Optimal Price, Cycle Time and Advertising for an Inventory Model of Deteriorating Items: A Geometric Programming Approach

Document Type : Research Paper

Authors

School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

Abstract

In recent years researchers have been interested in inventory models for deteriorating items along with determining the price of these items; given that in many real-world problems, changing the price can affect the demand level. Meanwhile, there are some other demand stimulation like advertising, multiple post-payments and discounting which can change and control the demand level of the items. In this paper, a new deteriorating inventory model was developed that considers these three demand stimulation along with pricing. The model has been converted and solved using geometric programming approach. Meanwhile, genetic algorithm was used as an alternative method to test the performance of GP approach. The model was implemented in real case study of food industry and numerical results and sensitivity analyses demonstrate the superiority of developed approach.

Keywords

References

Abad, P. L., and Jaggi, C. K. (2003). A joint approach for setting unit price and the length of the credit period for a seller when end demand is price sensitive. International Journal of Production Economics, Vol. 83(2), pp. 115–122.
Al-Amin Khan, M., Shaikh, A. A., Konstantaras, I., Bhunia, A. K., and Cárdenas-Barrón, L. E. (2020). Inventory models for perishable items with advanced payment, linearly time-dependent holding cost and demand dependent on advertisement and selling price. International Journal of Production Economics, Vol. 230, pp. 107804.
Arcelus, F. J., Shah, N. H., and Srinivasan, G. (2003). Retailer’s pricing, credit and inventory policies for deteriorating items in response to temporary price/credit incentives. International Journal of Production Economics, Vol. 81–82, pp. 153–162.
Bag, S., Chakraborty, D., and Roy, A. R. (2009). A production inventory model with fuzzy random demand and with flexibility and reliability considerations. Computers & Industrial Engineering, Vol. 56(1), pp. 411–416.
Barman, H., Pervin, M., Roy, S. K., and Weber, G.-W. (2021). Back-ordered inventory model with inflation in a cloudy-fuzzy environment. Journal of Industrial & Management Optimization, Vol. 17(4), pp. 1913.
Boyd, S. S., and Vandenberghe, L. (2004). Convex optimization. Optimization Methods and Software, Vol. 25(3), pp. 487–487.
Chowdhury, R. R., Ghosh, S. K., and Chaudhuri, K. S. (2014). An Inventory Model for Deteriorating Items with Stock and Price Sensitive Demand. International Journal of Applied and Computational Mathematics, Vol. 1(2), pp. 187–201.
Chung, K.-J., Eduardo Cárdenas-Barrón, L., and Ting, P.-S. (2014). An inventory model with non-instantaneous receipt and exponentially deteriorating items for an integrated three layer supply chain system under two levels of trade credit. International Journal of Production Economics, Vol. 155, pp. 310–317.
Cohen, M. A. (1977). Joint pricing and ordering policy for exponentially decaying inventory with known demand. Naval Research Logistics Quarterly, Vol. 24(2), pp. 257–268.
Das, S. K., Pervin, M., Roy, S. K., and Weber, G. W. (2021). Multi-objective solid transportation-location problem with variable carbon emission in inventory management: a hybrid approach. Annals of Operations Research. https://doi.org/10.1007/s10479-020-03809-z
Duffin, Richard James, Peterson, Elmor L., Zener, C. M. (1967). Geometric programming : Theory and application.
Dye, C.-Y., Ouyang, L.-Y., and Hsieh, T.-P. (2007). Inventory and pricing strategies for deteriorating items with shortages: A discounted cash flow approach. Computers & Industrial Engineering, Vol. 52(1), pp. 29–40.
Esmaeili, M., and Zeephongsekul, P. (2010). Seller – buyer models of supply chain management with an asymmetric information structure. International Journal of Production Economics, Vol. 123(1), pp. 146–154.
Ghare, P., and Schrader, S. (1963). A model for exponentially decaying inventory. Journal of Industrial Engineering, Vol. 14(5), pp. 238–243.
Ghiami, Y., and Williams, T. (2014). A two-echelon production-inventory model for deteriorating items with multiple buyers. International Journal of Production Economics, Vol. 159, pp. 233–240.
Ghiami, Y., Williams, T., and 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, Vol. 231(3), pp. 587–597.
Hasan, M. R., Mashud, A. H. M., Daryanto, Y., and Wee, H. M. (2020). A non-instantaneous inventory model of agricultural products considering deteriorating impacts and pricing policies. Kybernetes, ahead-of-p(ahead-of-print).
Huang, H., He, Y., and Li, D. (2018). Pricing and inventory decisions in the food supply chain with production disruption and controllable deterioration. Journal of Cleaner Production, Vol. 180, pp. 280–296.
Khakzad, A., and Gholamian, M. R. (2020). The effect of inspection on deterioration rate: An inventory model for deteriorating items with advanced payment. Journal of Cleaner Production, Vol. 254, pp. 120117.
Khan, M. A.-A., Shaikh, A. A., Panda, G. C., Konstantaras, I., and Taleizadeh, A. A. (2019). Inventory system with expiration date: Pricing and replenishment decisions. Computers & Industrial Engineering, Vol. 132, pp. 232–247.
Kochenberger, G. A. (1971). Inventory models: optimization by geometric programming. Decision Sciences, Vol. 2(2), pp. 193–205.
Kumar Roy, S., Pervin, M., and Wilhelm Weber, G. (2020). A two-warehouse probabilistic model with price discount on backorders under two levels of trade-credit policy. Journal of Industrial & Management Optimization, Vol. 16(2), pp. 553–578.
Lashgari, M., Taleizadeh, A. A., and Sana, S. S. (2015). An inventory control problem for deteriorating items with back-ordering and financial considerations under two levels of trade credit linked to order quantity. Journal of Industrial and Management Optimization, Vol. 12(3), pp. 1091–1119.
Lee, W. J. (1993). Determining Order Quantity and Selling Price by Geometric Programming : Optimal Solution , Bounds , and Sensitivity. Decision Sciences, Vol. 24(1), pp. 76–87.
Lee, W. J., and Kim, D. (1993). Optimal and heuristic decision strategies for integrated production and marketing planning. Decision Sciences, Vol. 24(6), pp. 1203.
Li, G., He, X., Zhou, J., and Wu, H. (2019). Pricing, replenishment and preservation technology investment decisions for non-instantaneous deteriorating items. Omega, Vol. 84, pp. 114–126.
Maihami, R., Karimi, B., and Fatemi Ghomi, S. M. T. (2016). Effect of two-echelon trade credit on pricing-inventory policy of non-instantaneous deteriorating products with probabilistic demand and deterioration functions. Ann Oper Res.
Maihami, R., and Nakhai Kamalabadi, I. (2012). 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(1), pp. 116–122.
Misra, R. B. (1975). Optimum production lot size model for a system with deteriorating inventory. International Journal of Production Research, Vol. 13(5), pp. 495–505.
Mondal, B., Biswas, S., Garai, A., and Roy, T. K. (2020). Posynomial Geometric Programming in EOQ Model with Interval Neutrosophic Number. In Studies in Computational Intelligence: Vol. 863 SCI (pp. 434–449). Springer.
Moradi, S., Omrani, H., and Emrouznejad, A. (2020). Global optimisation for a developed price discrimination model: A signomial geometric programming-based approach. Journal of the Operational Research Society. Vol. 72(3), pp. 612-627
Papachristos, S., and Skouri, K. (2003). An inventory model with deteriorating items, quantity discount, pricing and time-dependent partial backlogging. International Journal of Production Economics, Vol. 83(3), pp. 247–256.
Pervin, M., Kumar Roy, S., and Wilhelm Weber, G. (2020). Deteriorating inventory with preservation technology under price- and stock-sensitive demand. Journal of Industrial & Management Optimization, Vol. 16(4), pp. 1585–1612.
Pervin, M., Roy, S. K., and Weber, G.-W. (2018). Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration. Annals of Operations Research, Vol. 260(1–2), pp. 437–460.
Pervin, M., Roy, S. K., and Weber, G.-W. (2019). An integrated vendor-buyer model with quadratic demand under inspection policy and preservation technology. Hacettepe Journal of Mathematics and Statistics, pp. 1–22.
Qin, Y., Wang, J., and Wei, C. (2014). Joint pricing and inventory control for fresh produce and foods with quality and physical quantity deteriorating simultaneously. International Journal of Production Economics, Vol. 152, pp. 42–48.
Sadjadi, Seyed J, and Oroujee, M. (2005). Optimal Production and Marketing Planning. Computational Optimization and Applications, Vol. 30(2), pp.195–203.
Sadjadi, Seyed Jafar, Hamidi Hesarsorkh, A., Mohammadi, M., and Bonyadi Naeini, A. (2015). Joint pricing and production management: a geometric programming approach with consideration of cubic production cost function. Journal of Industrial Engineering International, Vol. 11(2), pp. 209–223.
Sana, S. S. (2010). Optimal selling price and lotsize with time varying deterioration and partial backlogging. Applied Mathematics and Computation, Vol. 217(1), 185–194.
Sarkar, B., and Saren, S. (2015). Partial Trade-Credit Policy of Retailer with Exponentially Deteriorating Items. International Journal of Applied and Computational Mathematics, Vol. 1(3), pp. 343–368.
Sarkar, B., Saren, S., and Cárdenas-Barrón, L. E. (2014). An inventory model with trade-credit policy and variable deterioration for fixed lifetime products. Annals of Operations Research, Vol. 229(1), pp. 677–702.
Soni, H. N. (2013). Optimal replenishment policies for non-instantaneous deteriorating items with price and stock sensitive demand under permissible delay in payment. International Journal of Production Economics, Vol. 146(1), pp. 259–268.
Srivastava, M., and Gupta, R. (2014). An EPQ model for deteriorating items with time and price dependent demand under markdown policy. OPSEARCH, Vol. 51(1), pp. 148–158.
Taghizadeh-Yazdi, M., Farrokhi, Z., and Mohammadi-Balani, A. (2020). An integrated inventory model for multi-echelon supply chains with deteriorating items: a price-dependent demand approach. Journal of Industrial and Production Engineering, Vol. 37(2–3), pp. 87–96.
Taleizadeh, A. A. (2014a). An economic order quantity model for deteriorating item in a purchasing system with multiple prepayments. Applied Mathematical Modelling, Vol. 38(23), pp. 5357–5366.
Taleizadeh, A. A. (2014b). An EOQ model with partial backordering and advance payments for an evaporating item. International Journal of Production Economics, Vol. 155, pp. 185–193.
Taleizadeh, A. A., and Nematollahi, M. (2014). An inventory control problem for deteriorating items with back-ordering and financial considerations. Applied Mathematical Modelling, Vol. 38(1), pp. 93–109.
Tavakoli, S., and Taleizadeh, A. A. (2017). An EOQ model for decaying item with full advanced payment and conditional discount. Annals of Operations Research, Vol. 259(1–2), pp. 415–436.
Tiwari, S., Cárdenas-Barrón, L. E., Khanna, A., and Jaggi, C. K. (2016). Impact of trade credit and inflation on retailer’s ordering policies for non-instantaneous deteriorating items in a two-warehouse environment. International Journal of Production Economics, Vol. 176, pp.154–169.
Wee, H.-M., and Law, S.-T. (1999). Economic production lot size for deteriorating items taking account of the time-value of money. Computers & Operations Research, Vol. 26(6), pp. 545–558.
Wu, J., Ouyang, L. Y., Cárdenas-Barrón, L. E., and Goyal, S. K. (2014). Optimal credit period and lot size for deteriorating items with expiration dates under two-level trade credit financing. European Journal of Operational Research, Vol. 237(3), pp. 898–908.
Wu, J., Skouri, K., Teng, J.-T., and Ouyang, L.-Y. (2014). A note on “optimal replenishment policies for non-instantaneous deteriorating items with price and stock sensitive demand under permissible delay in payment.” International Journal of Production Economics, Vol. 155(1), pp. 324–329.
International Journal of Supply and Operations Management
Volume 9, Issue 3
August 2022
Pages 281-298

Files

Share

How to cite

Statistics