Gerardo Berbeglia

A Hybrid Tabu Search and Constraint Programming Algorithm for the Dynamic Dial-a-Ride Problem

This paper introduces a hybrid algorithm for the dynamic dial-a-ride problem in which service requests arrive in real time. The hybrid algorithm combines an exact constraint programming algorithm and a tabu search heuristic. An important component of the tabu search heuristic consists of three scheduling procedures that are executed sequentially. Experiments show that the constraint programming algorithm is sometimes able to accept or reject incoming requests, and that the hybrid method outperforms each of the two algorithms when they are executed alone.

Checking the Feasibility of Dial-a-Ride Instances Using Constraint Programming

In the dial-a-ride problem (DARP), a fleet of vehicles must serve transportation requests made by users that need to be transported from an origin to a destination. In this paper we develop the first exact algorithm which is able to either efficiently prove the infeasibility or to provide a feasible solution. Such an algorithm could be used in a dynamic setting for determining whether it is possible or not to accept an incoming request. The algorithm includes solution space reduction procedures, and filtering algorithms for some DARP relaxations. Computational results show that the filtering algorithms are effective and that the resulting algorithm is advantageous on the more constrained instances.

The benefits of social influence in optimized cultural markets.

Social influence has been shown to create significant unpredictability in cultural markets, providing one potential explanation why experts routinely fail at predicting commercial success of cultural products. As a result, social influence is often presented in a negative light. Here, we show the benefits of social influence for cultural markets. We present a policy that uses product quality, appeal, position bias and social influence to maximize expected profits in the market. Our computational experiments show that our profit-maximizing policy leverages social influence to produce significant performance benefits for the market, while our theoretical analysis proves that our policy outperforms in expectation any policy not displaying social signals. Our results contrast with earlier work which focused on showing the unpredictability and inequalities created by social influence. Not only do we show for the first time that, under our policy, dynamically showing consumers positive social signals increases the expected profit of the seller in cultural markets. We also show that, in reasonable settings, our profit-maximizing policy does not introduce significant unpredictability and identifies “blockbusters”. Overall, these results shed new light on the nature of social influence and how it can be leveraged for the benefits of the market.

Counting feasible solutions of the traveling salesman problem with pickups and deliveries is #P-complete

Deciding whether or not a feasible solution to the Traveling Salesman Problem with Pickups and Deliveries (TSPPD) exists is polynomially solvable. We prove that counting the number of feasible solutions of the TSPPD is hard by showing that the problem is #P-complete.

Assortment Optimisation under a General Discrete Choice Model: A Tight Analysis of Revenue-Ordered Assortments

The assortment problem in revenue management is the problem of deciding which subset of products to offer to consumers in order to maximise revenue. A simple and natural strategy is to select the best assortment out of all those that are constructed by fixing a threshold revenue π and then choosing all products with revenue at least π. This is known as the revenue-ordered assortments strategy. Our first contribution is an analysis of the performance of the revenue-ordered assortments strategy making only minimal assumptions about the underlying discrete choice model: We assume that consumers behave rationally, in the sense that the probability of choosing a specific product x ∈ S when given a choice set S cannot increase if S is enlarged. This rationality assumption, known as regularity, is satisfied by almost all models studied in the revenue management and choice theory literature. This includes in particular all random utility models, as well as other models introduced recently such as the additive perturbed utility model, the hitting fuzzy attention model, and models obtained using a non-additive random utility function. We provide three types of revenue guarantees for revenue-ordered assortments: If there are k distinct revenues r1, r2, ..., rk associated with the products (listed in increasing order), then revenue-ordered assortments approximate the optimum revenue to within a factor of (A) 1/k; (B) 1/(1 + ln(rk/r1)), and (C) 1/(1 + ln υ), where υ is defined with respect to an optimal assortment S* as the ratio between the probability of just buying a product and that of buying a product with highest revenue in S*. These three guarantees are in general incomparable, that is, (A), (B), or (C) can be the largest depending on the instance. We also show that the three bounds (A), (B), and (C) are exactly tight, in the sense that none of the bounds remains true if multiplied by a factor (1+ ε) for any ε > 0. When applied to the special case of Mixed MNL models, bound (B) improves the recent analysis of revenue-ordered assortments by Rusmevichientong et al.(POMS, 2014), who showed a bound of 1/(e(1 + ln(rk/r1))). Our second contribution is to draw a connection between assortment optimisation and some pricing problems studied in the theoretical computer science literature by showing that these pricing problems can be restated as an assortment problem under a discrete choice model satisfying the above-mentioned rationality assumption. This includes unit demand envy-free pricing problems and the Stackelberg minimum spanning tree problem. Building on that connection, we then observe that a well-studied heuristic in that area called uniform pricing corresponds in fact to the revenue-ordered assortment strategy for the specifically constructed discrete choice models. As a consequence, our revenue guarantees for revenue-ordered assortments apply. Interestingly, the resulting bounds match and unify known results on uniform pricing that were proved separately in the literature for the envy-free pricing problems and the Stackelberg minimum spanning tree problem. This paper is available at https://arxiv.org/abs/1606.01371

Pricing policies for selling indivisible storable goods to strategic consumers

We study the dynamic pricing problem faced by a monopolistic retailer who sells a storable product to forward-looking consumers. In this framework, the two major pricing policies (or mechanisms) studied in the literature are the preannounced (commitment) pricing policy and the contingent (threat or history dependent) pricing policy. We analyse and compare these pricing policies in the setting where the good can be purchased along a finite time horizon in indivisible atomic quantities. First, we show that, given linear storage costs, the retailer can compute an optimal preannounced pricing policy in polynomial time by solving a dynamic program. Moreover, under such a policy, we show that consumers do not need to store units in order to anticipate price rises. Second, under the contingent pricing policy rather than the preannounced pricing mechanism, (i) prices could be lower, (ii) retailer revenues could be higher, and (iii) consumer surplus could be higher. This result is surprising, in that these three facts are in complete contrast to the case of a retailer selling divisible storable goods (Dudine et al. in Am Econ Rev 96(5):1706–1719, 2006). Third, we quantify exactly how much more profitable a contingent policy could be with respect to a preannounced policy. Specifically, for a market with N consumers, a contingent policy can produce a multiplicative factor of

Discrete choice models based on random walks

\Omega (\log N)

Bargaining Mechanisms for One-Way Games

Ω(logN) more revenues than a preannounced policy, and this bound is tight.