Target market selection and marketing effort under uncertainty: The selective newsvendor

Abstract

We consider a firm that markets, procures, and delivers a good with a single selling season in a number of different markets. The price for the good is market-dependent, and each market has an associated demand distribution, with parameters that depend on the amount of marketing effort applied. Given long procurement lead-times, the firm must decide which markets it will serve prior to procuring the good. We develop a profit maximizing model to address the firm’s integrated market selection, marketing effort, and procurement decisions. The model implicitly accounts for inventory pooling across markets, which reduces safety stock costs but increases model complexity. The resulting model is a nonlinear integer optimization problem, for which we develop specialized solution methods. For the case in which budget constraints exist, we provide a novel solution approach that uses a tailored branch-and-bound algorithm. Our approach solves a broad range of 3000 test instances in an average of less than 2 seconds, significantly outperforming a leading commercial global optimization solver.

Introduction

For products with short life cycles, effective operations and market planning are required to assess whether sales of a good will be profitable. This is especially true in the technology and fashion goods sectors, where low production costs often imply long procurement lead times. In such contexts, firms who market and sell such items must therefore place orders with low-cost suppliers far in advance of the selling season, and obtaining additional replenishments during the selling season often comes at a high cost. When committing to an initial supply quantity with a low cost supplier prior to observing demand, a number of planning decisions must be made, as the seller’s demand (which drives the initial procurement quantity) depends on the markets it chooses to supply and the amount of marketing effort applied in these markets.

As product life cycles decrease and assessing market entry risk becomes more critical, suppliers often find themselves faced with similar issues to those addressed in this paper. Claritas [8], a market research and strategic planning firm, cites several clients, including Eddie Bauer, who desire better knowledge of customers in order to minimize demand risk. Claritas [8] provides many success stories in assessing potential markets for suppliers of durable goods. Recently, Fisher, Raman, and McClelland [12] surveyed 32 leading retailers—all of which offer short-life-cycle products with unpredictable demand—to determine how effectively each company uses available data to understand customers. The majority of these retailers state that they must make better use of demand information in order to make profitable market selections. Carr and Lovejoy [6] also cite experience with an industrial product supplier who desires a strategy for selecting appropriate demands (or markets), while working within production capacity limits. In order to address these issues, we provide a model that can be used to justify where a seller should apply marketing effort, how it should set its capacity to satisfy demand, and which markets it should ultimately serve in order to maximize profit. The resulting model leads to an interesting new nonlinear and integer optimization problem, for which we develop tailored solution methods. Not only does this work provide contributions to the operations management and operations research methodologies literature, but it also addresses demand management and the interface between marketing and operations.

Many researchers have contributed to stream of the literature on stochastic inventory control and the newsvendor problem, for which Porteus [21] presents a nice overview. More recently, a review by Tsay, Nahmias, and Agrawal [28] provides research directions concerning supply chain contracts and competitive inventory management in the context of a single-period newsvendor setting. Moon and Silver [19] present heuristic approaches for solving the multi-item newsvendor problem with a budget constraint. While somewhat similar to our multiple-market problem, they require fixed demand distributions for every product. In contrast, we allow a supplier to “shape” the best demand distribution for a single product by selecting from different potential markets.

Another closely related stream of literature exists on demand selection problems. These models allow a supplier to choose which demands to serve and/or when to fulfill each demand, in contrast to typical product ordering-based decisions that do not consider the unique characteristics of customers. For deterministic demand selection models that address economic ordering decisions, multi-period lot sizing decisions with production capacity constraints, and lead-time flexibility of producers, see Geunes, Shen, and Romeijn [14], Taaffe and Geunes [26], and Charnsirisakskul, Griffin, and Keskinocak [7], respectively. Integrating pricing decisions into demand selection, Geunes, Romeijn, and Taaffe [13] study a production planning problem that addresses the relationship between product pricing and order acceptance/rejection decisions. Through these pricing decisions, the production planning model implicitly decides what demand levels the firm should satisfy in order to maximize contribution to profit after production.

Our work is based largely on the relationship between expected revenue and demand uncertainty, as is mean-variance optimization in portfolio management (see the seminal work by Markowitz [18]). The mean-variance approach attempts to achieve a desired rate of return while minimizing associated risk. We select an optimal set of markets based on expected revenues (or returns) and associated demand uncertainties (risk). Our modeling approach differs in that we do not place a minimum level on expected profit, nor do we focus on risk minimization while meeting a desired profit level. Moreover, we can influence the return of a selected market through advertising effort. For a more recent review of portfolio optimization and risk aversion, see Brealy and Myers [4].

Related papers on stochastic demand and demand selection include Petruzzi and Monahan [20], Carr and Duenyas [5], and Carr and Lovejoy [6]. Petruzzi and Monahan [20] address the choice between two demand sources, a primary and secondary (or outlet store) market. While these market demands might occur simultaneously, the firm must decide the preferred time to move the product to the secondary market. Carr and Duenyas [5] consider a sequential production system that receives demand for both make-to-stock and make-to-order products. A contractual obligation exists to produce make-to-stock demand, and the firm can supplement its production by accepting (and sequencing) additional make-to-order jobs in the production system. Carr and Lovejoy [6] examine an inverse newsvendor problem, which optimally chooses a demand distribution based on some pre-defined order quantity or capacity set by a supplier. Based on a set of demand portfolios, they determine the amount of demand to satisfy within each portfolio given that they cannot exceed some (a priori uncertain) capacity level. They also assume normality of demands and that all customer classes are priority ranked by some exogenous criteria. In contrast, we simultaneously select the set of demands to satisfy, the amount of advertising effort used to influence these demands, and an appropriate procurement quantity (which serves as our capacity level). Since the optimal choice of markets may change based on available marketing funds, we cannot provide an a priori ranking of demands, but allow the model to implicitly determine the most attractive set of markets.

The remainder of this paper is organized as follows. We define our base selective newsvendor model in Section 2, and show that although the resulting model is structurally identical to a class of optimization models found in the literature, the application to this context provides an intuitively appealing rule for comparing the attractiveness of different markets. In Section 3, we generalize the base model by accounting for the effect that targeted advertising has on individual market demand distributions. We address several functional forms of the advertising response function, assuming an unlimited budget or capacity. We then present the general selective newsvendor problem with limited market resources in Section 4, as well as a novel solution approach and computational results for the limited market resources problem. We summarize our findings in Section 5.