Optimal ordering quantities for substitutable deteriorating items under joint replenishment

• Autorzy: Mishraa V. , Shankerb K.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we study an inventory system for two substitutable deteriorating items where when an item is out of stock, the demand for it is met by the other item and any part of demand not met due to unavailability of the other item is lost. The level of inventory of both items deplete due to combined effect of demand fulfilment and deterioration. The rates of demand and deterioration are assumed to be deterministic and constant. Items are ordered jointly in each ordering cycle so as to take advantage of joint replenishment. The problem is formulated and a solution procedure is developed to determine the optimal ordering quantities that minimize the total inventory cost. An extensive numerical analysis is carried out to illustrate the parameters of the model. The results indicate that there is substantial improvement in the optimal total cost of the inventory system with substitution over the case without substitution.

Słowa kluczowe

EN

inventory control; substitutable items; deterioration; optimal ordering quantities; joint replenishment

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2017
• Tom: Vol. 46, no. 1
• Strony: 49--70
• Opis fizyczny: Bibliogr. 40 poz., rys.

Twórcy

autor

Mishraa V.

• Department of Computer Science and Engineering, Bipin Tripathi Kumaon Institute of Technology, Dwarahat, Almora, Uttarakhand, 263653, India

autor

Shankerb K.

• Department of Industrial and Management Engineering, Indian Institute of Technology, Kanpur, 208016, UP, India

Bibliografia

• [1] Anupindi, R., Dada M., Gupta, M. S. (1998) Estimation of consumer demand with stock out based substitution: an application to vending machine products. Marketing Science, 17, 406–423.
• [2] Bakker, M., Riezebos, J. and Teunter, R.H. (2012) Review of Inventory Systems with Deterioration since 2001. European Journal of Operational Research, 221, 275-284.
• [3] Bazaraa, M.S., Sherali, H.D., Shetty, C. M. (2013) Nonlinear Programming: Theory and Algorithms, 3rd edition. John Wiley and Sons.
• [4] Chandra, S. (1972) Strong pseudo convex programming. Indian Journal of Pure and Applied Mathematics, 3, 278-282.
• [5] Drezner, Z., Gurnani, H., Pasternack, B.A. (1995) EOQ model with substitution between products. Journal of Operations Research Society, 46, 887–891.
• [6] Ernst, R., Kouvelis, P. (1999) The effects of selling packaged goods on inventory decisions. Management Science, 45(8), 1142–1155.
• [7] Gerchak, Y., Grosfeld-Nir, A. (1999) Lot-sizing for substitutable, production-to-order parts with random functionality yields. The International Journal of Flexible Manufacturing Systems, 11, 371–377.
• [8] Goyal, S. K. and Giri, B. C. (2003) Recent trends in modeling of deteriorating inventory. European Journal of Operational Research, 134(1), 1–16.
• [9] Gurnani, H., Drezner, Z. (2000) Deterministic hierarchical substitution inventory models. Journal of Operations. Research Society, 51, 129–133.
• [10] Harris, F.W. (1915) Operations and Cost. A. W. Shaw Company, Chicago, 48–54.
• [11] Hong, S., Kim, Y. (2009) A genetic algorithm for joint replenishment based on the exact inventory cost. Computers and Operations Research, 36 (1), 167–175.
• [12] Hsieh, Y.-J. (2013) Demand switching criteria for multiple products: An inventory cost analysis. Omega, 39, 130–137.
• [13] Huang Hu and Ke Hua (2014) Pricing decision problem for substitutable products based on uncertainty theory. Journal of Intelligent Manufacturing, 1-12. DOI 10.1007/s10845-014-0991-7.
• [14] Khanlarzade, N., Yegane, B. Y., Kamalabadi, I. N. and Farughi, H. (2014) Inventory control with deteriorating items: A state-of-the-art literature review. International Journal of Industrial Engineering Com putations, 5, 179-198.
• [15] Khouja, M. and Goyal, S. (2008) A review of the joint replenishment problem literature: 1989-2005. European Journal of Operational Research, 186(1), 1-16.
• [16] Kim, S.-W., Bell, P.C. (2011) Optimal pricing and production decisions in the presence of symmetrical and asymmetrical substitution. Omega, 39(5), 528-538.
• [17] Krommyda, I.P., Skouri, K., Konstantaras, I. (2015) Optimal ordering quantities for substitutable products with stock-dependent demand. Applied Mathematical Modelling, 39(1), 147-164.
• [18] Li, R., Hongjie, L., Mawhinney, J. R. (2010) A Review on Deteriorating Inventory Study. Journal of Service Science & Management, 3, 117-129.
• [19] Li, H., You, T. (2012) Capacity commitment and pricing for substitutable products under competition. Journal of System Science and System Engineering, 21(4), 443-460.
• [20] Li, X., Nukala, S., Mohebbi, S. (2013) Game theory methodology for optimizing retailers’ pricing and shelf-space allocation decisions on competing substitutable products. International Journal of Advanced Manufacturing Technology, 68, 375–389.
• [21] Mishra, B.K., Raghunathan, S. (2004) Retailer-vs.vendor-managed inventory and brand competition. Management Science, 50(4), 445–457.
• [22] Parlar, M., Goyal, S. (1984) Optimal ordering decisions for two substitutable products with stochastic demands. Opsearch, 21, 1–15.
• [23] Pasternack B., Drezner, Z. (1991) Optimal inventory policies for substitutable commodities with stochastic demand. Naval Research Logistic, 38, 221–240.
• [24] Porras, E., Dekker, R. (2008) Generalized solutions for the joint replenishment problem with correction factor. International Journal of Production Economics, 113 (2), 834–851.
• [25] Raafat, F. (1991) Survey of literature on continuously deteriorating inventory model. Journal of the Operational Research Society, 42(1), 27–37.
• [26] Rasouli, N., NakhaiKamalabadi, I. (2014) Joint pricing and inventory control for seasonal and substitutable goods mentioning the symmetrical and asymmetrical substitution. International Journal of Engineering (IJE), TRANSACTIONS C: Aspects, 27, 9, 1385-1394.
• [27] Salameh, M.K., Yassine, A.A., Maddah, B., Ghaddar, L. (2014) Joint replenishment model with substitution. Applied Mathematical Modelling, 38 (14), 3662-3671.
• [28] Schulz, A., Telha, C. (2011) Approximation algorithms and hardness results for the joint replenishment problem with constant demands. Lecture Notes in Computer Science, 6942, 628–639.
• [29] Taleizadeh, A.A. (2014a) An inventory control problem for deteriorating items with backordering and financial engineering considerations. Applied Mathematical Modeling, 38, 93–109.
• [30] Taleizadeh, A.A. (2014b) An economic order quantity model with partial backordering and advance payments for an evaporating item. International Journal of Production Economics, 155, 185–193.
• [31] Taleizadeh, A.A. (2014c) An economic order quantity model for deteriorating item in a purchasing system with multiple prepayments. Applied Mathematical Modeling, 38, 5357–5366.
• [32] Taleizadeh, A.A. (2015a) Joint optimization of price, replenishment frequency, replenishment cycle and production rate in vendor managed inventory system with deteriorating items. International Journal of Production Economics, 159, 285-295.
• [33] Taleizadeh, A.A. (2015b) Joint replenishment policy with backordering and Special Sale. International Journal of Systems Science, 46(7), 1172-1198.
• [34] Taleizadeh, A.A. (2016) Pricing and ordering decisions of two competing supply chains with different composite policies: a Stackelberg gametheoretic approach. International Journal of Production Research, 54(9), 2807-2836.
• [35] Tat R., Taleizadeh, A.A. and Esmaeili, M. (2015) Developing EOQ model with non-instantaneous deteriorating items in vendor-managed inventory (VMI) system. International Journal of Systems Science, 46(7), 1257-1268.
• [36] Whitin, T. M. (1957) The Theory of Inventory Management, 2nd ed. Princeton University Press, Princeton, NJ.
• [37] Wilson, R.H. (1934) A scientific routine for stock control. Harvard Business Review, 13, 116-128.
• [38] Xue, Z., Song, J. (2007) Demand management and inventory control for substitutable products. Working paper, The Fuqua School of Business, Duke University, Durham, NC.
• [39] Ye, T. (2014) Inventory management with simultaneously horizontal and vertical substitution. International Journal of Production Economics, 156, 16-324.
• [40] Zhao, J., Wei, J., Li, Y. (2014) Pricing decisions for substitutable products in a two-echelon supply chain with firms different channel powers. International Journal of Production Economics, 153, 243–252.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).