temporary sale problem with unknown termination date, The

INFOR, Feb 2001 by F J Arcelus, T P M Pakkala, G Srinivasan

THE TEMPORARY SALE PROBLEM WITH UNKNOWN TERMINATION DATE1

ABSTRACT

Temporary sales are quite prevalent in practice, due to the changing power patterns between retailers and manufacturers, which has tended to shift sales promotion policies away from advertising and more towards price promotions. This paper models a common practical situation not covered in the literature, namely the familiar "while supply lasts" case, where the ending date of the discount is unknown. This is done through the introduction of a decision variable - a reordering point inventory level, which triggers the need for a new order, if the existing inventory level does not exceed such a point.

RESUME

Les ventes temporaires sont assez courantes en pratique, dfi aux changes de pouvoir entre fabricants et detaillants, ce qui a conduit la promotion des ventes loin de la publicite et vers la promotion des prix. Cet article modele une situation pratique habituelle pas etudie auparavant. C'est a dire, le cas familier "pendant que durent les reserves", ou la date de fin de rabais est inconnue. Ceci est fait a travers de l'introduction d'une variable de decision - un niveau minimal d'inventoire necessaire pour faire une nouvelle commande, si le niveau actuel d'inventoire West pas superieur a ce minimum.

1. INTRODUCTION

This paper considers the decision process of a profit-maximizing retailer when a wholesaler unexpectedly announces a temporary sale, valid while supplies last and hence for an unknown duration. At issue is the evaluation of the trade-off between the lower purchasing costs per unit, obtained from acquiring merchandise at the cheaper price for a period of time that will end at a random point and the resulting higher inventory costs, arising from the acquisition of larger than normal order sizes. The model handles the uncertain ending date through the development of an ordering policy characterized by two decision variables, q and r. The latter is the reorder point defined as the inventory level which triggers the need for placing a new order, whenever the inventory level does not exceed such a point. The size of such an order is determined so as to bring the inventory level up to q + r. The ordering policy is also affected by the level of inventory on hand at the announcement time. Given the unexpected nature of the announcement, the retailer cannot adjust its policies beforehand to have no inventory at announcement time. Also, for reasons described later, consideration is given in this paper only to the class of (q, r) policies which result in equal-order sizes and reorder points for all ordering cycles. Such equal-size (q, r) heuristics are operationally quite popular, due to the easiness with which they can be implemented, even though they don't necessarily yield optimal solutions.

Temporary sale announcements, with retailers being offered price discounts while supplies last, in exchange for an increase in the size of their orders, are well known, specially in the non-durable consumer goods sector (e.g. Blattberg and Neslin, 1990; The Economist, 1998). Examples of this practice occur due to overestimation of demand on the part of the wholesaler/manufacturer or at "demand disruption" times, i.e. when transportation strikes, floods or other calamities prevent a vendor, manufacturer or wholesaler, from delivering the merchandise to the usual markets. Then, the question for the manufacturer is how to liquidate this unwanted merchandise as expeditiously as possible in other markets where deliveries are still possible and the question for the retailer is to develop the appropriate ordering policy in response to the unexpected announcement of a temporary sale of random duration. In more general terms, whenever a vendor needs to dispose of unwanted merchandise, one-time-only sales have become a staple in retailing, even if its profitability has been brought into question (e.g. Lal, et al., 1996) and despite the push towards "every-day-low-purchase-price" strategies, themselves also in question (e.g. Hoch, et al, 1994). Further, the main rationale for the saliency of temporary sales is the changing manufacturing-retailer relationship, in favour of the latter. Such change has been well documented for many sectors of the economy, such as food, hardware, furniture, apparel and the like (e.g. Buzzell, et al, 1990; Fisher and Roman, 1996; Kumar, 1996; Messinger and Narashimhan, 1995). One of its main consequences is the increase in the importance of price reduction tools at the expense of advertising within the firm's overall sales promotion strategy (e.g. Blattberg, et al, 1995).

In view of this increase in its applicability, the temporary price discount problem has been lately subject to a wide variety of revisions, in an effort to adapt the original model of Baker (1976) to more modern concerns. Baker's (1976) study includes the standard temporary sales, deterministic, cost-minimizing, constant-demand model which appears in many textbooks of the subject (e.g. Tersine, 1994). The retailer is confronted with a special sale opportunity at a point in time where the inventory level is zero. The discount period is a one-time-only offer (take it or leave it). At issue is the determination of the special quantity to order so as to minimize the costs of ordering and holding and purchasing. Extensions to this basic model have dealt with the price/demand relationship (e.g. Arcelus and Srinivasan, 1998; Ardalan, 1991), the length of the discount period (e.g. Arcelus and Srinivasan, 1992, 1995; Ardalan, 1988; Aull-Hyde, 1992; Tersine and Gengler, 1982; Tersine and Grasso, 1978; Tersine and Price, 1981; Tersine and Schwarzkopf, 1989), various cost structures (e.g. Tersine and Barman, 1995), distribution of discount benefits (Arcelus and Srinivasan, 1998), level of initial inventory at the time of announcement (e.g. Arcelus and Srinivasan, 1992; Ardalan, 1988; Aull-Hyde, 1996), backlogging (Aull-Hyde, 1996) and simultaneous fluctuations of various parameters (e.g. Lev and Weiss, 1990).