New product introduction against a predator: A bilevel mixed‐integer programming approach

Abstract

Abstract:We consider a scenario with two firms determining which products to develop and introduce to the market. In this problem, there exists a finite set of potential products and market segments. Each market segment has a preference list of products and will buy its most preferred product among those available. The firms play a Stackelberg game in which the leader firm first introduces a set of products, and the follower responds with its own set of products. The leader's goal is to maximize its profit subject to a product introduction budget, assuming that the follower will attempt to minimize the leader's profit using a budget of its own. We formulate this problem as a multistage integer program amenable to decomposition techniques. Using this formulation, we develop three variations of an exact mathematical programming method for solving the multistage problem, along with a family of heuristic procedures for estimating the follower solution. The efficacy of our approaches is demonstrated on randomly generated test instances. This article contributes to the operations research literature a multistage algorithm that directly addresses difficulties posed by degeneracy, and contributes to the product variety literature an exact optimization algorithm for a novel competitive product introduction problem.

Optimizing assortment and pricing of multiple retail categories with cross-selling

“…To incorporate this consumer choice model in a mathematical program for planning purposes, it is necessary to estimate reservation prices for different products across distinct customer segments. This can be achieved using different techniques, including conjoint analysis (see, for example, [12,13,16,17,19,34,35,42], and references therein).…”

A two-stage stochastic mixed-integer programming approach to the competition of biofuel and food production

“…The biofuel and food production problem is solved using CPLEX version 12.2 on a desktop computer with 3.40 GHz and 16 GB memory. The epsilon value (or duality gap tolerance), which gives the difference between the upper and lower bounds in the decomposition algorithm, is set to 0.01, similar to that of former research applying Benders decomposition (Freund, 2004;Smith et al, 2009). The solution time for the stochastic model and Benders decomposition is set to one hour (3,600 CPU seconds), since a memory problem is observed for longer times.…”

A mixed-integer bilevel programming approach for a competitive prioritized set covering problem

“…This concern is especially relevant in the presence of predatory firms that explicitly seek to minimize the leader's profit. Smith et al [30] study a two-stage product introduction game similar to the one mentioned above, but in which the follower seeks to minimize the leader's profit. In this case, the leader establishes a product introduction strategy that is robust to any possible actions taken by the follower.…”

“…The current study, by contrast, focuses on the case in which the follower simply acts to maximize its own profits rather than to minimize the leader's profits. It is worth noting that the algorithm employed in [30] is based on the principle that the leader's objective function is limited by the worst-possible follower's response to the leader's actions. As a result, this algorithm is not valid for the problem considered here, and the approach taken in the present paper must be fundamentally different from the one taken in [30].…”