* Corresponding author. Tel.: 1-405-744-5105; fax: 1-405-744- 5180. E-mail address: wendy@okway.okstate.edu (H.S. Lau) Int. J. Production Economics 66 (2000) 1}12 Demand uncertainty and returns policies for a seasonal product: An alternative model Amy Hing-Ling Lau, Hon-Shiang Lau*, Keith D. Willett College of Business Administration, Oklahoma State University, 201 Stillwater, OK 74078-055, USA Received 4 August 1998; accepted 25 May 1999 Abstract Marvel and Peck [International Economic Review 36 (1995) 691}714] considered the following seasonal-product problem: A manufacturer sets wholesale price ($p  /unit) and return credit ($r/unit); the retailer then sets retailer price ($p  /unit) and order quantity (Q). How should the manufacturer set p  and r? Demand uncertainty consists of two components: `valuationa and `customers' arrivalsa. Our more realistic models reveal e!ects unobservable from Mar- vel}Peck's. E.g.: (i) Setting r'0 bene"ts the manufacturer much more than the retailer. (ii) `Valuationa (but not `customer-arrivala) uncertainty is imperative for the retailer; without it, the manufacturer can set p  and r such that he reaps most of the pro"ts.  2000 Elsevier Science B.V. All rights reserved. Keywords: Newsboy problem; Pricing; Returns policy; Demand uncertainty; Supply-chain interaction 1. Introduction Recently, Marvel and Peck [1] posed the follow- ing problem in the economics literature: The manufacturer wholesales a product to the retailer for $p  /unit. Units of the product that the retailer could not sell may be returned to the manufacturer for a $r/unit reimbursement. The retailer buys Q units from the manufacturer and attempts to retail them to his customers at $p  /unit. For any given p  and r set by the manufacturer, the retailer will set p  and Q that maximize the retailer's own expected pro"t. Re- cognizing this, how would (or should) the manu- facturer set p  and r? The model used by Marvel and Peck [1] to answer the above questions uses a couple of key assumptions. There are several di!erent plausible variations of these assumptions; unfortunately, us- ing a di!erent variation leads to very di!erent model behavior (i.e., conclusions on how the manu- facturer and retailer would/should set their prices and quantities). The purposes of this paper are to: (i) present some realistic variations of the Mar- vel}Peck (hereafter `MPa) model; (ii) sketch the necessary solution methodologies for these vari- ations; and (iii) use the numerical solutions ob- tained from the modi"ed models to present alternative answers to the question posed by MP. It will be seen that the answers obtained with our models di!er considerably from the answers ob- tained from MP's model. This paper assumes fam- iliarity with MP's [1] paper, and uses as much as possible the same symbols de"ned there; also, their 0925-5273/00/$ - see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 5 2 7 3 ( 9 9 ) 0 0 0 8 4 - 5