### International Journal of Mathematical, Engineering and Management Sciences

#### ISSN: 2455-7749

Inventory Policies for Price-Sensitive Stock-Dependent Demand and Quantity Discounts

#### Inventory Policies for Price-Sensitive Stock-Dependent Demand and Quantity Discounts

Nita H. Shah
Department of Mathematics, Gujarat University, Ahmedabad-380009, Gujarat, India.

Monika K. Naik
Department of Mathematics, Gujarat University, Ahmedabad-380009, Gujarat, India.

;
Accepted on August 04, 2017

Abstract

It was usually observed in typical EOQ inventory models that the holding cost, the purchasing cost and the demand rate are constant and the purchasing cost is irrespective of the order size. But practically, the demand rate is based on various factors including sale price, seasonality and availability. Due to the lengthening of shortage periods, the holding cost per unit item increases. Also with the inclusion of quantity discounts, the unit purchasing cost is usually decreased for higher order sizes. This article addresses jointly with the inconsistency of the rate of demand, unit purchasing cost and unit holding cost for deteriorating items. This paper proposes a model based on an inventory problem including selling price of products and stock-dependent market demand rate, holding cost based on storage time and purchasing cost is influenced by order size by offering all units quantity discounts. An algorithm for estimating the optimum solution of decision variables by maximizing total profit and minimizing the overall cost of the model is developed in this paper. Validation of the developed model is confirmed with the help of a numerical example along with the sensitivity-analysis of decision variables by varying various inventory parameters.

Keywords- Deteriorating items, Quantity discounts, Price-sensitive stock-dependent demand rate, Storage-time dependent holding cost, Order- size dependent purchasing cost.

Citation

Shah, N. H., & Naik, M. K. (2018). Inventory Policies for Price-Sensitive Stock-Dependent Demand and Quantity Discounts. International Journal of Mathematical, Engineering and Management Sciences, 3(3), 245-257. https://dx.doi.org/10.33889/IJMEMS.2018.3.3-017.

Conflict of Interest

Acknowledgements

The authors will like to thank reviewers for their constructive comments. The authors thank DST-FIST MSI-097 for technical support to carry out this research.

References

Alfares, H. K. (2007). Inventory model with stock-level dependent demand rate and variable holding cost. International Journal of Production Economics, 108(1), 259-265.

Alfares, H. K. (2014). Production-inventory system with finite production rate, stock-dependent demand, and variable holding cost. RAIRO-Operations Research, 48(1), 135-150.

Alfares, H. K. (2015). Maximum-profit inventory model with stock-dependent demand, time-dependent holding cost, and all-units quantity discounts. Mathematical Modelling and Analysis, 20(6), 715-736.

Alfares, H. K., & Ghaithan, A. M. (2016). Inventory and pricing model with price-dependent demand, time-varying holding cost, and quantity discounts. Computers of Industrial Engineering, 94,170-177.

Anand, A., & Bansal, G. (2016). Predicting customer’s satisfaction (dissatisfaction) using logistic regression. International Journal of Mathematical, Engineering and Management Sciences, 1(2), 77-88.

Burwell, T. H., Dave, D. S., Fitzpatrick, K. E., & Roy, M. R. (1997). Economic lot size model for price-dependent demand under quantity and freight discounts. International Journal of Production Economics, 48(2), 141-155.

Chang, H. C. (2013). A note on an economic lot size model for price-dependent demand under quantity and freight discounts. International Journal of Production Economics, 144(1), 175-179.

Datta, T. K. (2013). An inventory model with price and quality dependent demand where some items produced are defective. Advances in Operations Research.

Datta, T. K., & Paul, K. (2001). An inventory system with stock-dependent, price-sensitive demand rate. Production Planning and Control, 12(1), 13-20.

Ding, Z. (2010, November). An inventory coordination scheme of single-period products under price-dependent demand. In E-Product E-Service and E-Entertainment (ICEEE), 2010 International Conference on (pp. 1-4). IEEE.

Ferguson, M., Jayaraman, V., & Souza, G. C. (2007). Note: An application of the EOQ model with nonlinear holding cost to inventory management of perishables. European Journal of Operational Research, 180(1), 485-490.

Goh, M., & Sharafali, M. (2002). Price-dependent inventory models with discount offers at random times. Production and Operations Management, 11(2), 139-156.

Hou, K. L. & Lin, L. C. (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, 37(15), 1131-1139.

Khanna A., Gautam P., & Jaggi C. K. (2017). Inventory modeling for deteriorating imperfect quality items with selling price dependent demand and shortage backordering under credit financing. International Journal of Mathematical, Engineering and Management Sciences, 2(2), 110-124.

Kumar, M., Chauhan A., & Kumar R. (2012). A deterministic inventory model for deteriorating items with price dependent demand and time varying holding cost under trade credit. International Journal of Soft Computing and Engineering, 2(1), 2231-2307.

Lee, Y. P. & Dye, C. Y. (2012). An inventory model for deteriorating items under stock-dependent demand and controllable deterioration rate. Computers and Industrial Engineering, 63(2), 474-482.

Min, J. & Zhou, Y. W. (2009). A perishable inventory model under stock-dependent selling rate and shortage-dependent partial backlogging with capacity constraint. International Journal of Systems Science, 40(1), 33-44.

Mondal, B., Bhunia, A. K., & Maiti, M. (2003). An inventory system of ameliorating items for price dependent demand rate. Computers and Industrial Engineering, 45(3), 443-456.

Mukhopadhyay, S., Mukherjee, R. N., & Chaudhari, 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, 36(1), 25-33.

Ouyang, L. Y., Wu, K. S. & Yang, C. T. (2008). Retailer's ordering policy for non-instantaneous deteriorating items with quantity discount, stock-dependent demand and stochastic backorder rate. Journal of the Chinese Institute of Industrial Engineers, 25(1), 62-72.

Panda, D., Maiti, M. K., & Maiti, M. (2010). Two warehouse inventory models for single vendor multiple retailers with price and stock dependent demand. Applied Mathematical Modelling, 34(11), 3571-3585.

Pando, V., José, L. A., Laguna, J. G., & Sicilia, J. (2013). An economic lot-size model with non-linear holding cost hinging on time and quantity. International Journal of Production Economics, 145(1), 294-303.

Pando, V., Laguna, J. G., José, L. A., & Sicilia, J. (2012). Maximizing profits in an inventory model with both demand rate and holding cost per unit time dependent on the stock level. Computers and Industrial Engineering, 62(2), 599-608.

Sana, S., & Chaudhari K. S. (2004). A stock-review EOQ model with stock-dependent demand, quadratic deterioration rate. Advanced Modeling and Optimization, 6(2), 25-32.

San-José, L. A., & García-Laguna, J. (2009). Optimal policy for an inventory system with backlogging and all-units discounts: Application to the composite lot size model. European Journal of Operational Research, 192(3), 808-823.

Shah, N. H. (2012). Ordering policy for inventory management when demand is stock-dependent and a temporary price discount is linked to order quantity. Revista Investigación Operacional, 33(3), 233-244.

Teng, J. T., Chang, C. T., & Goyal, S. K. (2005). Optimal pricing and ordering policy under permissible delay in payments. International Journal of Production Economics, 97(2), 121-129.

Transchel, S., & Minner, S. (2008). Coordinated lot-sizing and dynamic pricing under a supplier all-units quantity discount. BuR-Business Research, 1(1), 125-141.

Wee, H. M. (1999). Deteriorating inventory model with quantity discount, pricing and partial backordering. International Journal of Production Economics, 59(1), 511-518.

Weng, Z. K. (1995). Modeling quantity discounts under general price-sensitive demand functions: Optimal policies and relationships. European Journal of Operational Research, 86(2), 300-314.

Yang P. C. (2004). Pricing strategy for deteriorating items using quantity discount when demand is price sensitive. European Journal of Operational Research, 157(2), 389-397.

Yang, H. L., Teng, J. T., & Chern, M. S. (2010). An inventory model under inflation for deteriorating items with stock-dependent consumption rate and partial backlogging shortages. International Journal of Production Economics, 123(1), 8-19.

Zhao, M., & Zhong, B., (2008). Inventory model with stock-level dependent demand rate and variable holding cost. Journal of Chongqing Institute of Technology (Natural Science), 10, 23.