2016)

    Google Scholar 

  26. Nath, V., Kumar, R., Agrawal, R., Gautam, A., Sharma, V.: Consumer adoption of green products: modeling the enablers. Glob. Bus. Rev. 14(3), 453–470 (2013)

    Google Scholar 

  27. Panda, S., Modak, N.M.: Exploring the effects of social responsibility on coordination and profit division in a supply chain. J. Clean. Prod. 139, 25–40 (2016)

    Google Scholar 

  28. Panda, S., Modak, N.M., Sana, S.S., Basu, M.: Pricing and replenishment policies in dual-channel supply chain under continuous unit cost decrease. Appl. Math. Comput. 256, 913–929 (2015)

    Google Scholar 

  29. Panda, S., Modak, N.M., Cárdenas-Barrón, L.E.: Coordinating a socially responsible closed-loop supply chain with product recycling. Int. J. Prod. Econ. 188, 11–21 (2017)

    Google Scholar 

  30. Papachristos, S., Konstantaras, I.: Economic ordering quantity models for items with imperfect quality. Int. J. Prod. Econ. 100(1), 148–154 (2006)

    Google Scholar 

  31. Pattnaik, M.: An entropic order quantity model (EnOQ) under instant deterioration of perishable items with price discounts. Int. Math. Forum 5(52), 2581–2590 (2010)

    Google Scholar 

  32. Pattnaik, M.: An entropic order quantity (EnOQ) model with post deterioration cash discounts. Int. J. Contemp. Math. Sci. 6(19), 931–939 (2011)

    Google Scholar 

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

    Google Scholar 

  34. Priyan, S., Manivannan, P.: Optimal inventory modeling of supply chain system involving quality inspection errors and fuzzy defective rate. Opsearch 54(1), 21–43 (2017)

    Google Scholar 

  35. Priyan, S., Palanivel, M., Uthayakumar, R.: Integrated procurement-production inventory model for defective items with variable setup and ordering cost. Opsearch 52(4), 692–713 (2015)

    Google Scholar 

  36. Ross, S.M.: Stochastic Processes, 2nd edn. Wiley, New York (1996)

    Google Scholar 

  37. Rosenblatt, M.J., Lee, H.L.: Economic production cycles with imperfect production processes. IIE Trans. 18(1), 48–55 (1986)

    Google Scholar 

  38. Roy, M.D., Sana, S.S., Chaudhuri, K.: An economic order quantity model of imperfect quality items with partial backlogging. Int. J. Syst. Sci. 42(8), 1409–1419 (2011)

    Google Scholar 

  39. Saha, S., Sarmah, S.P., Modak, N.M.: Single versus dual-channel: a strategic analysis in perspective of retailer’s profitability under three-level dual-channel supply chain. Asia Pac. Manag. Rev. 23(2018), 148–160 (2017)

    Google Scholar 

  40. Sahoo, P., Kumar, R.: Efficiency and futures trading-price nexus in Indian commodity futures markets. Global Bus. Rev. 10(2), 187–201 (2009)

    Google Scholar 

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

    Google Scholar 

  42. Sana, S.S.: Optimal selling price and lotsize with time varying deterioration and partial backlogging. Appl. Math. Comput. 217(1), 185–194 (2010)

    Google Scholar 

  43. Schwaller, R.L.: EOQ under inspection costs. Prod. Inventory Manag. J. 29(3), 22–24 (1988)

    Google Scholar 

  44. Shah, N.H., Shah, D.B., Patel, D.G.: Optimal credit period and ordering quantity for credit dependent trended demand and deteriorating items with maximum lifetime. Control Cybern. 44(2), 311–320 (2015)

    Google Scholar 

  45. Singh, N., Vaish, B., Singh, S.R.: A three-level integrated inventory model with time dependent demand and production rate under a trade credit policy for both distributor and retailer. Control Cybern. 43(3), 439–469 (2014)

    Google Scholar 

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

    Google Scholar 

  47. Tripathy, P.K., Pattnaik, M.: An entropic order quantity model with fuzzy holding cost and fuzzy disposal cost for perishable items under two component demand and discounted selling price. Pak. J. Stat. Oper. Res. 4(2), 93–110 (2008)

    Google Scholar 

  48. Vörös, J.: Economic order and production quantity models without constraint on the percentage of defective items. CEJOR 21(4), 867–885 (2013)

    Google Scholar 

  49. Wee, H.M., Yu, J., Chen, M.C.: Optimal inventory model for items with imperfect quality and shortage backordering. Omega 35(1), 7–11 (2007)

    Google Scholar 

  50. Yang, P.C.: Pricing strategy for deteriorating items using quantity discount when demand is price sensitive. Eur. J. Oper. Res. 157(2), 389–397 (2004)

    Google Scholar 

  51. Yoo, S.H., Kim, D., Park, M.S.: Economic production quantity model with imperfect-quality items, two-way imperfect inspection and sales return. Int. J. Prod. Econ. 121(1), 255–265 (2009)

    Google Scholar 

  52. Zhang, X.I.N., Gerchak, Y.I.G.A.L.: Joint lot sizing and inspection policy in an EOQ model with random yield. IIE Trans. 22(1), 41–47 (1990)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Burdwan Raj College, University of Burdwan, Bardhaman, West Bengal, 713104, India

    Sudipta Sinha

  2. Palpara Vidyamandir, Palpara, Nadia, Chakdaha, West Bengal, 741222, India

    Nikunja Mohan Modak

  3. Kishore Bharati Bhagini Nivedita College, Behala, Kolkata, 700060, India

    Shib Sankar Sana

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  1. Sudipta Sinha
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  3. Shib Sankar Sana
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Correspondence to Shib Sankar Sana.

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Sinha, S., Modak, N.M. & Sana, S.S. An entropic order quantity inventory model for quality assessment considering price sensitive demand. OPSEARCH 57, 88–103 (2020). https://doi.org/10.1007/s12597-019-00406-y

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