A stochastic and asymmetric-information framework for a dominant-manufacturer supply chain. (English) Zbl 1137.90351

Summary: Consider a dominant manufacturer wholesaling a product to a retailer, who in turn retails it to the consumers at $ p/unit. The retail-market demand volume varies with p according to a given demand curve. This basic system is commonly modeled as a manufacturer-Stackelberg ([mS]) game under a “deterministic and symmetric-information” (“det-sym-i”) framework. We first explain the logical flaws of this framework, which are (i) the dominant manufacturer-leader will have a lower profit than the retailer under an iso-elastic demand curve; (ii) in some situations the system’s “correct solution” can be hyper-sensitive to minute changes in the demand curve; (iii) applying volume discounting while keeping the original [mS] profit-maximizing objective leads to an implausible degenerate solution in which the manufacturer has dictatorial power over the channel. We then present an extension of the “stochastic and asymmetric-information” (“sto-asy-i”) framework proposed by A. Lau and H.-S. Lau [Eur. J. Oper. Res. 161, No. 1, 203–223 (2005; Zbl 1067.90117)], coupled with the notion that a profit-maximizing dominant manufacturer may implement not only [mS] but also “[pm]”–i.e., using a manufacturer-imposed maximum retail price. We show that this new framework resolves all the logical flaws stated above. Along the way, we also present a procedure for the dominant manufacturer to design a profit-maximizing volume-discount scheme using stochastic and asymmetric demand information.Using our sto-asy-i framework to resolve the logical flaws of the det-sym-i framework also reveals two noteworthy points: (i) the attractiveness of the perfectly legal but overlooked channel-coordination mechanism [pm]; and (ii) volume discounting as a means for the dominant manufacturer to benefit from information known only to the retailer.


90B10 Deterministic network models in operations research
90B05 Inventory, storage, reservoirs


Zbl 1067.90117
Full Text: DOI


[1] Arcelus, F.J.; Srinivasan, G., Inventory policies under various optimizing criteria and variable markup rates, Management science, 33, 6, 756-762, (1987)
[2] Corbett, C.J.; Zhou, D.; Tang, C.S., Designing supply contracts: contract type and information asymmetry, Management science, 50, 4, 550-559, (2004) · Zbl 1232.90036
[3] Deneckere, R.; Marvel, H.P.; Peck, J., Demand uncertainty and price maintenance: markdowns as destructive competition, American economic review, 87, 4, 619-641, (1997)
[4] Dowrick, S., Von Stackelberg and Cournot duopoly: choosing roles, The rand journal of economics, 17, 2, 251-260, (1986)
[5] Ertek, G.; Griffin, P.M., Supplier- and buyer-driven channels in a two-stage supply chain, IIE transactions, 34, 8, 691-700, (2002)
[6] Flath, D.; Nariu, T., Demand uncertainty and resale price maintenance, Contemporary economic policy, 18, 4, 397-403, (2000)
[7] Gal-Or, E., First mover and second mover advantages, International economic review, 26, 3, 649-653, (1985) · Zbl 0573.90106
[8] Gogeshvili, M., Resale price maintenance—a dilemma in EU competition law, Georgian law review, 5, 2/3, 281-317, (2002)
[9] Ha, A.Y., Supplier-buyer contracting: asymmetric cost information and cutoff level policy for buyer participation, Naval research logistics, 48, 1, 41-64, (2001) · Zbl 0981.90036
[10] IMSL Math/Library, 1994. Visual Numerics, Texas.
[11] Lau, H.-S.; Lau, A., Manufacturer’s pricing strategy and return policy for a single-period commodity, European journal of operational research, 116, 2, 291-304, (1999) · Zbl 1009.90005
[12] Lau, A.; Lau, H.-S., Effects of a demand-curve’s shape on the optimal solutions of a multi-echelon inventory/pricing model, European journal of operational research, 147, 3, 530-548, (2003) · Zbl 1026.90002
[13] Lau, A.; Lau, H.-S., Some two-echelon supply-chain games: improving from deterministic – symmetric-information to stochastic – asymmetric-information models, European journal of operational research, 161, 1, 203-223, (2005) · Zbl 1067.90117
[14] Levy, M.; Weitz, B.A., Retail management, (2001), McGraw-Hill/Irwin Boston
[15] Li, S.X.; Huang, Z.M.; Zhu, J.; Chau, P.Y.K., Cooperative advertising, game theory and manufacturer – retailer supply chains, Omega, 30, 5, 347-357, (2002)
[16] Parlar, M.; Wang, Q., Discounting decisions in a supplier – buyer relationship with a linear buyer’s demand, IIE transactions, 26, 2, 34-41, (1994)
[17] Pasternack, B.A., Using revenue sharing to achieve channel coordination for a newsboy type inventory model, (), 117-136 · Zbl 1175.90033
[18] Reiffen, D., On the equivalence of resale price maintenance and quantity restrictions, International journal of industrial organization, 17, 2, 277-288, (1999)
[19] Tsay, A.A., The quantity flexibility contract and supplier – customer incentives, Management science, 45, 10, 1339-1358, (1999) · Zbl 1231.90065
[20] Viswanathan, S.; Wang, Q., Discount pricing decisions in distribution channels with price-sensitive demand, European journal of operational research, 149, 3, 571-587, (2003) · Zbl 1033.90006
[21] Weng, Z.K., Modeling quantity discounts under general price-sensitive demand functions: optimal policies and relationships, European journal of operational research, 86, 2, 300-314, (1995) · Zbl 0906.90102
[22] Weng, Z.K., Channel coordination and quantity discounts, Management science, 41, 9, 1509-1522, (1995) · Zbl 0861.90067
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.