An inventory lot Sizing model of deteriorating items with time and price dependent demand, by considering the time value of money

Subject Areas : Design of Experiment

Rashin Babaei ¹ , Davood mohammaditabar ²

1 - Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran.
2 - Department Of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran.

Received: 2023-10-29 Accepted : 2024-06-29 Published : 2024-06-30

Keywords: lot sizing, deterioration, time value of money, price dependent demand, time dependent demand, partial backorder.,

Abstract :

In this paper, an inventory lot sizing model is proposed for a single deteriorating product with time and price dependent demand, by considering the time value of money.it is assumed the rate of deterioration is constant, the interest is compounded continuously, and the shortage happens in the form of partial backorder. The product is purchased from several suppliers at different prices and sold at a unique price. The closed form solution is presented for a special case with no shortage. A numerical example is solved and analyzed in the GAMS software. It is shown that with an increase in the rate of deterioration, the model decreases the selling price in order to stimulate the demand and deplete the positive inventory faster to avoid extensive deteriorations. In addition, the fraction of time with positive inventory level is reduced. The sensitivity analysis of the interest rate showed that as the interest rate increases, the model increases the economic order size while reduces the selling price in order to get higher positive net cash flows as soon as possible. With the increase of the shortage costs, the model tried to expose less shortage by increasing the fraction of time with positive inventory level. This resulted in more deterioration in the inventory and required larger order size.

References:

Aggarwal S.P., & Jaggi C.K. (1989). "Ordering policy for decaying inventory", International Journal of Systems Science, Vol. 20, PP. 151-5.
Begum R., Sahoo R.R., & Sahu S.K. (2012)." A replenishment policy for items with price-dependent demand, time-proportional deterioration and no shortages", International Journal of Systems Science, 43:5, 903-910, DOI: 10.1080/00207721.543481.
Chaudhary R. R, & Sharma.V. (2015). "A model for Weibull deteriorate items with price dependent demand rate and inflation", Indian Journal of Science and Technology, Vol 8(10), 975–981.
Cohen M.A. (1977). "Joint pricing and ordering policy for exponentially decaying inventory with known demand", Naval Research Logistics Quarterly, Vol. 24, PP. 257-68.
Dye C.Y. (2007). "Joint pricing and ordering policy for a deteriorating inventory with partial backlogging", The International Journal of Management Science, Vol. 35, PP. 184-189.
Eilon S., & Mallaya R.V. (1966). "Issuing and pricing policy of semi-perishables", Proceedings of the 4th International Conference on Operational Research, New York: Wiley- Inter science.
Ghare P.M., & Schrader G.F. (1963). "A model for exponentially decaying inventory", Journal of Industrial Engineering, Vol. 14, No. 5, PP. 238-43.
Ghiami, Y. (2023). An analysis on production and inventory models with discounted cash-flows. Omega, 117, 102847.
Ghiami Y., Williams T., & Wu Y. (2013)." A two-echelon inventory model for a deteriorating item with stock-dependent demand, partial backlogging and capacity constraints", European Journal of Operational Research, 231, 587–597.

Ghosh S.K., & Chaudhuri K.S. (2006). "An EOQ model with a quadratic demand, time-proportional deterioration and shortages in all cycles", International Journal of Systems Science, Vol. 37, No. 10, PP. 663-672.
Hadley, G. A Comparison of Order Quantities Computed Using the Average Annual Cost and the Discounted Cost. // Management Science, 10, (1964), pp. 472-476.
Kang S., & Kim I. (1983). "A study on the price and production level of the deteriorating inventory system", International Journal of production Research, Vol. 21, PP. 899-908.
Maihami R., & Nakhai Kamalabadi I. (2012)."Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand", Int. J. Production Economics, 136, 116–122.
Mukhopadhyay S., Mukherjee R.N., & Chaudhuri K.S. (2005). "An EOQ model with two-parameter Weibull distribution deterioration and price-dependent demand", International Journal of Mathematical Education in Science and Technology, Vol. 36, No. 1, PP. 25-33.
Ouyang L. Y., Hsieh T.P., Dye C. Y., & Chang. H.C. (2003)."An inventory model for deteriorating items with stock-dependent demand under the conditions of inflation and time value of money", The Engineering Economist: A Journal Devoted to the Problems of Capital Investment, 48:1, 52-68, DOI: 10.1080/00137910308965051.
Pal S., Mahapatra G.S., & Samanta G.P. (2015)." A production inventory model for deteriorating item with ramp type demand allowing inflation and shortages under fuzziness", Economic Modelling, 46, 334–345.
Panda S., Saha S., & Basu M. (2013)." Optimal pricing and lot-sizing for perishable inventory with price and time dependent ramp-type demand", International Journal of Systems Science, 44:1, 127-138, DOI: 10.1080/00207721.2011.598956.
Sarkar B., & Sarkar S. (2013). "Variable deterioration and demand—an inventory model", Economic Modelling, 31,548–556.
Sarkar B., Saren Sh., & Wee H. M. (2013)."An inventory model with variable demand, component cost and selling price for deteriorating items", Economic Modelling, 30, 306–310.
Sankar Sana Sh. (2010). "Optimal selling price and lotsize with time varying deterioration and partial backlogging", Applied Mathematics and Computation, 217,185–194.
Sicilia J., Gonzalez M., & Febles J. (2014)." An inventory model for deteriorating items with shortages and time-varying demand", International Journal of Production Economics, http://dx.doi.org/10.1016/j.ijpe.2014.01.024i.
Taleizadeh A.A., & Nematollahi M. (2014)."An inventory control problem for deteriorating items with back-ordering and financial considerations", Applied Mathematical Modelling, 38, 93–109.
Tan Y., & Weng M. X. (2012)." A discrete-in-time deteriorating inventory model with time-varying demand, variable deterioration rate and waiting-time-dependent partial backlogging", International Journal of Systems Science, DOI:10.1080/00207721.2012.659692.
Valliathal M., & Uthayakumar R. (2011). "A new study of an EOQ model for deteriorating items with shortages under inflation and time discounting", Iranian Journal of Operations Research, Vol. 2, No. 2, pp. 48-62.
Vikas S., Anand C., & Mukesh K. (2016). "EOQ models with optimal replenishment policy for perishable items taking account of time value of money", Indian Journal of Science and Technology, Vol 9(25), DOI: 10.17485/ijst/2016/v9i25/46568.
Wee H.M. (1997) "A replenishment policy for items with a price-dependent demand and varying rate of deterioration", Production Planning and Control, Vol. 8, PP. 494-9.
Wee H.M., & Law S.H. (1999)." Economic production lot size for deteriorating items taking account of time value of money", Computer and Operations Research, Vol. 26, 545-558.