Optimal Ordering Quantities for Substitutable Items Under Joint Replenishment with Cost of Substitution

• Autorzy: Vinod Kumar Mishra , Kripa Shanker
• Języki publikacji: EN

Abstrakty

EN

An inventory system of two mutually substitutable items has been studied where an item is out of stock, 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. In the event of substitution, there is an additional cost of substitution involved for each unit of the substituted item. The demands are assumed to be deterministic and constant. Items are ordered jointly in each ordering cycle, in order to take advantage of joint replenishment. The problem is formulated and a solution procedure is suggested to determine the optimal ordering quantities that minimize the total inventory cost. The critical value of the substitution rate is defined to help in deciding the optimal value of decision parameters. Extensive numerical experimentation is carried out, which shows that prior knowledge of the critical value of the substitution rate helps to minimize the total inventory cost. Sensitivity analysis is carried out for the improvement in the optimal total cost with substitution as compared to the case without substitution to draw insights into the behaviour of the model. (original abstract)

Słowa kluczowe

EN

Inventories; Inventory models; Sensitivity analysis

PL

Zapasy; Modele zapasów; Analiza wrażliwości

• Czasopismo: Operations Research and Decisions
• Rocznik: 2017
• Tom: 27
• Numer: nr 1
• Strony: 77--104

Twórcy

autor

Vinod Kumar Mishra

• Bipin Tripathi Kumaon Institute of Technology, Dwarahat, India

autor

Kripa Shanker

• Indian Institute of Technology, Kanpur, India

Bibliografia

• [1] AVRIEL M., Nonlinear Programming, Analysis and Methods, Dover Publications, New York 2003.
• [2] BAZARAA M.S., SHERALI H.D., SHETTY C.M., Nonlinear Programming. Theory and Algorithms, 3rd Ed., Wiley, 2013.
• [3] DREZNER Z., GURNANI H., PASTERNACK B.A., EOQ model with substitution between products, J. Oper. Res. Soc., 1995, 46, 887-891.
• [4] ERNST R., KOUVELIS P., The effects of selling packaged goods on inventory decisions, Manage. Sci., 1999, 45 (8), 1142-1155.
• [5] GERCHAK Y., GROSFELD-NIR A., Lot-sizing for substitutable, production-to-order parts with random functionality yields, Int. J. Flex. Manuf. Sys., 1999, 11, 371-377.
• [6] GURNANI H., DREZNER Z., Deterministic hierarchical substitution inventory models, J. Oper. Res. Soc., 2000, 51, 129-133.
• [7] HONG S., KIM Y., A genetic algorithm for joint replenishment based on the exact inventory cost, Comp. Oper. Res., 2009, 36 (1), 167-175.
• [8] HSIEH Y.-J., Demand switching criteria for multiple products. An inventory cost analysis, Omega, 2013, 39, 130-137.
• [9] HU H., HUA K., Pricing decision problem for substitutable products based on uncertainty theory, J. Int. Manuf., 2017, 28 (3), 503-514.
• [10] KHOUJA M., GOYAL S., A review of the joint replenishment problem literature. 1989-2005, Eur. J. Oper. Res., 2008, 186 (1), 1-16.
• [11] KIM S.-W., BELL P.C., Optimal pricing and production decisions in the presence of symmetrical and asymmetrical substitution, Omega, 2011, 39 (5), 528-538.
• [12] KROMMYDA I.P., SKOURI K., KONSTANTARAS I., Optimal ordering quantities for substitutable products with stock-dependent demand, Appl. Math. Model., 2015, 39 (1), 147-164.
• [13] LI H., YOU T., Capacity commitment and pricing for substitutable products under competition, J. Sys. Sci. Sys. Eng., 2012, 21 (4), 443-460.
• [14] LI X., NUKALA S., MOHEBBI S., Game theory methodology for optimizing retailers' pricing and shelf-space allocation decisions on competing substitutable products, Int. J. Adv. Manuf. Techn., 2013, 68, 375-389.
• [15] MISHRA B.K., RAGHUNATHAN S., Retailer-vs.-vendor-managed inventory and brand competition, Manage. Sci., 2004, 50 (4), 445-457.
• [16] PARLAR M., GOYAL S., Optimal ordering decisions for two substitutable products with stochastic demands, Opsearch, 1984, 21, 1-15.
• [17] PASTERNACK B., DREZNER Z., Optimal inventory policies for substitutable commodities with stochastic demand, Naval Res. Log., 1991, 38, 221-240.
• [18] PORRAS E., DEKKER R., An efficient optimal solution method for the joint replenishment problem with minimum order quantities, Eur. J. Oper. Res., 2006, 174 (3), 1595-1615.
• [19] PORRAS E., DEKKER R., Generalized solutions for the joint replenishment problem with correction factor, Int. J. Prod. Econ., 2008, 113 (2), 834-851.
• [20] RASOULI N., NAKHAI KAMALABADI I., Joint pricing and inventory control for seasonal and substitutable goods mentioning the symmetrical and asymmetrical substitution, Int. J. Eng., Trans., C. Aspects, 2014, 27, 9, 1385-1394.
• [21] SALAMEH M.K., YASSINE A.A., MADDAH B., GHADDAR L., Joint replenishment model with substitution, Appl. Math. Model., 2014, 38 (14), 3662-3671.
• [22] SCHULZ A., TELHA C., Approximation algorithms and hardness results for the joint replenishment problem with constant demands, Lecture Notes Comp. Sci., 2011, 6942, 628-639.
• [23] XUE Z., SONG J., Demand management and inventory control for substitutable products, Working paper, The Fuqua School of Business, Duke University, Durham 2007.
• [24] YE T., Inventory management with simultaneously horizontal and vertical substitution, Int. J. Prod. Econ., 2014, 156, 316-324.
• [25] ZHAO J., WEI J., LI Y., Pricing decisions for substitutable products in a two-echelon supply chain with firms different channel powers, Int. J. Prod. Econ., 2014, 153, 243-252.

Identyfikatory

DOI

10.5277/ord170105