Inventory Model for Non – Instantaneous Deteriorating Items, Stock Dependent Demand, Partial Backlogging, and Inflation over a Finite Time Horizon

Document Type : Research Paper

Authors

SRM University, Delhi - NCR, Sonepat, Haryana, India

Abstract

In the present study, the Economic Order Quantity (EOQ) model of two-warehouse deals with non-instantaneous deteriorating items, the demand rate considered as stock dependent and model affected by inflation under the pattern of time value of money over a finite planning horizon. Shortages are allowed and partially backordered depending on the waiting time for the next replenishment. The main objective of this work is to minimize the total inventory cost and finding the optimal interval and the optimal order quantity. An algorithm is designed to find the optimum solution of the proposed model. Numerical examples are given to demonstrate the results. Also, the effect of changes in the different parameters on the optimal total cost is graphically presented.

Keywords

Main Subjects


Buzacott, JA. , (1975). Economic order quantities with inflation. Operations Research Quarterly, Vol. 26(3), pp. 553–558. 
Chang, CT., Teng, JT., & Goyal, SK., (2010). Optimal replenishment policies for non-instantaneous deteriorating items with stock-dependent demand. International Journal of Production Economics, Vol. 123(1), pp. 62–68.

Cheng, M., Zhang, B., & Wang, G., (2011). Optimal policy for deteriorating items with trapezoidal type demand and partial backlogging. Applied Mathematical Modelling, 35(7), 3552–3560. Chung, K.J., (1996). Optimal ordering time interval taking account of time value. Production Planning and Control, Vol. 7(3), pp. 264–267.

Chung, K.J., (2009). A complete proof on the solution procedure for non-instantaneous deteriorating items with permissible delay in payment. Computers & Industrial Engineering, Vol. 56(1), pp. 267–273.

Data, T.K., Pal, A.K., (1991). Effects of inflation and time value of money on an inventory model with linear time dependent demand rate and shortages. European Journal of Operational Research, Vol. 52(3), pp. 326–333.

Deb, M., Chaudhuri, K.S., (1986). An EOQ model for items with finite rate of production and variable rate of deterioration. Opsearch, Vol. 23(1), pp. 175-181.

Dye, C.Y., (2013). The effect of preservation technology investment on a non-instantaneous deteriorating inventory model. Omega, Vol. 41(5), pp. 872–880.

Dye, C.Y., Ouyang, L.Y., & Hsieh, T.P., (2007). Deterministic inventory model for deteriorating items with capacity constraint and time-proportional backlogging rate. European Journal of Operational research, Vol. 178(3), pp. 789-807.

Geetha, K.V., Uthayakumar, R., (2009). Economic design of an inventory policy for non-instantaneous deteriorating items under permissible delay in payments. Journal of Computational and Applied Mathematics, Vol. 233(10), pp. 2492-2505.

Ghare, P.M., Schrader, G.H., (1963). A model for exponentially decaying inventory system. International Journal of Production Research, Vol. 21, pp. 449-460.

Goyal, S.K., Giri, B.C., (2001). Recent trends in modeling of deteriorating inventory. European Journal of Operational Research, Vol. 134(1), pp. 1-16.

Guchhaita, P., Maiti , M. K., & Maiti, M., (2013). Two storage inventory model of a deteriorating item with variable demand under partial credit period. Applied Soft Computing, Vol. 13(1), pp. 428–448.

Guria, A., Das, B., Mondal, S., & Maiti, M., (2013). Inventory policy for an item with inflation induced purchasing price, selling price and demand with immediate part payment. Applied Mathematical Modelling, Vol. 37(1), pp. 240–257.
Hartley R.V. (1976). Operations Research—A Managerial Emphasis. Good Year Publishing Company, California, pp. 315-317.

Hou KL, Lin LC (2006) An EOQ model for deteriorating items with price- and stock-dependent selling rates under inflation and time value of money. International Journal of Systems Science, Vol. 37, pp. 1131-1139.

Hsieh TP, Dye CY, Ouyang LY (2008) determining optimal lot size for a two-warehouse system with deterioration and shortages using net present value. European Journal of Operational Research, Vol. 191, pp. 182–192.

Kumar N, Singh S R, Kumari R (2008) a Two-Warehouse inventory model without shortage for exponential demand rate and an optimum release rule. Ultra Scientist of Physical Sciences, Vol. 20, pp. 395-402.

Kumar N and Kumar S (2016) Effect of learning and salvage worth on an inventory model for deteriorating items with inventory-dependent demand rate and partial backlogging with capability constraints. Uncertain Supply Chain Management, Vol. 4, pp. 123-136.

Kumar N, Singh S R, Kumari R (2011) a deterministic Two-warehouse Inventory Model for Deteriorating Items with Sock-dependent Demand and Shortages under the Conditions of Permissible Delay. International Journal of Mathematical Modeling and Numerical Optimizations, Vol. 11, pp. 357-375.

Kumar N, Singh S R, Kumari R (2013) Learning effect on an inventory model with two-level storage and partial backlogging under inflation. International Journal of Services and Operations Management, Vol. 16, pp. 105–122.

Kumar N, Singh S R, Kumari R (2014) Effect of Salvage Value on a Two-Warehouse Inventory Model for Deteriorating Items with Stock-Dependent Demand Rate and Partial Backlogging .International Journal of Operational Research, Vol. 19, pp. 479–496.

Lee C, Ma C (2000) optimal inventory policy for deteriorating items with two-warehouse and timedependent demands. Production Planning and Control, Vol. 11, pp. 689–696.

Liao J (2008) An EOQ model with non-instantaneous receipt and exponential deteriorating item under two-level trade credit. International Journal of Production Economics, Vol. 113, pp. 852–861
Maihami R, Abadi INK (2012a) Joint control of inventory and its pricing for non-instantaneously deteriorating items under permissible delay in payments and partial backlogging. Mathematical and Computer Modelling, Vol. 55, pp. 1722–1733.
Maihami R, Kamalabadi IN (2012b) Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand. International. Journal of Production Economics, Vol. 136, pp. 116–122.

Min J, Zhou YW (2009) a perishable inventory model under stock-dependent selling rate and shortage dependent partial backlogging with capacity constraint. International Journal of Systems Science, Vol. 40, pp. 33-44.

Misra RB (1979) A note on optical inventory management under inflation. Naval Research Logistics Quarterly, Vol.  26, pp. 161–165.

Ouyang LY, Wu KS, Yang CT (2006) A study on an inventory model for non-instantaneous deteriorating items with permissible delay in payments. Computers & Industrial Engineering, Vol. 51, pp. 637–651.

Pakkala, T.P.M., Achary, K.K., (1992). A deterministic inventory model for deteriorating items with two warehouses and finite replenishment rate. European Journal of Operational Research, Vol. 57, pp. 71-76.

Philip GC (1974) A generalized EOQ model for items with weibull distribution. AIIE Transactions, Vol. 6, pp.159-162.

Ray J, Chaudhuri KS (1997) An EOQ model with stock-dependent demand, shortage, inflation and time discounting. International Journal of Production Economics, Vol. 53, pp. 171-180.

Roy MD, Sana SS, and Chaudhuri KS (2011) An economic order quantity model of imperfect quality items with partial backlogging. International Journal of Systems Science, Vol. 42, pp. 1409-1419.

Sarkar B, Sarkar S (2013) An improved inventory model with partial backlogging, time varying deterioration and stock-dependent demand. Economic Modelling, Vol. 30, pp. 924–932.

Sarkar T, Ghosh SK, Chaudhuri KS (2012) An optimal inventory replenishment policy for a deteriorating item with time-quadratic demand and time-dependent partial backlogging with shortages in all cycles. Applied Mathematics and Computation, Vol. 218, pp. 9147–9155.

Sarker BR, Pan H (1994) Effects of inflation and time value of money on order quantity and allowable shortage. International Journal of Production Economics, Vol. 34, pp. 65–72.

Sarma KVS (1983) A deterministic inventory model with two levels of storage and an optimum release rule. Opsearch 20:175-180. Sarma KVS, Sastry MP (1988) Optimum inventory for systems with two levels of storage. Industrial Engineering Journal, Vol. 8, pp. 12-19.
Sett BK, Sarkar B, Goswami A (2012) A two-warehouse inventory model with increasing demand and time varying deterioration. Scientia Iranica E, Vol. 19, pp. 1969–1977.

Taleizadeh AA, Pentico DW (2013a) An economic order quantity model with a known price increase and partial backordering. European Journal of Operational Research, Vol. 228, pp. 516–525.

Taleizadeh AA, Pentico DW, Jabalameli MS Aryanezhad M (2013b) An EOQ model with partial delayed payment and partial backordering. Omega, Vol. 41, pp. 354–368.

Tan Y, Weng MX (2013) 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, Vol. 44, pp. 1483-1493.

Tayal S, Singh S R, Sharma S (2015) An inventory model for deteriorating items with seasonal products and an option of an alternative market. Uncertain Supply Chain Management, Vol. 3, pp. 69-86.

Thangam A, Uthayakumar R (2010) An inventory model for deteriorating items with inflation induced demand and exponential partial backorders–a discounted cash flow approach. International Journal of Management Science and Engineering Management, Vol. 5, pp. 170-174.

Tolgari JT, Mirzazadeh A, Jolai A (2012) An inventory model for imperfect items under inflationary conditions with considering inspection errors. Computers and Mathematics with Applications, Vol. 63, pp. 1007–1019.

Tripathy CK, Pradhan LM (2010) An EOQ model for Weibull deteriorating items with power demand and partial backlogging. International Journal of Contemporary Mathematical Sciences, Vol. 5, pp. 1895-1904.

Valliathal M, Uthayakumar R (2010) The Production - Inventory Problem for Ameliorating/ Deteriorating Items with Non-Linear Shortage Cost under Inflation and Time Discounting. Applied Mathematical Sciences, Vol. 4, pp. 89–304.

Wu KS, Ouyang LY, Yang CT (2006) An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging. International Journal of Production Economics, Vol. 101, pp. 369-384.

Yang HL (2004) Two-warehouse inventory models for deteriorating items with shortages under inflation. European Journal of Operational Research, Vol. 157, pp. 344–356.

Yang HL (2006) Two-warehouse partial backlogging inventory models for deteriorating items under inflation. International Journal of Production Economics, Vol. 103, pp. 362–370.
Yang HL (2011) A partial backlogging production-inventory lot-size model for deteriorating items with time-varying production and demand rate over a finite time horizon. International Journal of Systems Science, Vol. 42, pp. 1397-1407.

Yang HL (2012) Two-warehouse partial backlogging inventory models with three-parameter Weibull distribution deterioration under inflation. International Journal of Production Economics, Vol. 138, pp. 107–116.

Yang HL, Chang CT (2013) A two-warehouse partial backlogging inventory model for deteriorating items with permissible delay in payment under inflation. Applied Mathematical Modelling, Vol. 37, pp. 2717–2726.