Coordination of Pricing and Order Quantity for Two Replaceable and Seasonal Products

Document Type : Original Article

Authors

1 Department of Industrial and System Engineering, Tabriat Modares University, Iran

2 Group for Research in Decision Analysis (GERAD), HEC Montreal University, Canada

3 Department of Industrial Engineering, University of Kurdistan, Kurdistan, Iran

Abstract

This paper deals with the coordination of pricing and order quantity decisions for two seasonal and substitutable goods in one firm. We assume that the customers are price sensitive and they are willing to buy the cheaper products, which is known as one way and customers-based price driven substitution. First, a mathematical model is developed for one firm, which contains two replaceable products considering seasonality. The model aims to maximize the profit by determining optimal dynamic prices, order quantities and the number of periods for both of the products. Then, we show that the objective function is strictly concave of price and has a unique maximum solution. Next, an exact algorithm based on the Karush Kuhn Tucker (KKT) conditions is presented to determine the optimal decisions. Finally, a numerical example accompanied by sensitivity analysis on key parameters  is developed  to illustrate the efficiency of solution procedure and the algorithm.

Keywords


1. Zhang, C,T., Wang, H,X. and Ren, M,L,” Research on pricing and
coordination strategy of green supply chain under hybrid 
production mode”, Computers and Industrial Engineering, Vol.
72, (2014), 24-31. 
2. Xie, Y., Tai, A,H. Ching, W,K. and Siu, T,K, “ Pricing strategy for
a two-echelon supply chain with optimized return effort level”,
International Journal of Production Economics, Vol. 182,
(2016), 185-195. 
3. Seifbarghy, M., Kalaei, M. and Rasouli, N, “ Supplier selection and
order quantity assignment using conditional entropy and
Chebyshev goal programming approach”, 12th International
Conference of Iranian Operations Research Society, (2019),
4337- 4350. 
4. Li, Y., Zhang, S. and Han, J, “Dynamic pricing and periodic
ordering for a stochastic inventory system with deteriorating
items”, Automatica, Vol. 76, (2017), 200-213. 
5. Shaikh, A.A., Khan, M.A.A., Panda, G.C. and Konstantaras, I,
“Price discount facility in an EOQ model for deteriorating items
with stock-dependent demand and partial backlogging”,
International Transactions in Operational Research, Vol. 26,
No. 4, (2019), 1365-1396. 
6. Aviv, Y. and Pazgal, A,” Optimal Pricing of Seasonal Products in
the Presence of Forward-Looking Consumers and Prospects”,
Journal of Manufacturing and Service Operations
Management, Vol. 10, (2008), 339-359. 
7. You, S.P and Chen, C.T, “Dynamic pricing of seasonal goods with
spot and forward purchase demands”, Journal of Computers and
Mathematics with Applications, Vol. 54, (2007), 490–498. 
8. Chopra, S. and Meindle, P “Supply chain management Strategy,
Planning, and Operations (3rd Ed)”, New jersey: Prentice-Hall,
(2007). 
9. Transchel, S, “ Inventory management under price-based and
stockout-based substitution”, European Journal of Operational
Research, Vol. 262, No. 3, (2017), 996-1008  
10. Kim, S. and Bell, P.C, “Optimal pricing and production decision in
the presence of symmetrical and asymmetrical substitution”,
Omega, Vol. 39, (2011), 528-538. 
11. Rasouli, N. and Nakhai, I, “Joint Pricing and Inventory Control for
Seasonal and Substitutable Goods Mentioning the Symmetrical
and Asymmetrical Substitution”, International Journal of
Engineering Transaction C Aspects, Vol. 27, No. 9, (2014),
1385-1392. 
12. Wang, C., Huang, R. Pricing for seasonal deteriorating products
with price- and ramp-type time-dependent demand. Computers &
Industrial Engineering, Vol. 77, (2014), 29-34. 
13.  Due, J., Zhang, J. and Hua, G, “Pricing and inventory management
in the presence of strategic customers with risk preference and
decreasing value”, International Journal of Production
Economics, Vol. 164, (2015), 160-166. 
14. Rabbani, M., Pourmohammad Zia, N. and, Rafiei, H, “Joint optimal
dynamic pricing and replenishment policies for items with
simultaneous quality and physical quantity deterioration”,
Applied Mathematics and Computation, Vol. 287, (2016), 149160.
15.  Naimi Sadigh, A., Chaharsooghi, S. K. and Sheikhmohammady,
M, “A game theoretic approach to coordination of pricing,
advertising, and inventory decisions in a competitive supply
chain”, Journal of Industrial and Management Optimization,
Vol. 12, (2016), 337-355  
16. Aminnaseri, M. R. and Azari Khojasteh, M, “Price competition
between two leader–follower supply chains with risk-averse
retailers under demand uncertainty”, The International Journal
of Advanced Manufacturing Technology, Vol. 79, (2015), 377393.
17. Bian, W., Shang, J. and Zhang, J, “Two-way information sharing
under supply chain competition”, International Journal of
Production Economics, Vol. 178,  (2016), 82-94  
18. Taleizadeh, A.A. and Rasouli-Baghban A, “Pricing and lot sizing
of a decaying item under group dispatching with time-dependent
demand and decay Rates”, Scientia Iranica, Vol. 25, No. 3,
(2018), 1656-1670. 
19. Karakul, M. and Chan, L “Analytical and managerial implications
of integrating product substitutability in the joint pricing and
procurement problem”, European Journal of Operational
Research, Vol. 190,  ) 2008(, 179–204. 
20. Karakul, M. and Chan, L.M.A, “Joint pricing and procurement of
substitutable products with random demands- A technical note”,
European Journal of Operational Research, Vol. 201, (2010),
324-328. 
21.  Soleimani, F., Arshadikhamseh, A. and Naderi, B, “Optimal
decisions in a dual-channel supply chain under simultaneous
demand and production cost disruptions”, Annals of Operations
Research, (2014), 1-21  
22. Dong, L., Kouvelis, P. and Tian, Z, “Dynamic pricing and
inventory control of substitute products”, Journal of
manufacturing and service operations management, Vol. 11,
(2009), 317-339. 
23.
 Noori-daryan M., Taleizadeh, A.A. and Jolai, F, “Analyzing
pricing, promised delivery lead time, supplier-selection, and
ordering decisions of a multi-national supply chain under 
uncertain environment”,  International Journal of Production
Economics, Vol. 209, (2019), 236-248.
 
24. Moradinasab, N., Aminnaseri, M., Behbahani, T.J. and Jafarzadeh,
H, “Competition and cooperation between supply chains in multiobjective
petroleum green supply chain: A game theoretic
approach”, Journal of Cleaner Production, Vol. 170, (2018),
818-841. 
25. Elyasi, M., Jafarzadeh, H. and Khoshalhan, F, “An economical
order quantity model for items with imperfect quality: A noncooperative
dynamic
game
theoretical model”, 3
rd
 International
Logistics & Supply Chain Conference, (2012). 
26. Frasi, E., Yousefi Yegane, B. and Moniri, A, “Simultaneous
Pricing, Routing, and Inventory Control for Perishable Goods in
a Two-echelon Supply Chain”, International Journal of
Engineering Transaction A Basics, Vol. 31, No. 7, (2018), 10741081.
27. Fattahi, P., Tanhatalab, M. and Bashiri, M, “Bi-objectives
Approach for a Multi-period Two Echelons Perishable Product
Inventory-routing Problem with Production and Lateral
Transshipment”, International Journal of Engineering
Transaction C Aspects, Vol. 30, No. 6, (2017), 876-886.