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A production-inventory model with promotional effort, variable production cost and probabilistic deterioration

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Abstract

This article presents an economic production quantity (EPQ) model for deteriorating items involving probabilistic deterioration where the demand is dependent on sales team’s initiatives. Here, we assumed that the production rate is variable and the unit production cost is the function of the production rate. The unit selling price is calculated by a mark-up over the unit production cost. This model aids in minimizing the total inventory cost of the manufacturer by finding the optimal cycle length and the quantity. On this backdrop, a few theorems have been developed and, the necessary and sufficient conditions of the existence and uniqueness of the optimal solutions are suggested. Moreover, numerical examples and sensitivity analysis were also carried out. The results reveal that the total cost will be minimized when the deterioration follows uniform distribution and when the initiatives of the sales team equal to one.

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References

  • Bhandari RM, Sharma PK (1999) The economic production lot size model with variable cost function. Opsearch 36:137–150

    Google Scholar 

  • Cárdenas-Barrón LE, Sana SS (2014) A production-inventory model for a two-echelon supply chain when demand is dependent on sales teams’ initiatives. Int J Prod Econ 155:249–258

    Article  Google Scholar 

  • Covert RP, Philip GC (1973) An EOQ model for items with Weibull distribution deterioration. AIIE Trans 5:323–326

    Article  Google Scholar 

  • Ghare PM, Schrader GF (1963) A model for exponentially decaying inventory. J Ind Eng Chem 14:238–243

    Google Scholar 

  • Ghosh SK, Khanra S, Chaudhuri KS (2011) Optimal price and lot size determination for a perishable product under conditions of finite production, partial backordering and lost sale. Appl Math Comput 217:6047–6053

    MathSciNet  MATH  Google Scholar 

  • Guchhait P, Maiti MK, Maiti M (2013) 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

    Article  Google Scholar 

  • Khouja M (1995) The economic production lot size model under volume flexibility. Comput Oper Res 22:515–525

    Article  MATH  Google Scholar 

  • Krishnamoorthi C (2012) An economic production lot size model for product life cycle (maturity stage) with defective items with shortages. Opsearch 49:253–270

    Article  MathSciNet  MATH  Google Scholar 

  • Krishnan H, Kapuscinski RK, Butz DA (2004) Coordinating contracts for decentralized supply chain with retailer promotional effect. Manage Sci 50:48–62

    Article  Google Scholar 

  • Liao JJ (2007) On an EPQ model for deteriorating items under permissible delay in payments. Appl Math Model 31:393–403

    Article  MATH  Google Scholar 

  • Mahata GC (2011) Optimal strategy for an EOQ model with non instantaneous receipt and exponentially deteriorating items under permissible delay in payments. Int J Manag Sci Eng Manag 6:450–458

    Google Scholar 

  • Maihami R, Karimi B (2014) Optimizing the pricing and replenishment policy for non-instantaneous deteriorating items with stochastic demand and promotional efforts. Comput Oper Res 51:302–312

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Misra RB (1975) Optimum production lot size model for a system with deteriorating inventory. Int J Prod Res 13:495–505

    Article  Google Scholar 

  • Mondal B, Bhunia AK, Maiti M (2009) Inventory models for defective items incorporating marketing decisions with variable production cost. Appl Math Model 33:2845–2852

    Article  MathSciNet  MATH  Google Scholar 

  • Palanivel, M, Uthayakumar R (2013) An EPQ model for deteriorating items with variable production cost, time dependent holding cost and partial backlogging under inflation. Opsearch. doi.10.1007/s12597-013-0168-8.

  • Palanivel M, Uthayakumar R (2014a). An EPQ model with variable production, probabilistic deterioration and partial backlogging under inflation. Journal of Management Analytics. 10.1080/23270012.2014.971889/

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

    MATH  Google Scholar 

  • Sana SS (2010) Optimal selling price and lot size with time varying deterioration and partial backlogging. Appl Math Comput 217:185–194

    MathSciNet  MATH  Google Scholar 

  • Sana SS (2011a) An EOQ model of homogeneous products while demand is salesmen’s initiatives and stock sensitive. Comput Math Appl 62:577–587

    Article  MathSciNet  MATH  Google Scholar 

  • Sana SS (2011b) An EOQ model for salesmen’s initiatives, stock and price sensitive demand of similar products – a dynamical system. Appl Math Comput 218:3277–3288

    MathSciNet  MATH  Google Scholar 

  • Sana SS (2013) Sales team’s initiatives and stock sensitive demand—A production control policy. Econ Model 31:783–788

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Taylor TA (2002) Supply chain coordination under channel rebates with sales effort effects. Manage Sci 48:992–1007

    Article  MATH  Google Scholar 

  • Tsao Y (2008) Chung, Sheen, GJ. Dynamic pricing, promotion and replenishment policies for a deteriorating item under permissible delay in payments. Comput Oper Res 35:62–80

    Article  Google Scholar 

Download references

Acknowledgments

Authors wish to express their gratitude to the editors and reviewers for their constructive suggestions and corrections to enhance the clarity of the present paper. The research work is supported by DST INSPIRE, Ministry of Science and Technology, Government of India under the Grant No. DST/INSPIRE Fellowship/2011/413B dated 15.01.2014, and UGC-SAP, Department of Mathematics, Gandhigram Rural Institute, Deemed University, Gandhigram 624302, Tamilnadu, India.

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Palanivel, M., Uthayakumar, R. A production-inventory model with promotional effort, variable production cost and probabilistic deterioration. Int J Syst Assur Eng Manag 8 (Suppl 1), 290–300 (2017). https://doi.org/10.1007/s13198-015-0345-7

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  • DOI: https://doi.org/10.1007/s13198-015-0345-7

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