LiBiT algorithm

The algorithm designed to solve static pricing problems under mixed multinomial logit deman

Stable allocations for choice-based collaborative price setting

Horizontal price agreements can fall within the scope of exemptions to antitrust competition if they are expected to create pro-consumer benefits. Inspired by such horizontal agreements, we introduce a cooperative game in which a set of transport operators can collectively decide at what price to offer sustainable urban mobility services to a pool of travelers. The travelers choose amongst the mobility services according to a multinomial logit model, and the operators aim at maximizing their joint profit under a constant market share constraint. After showing that various well-known allocation rules (i.e., proportional rules and the Shapley value) do not always generate core allocations, we present a core-guaranteeing allocation rule, the market share exchange rule. This rule first allocates to each transport operator the profit he or she generates under collaboration, and then subsequently compensates those transport operators that lose part of their market share, which is paid by the ones that receive some extra market share. This exchange of market share is facilitated by a unique price, which can be expressed as the additional return by cooperating per unit of market share. Finally, we show that, under some natural conditions, the market share exchange rule still sustains the collaboration when the transport operators need to pay back part of the joint profit to society

Static Pricing Problems under Mixed Multinomial Logit Demand

Price differentiation is a common strategy for many transport operators. In this paper, we study a static multiproduct price optimization problem with demand given by a continuous mixed multinomial logit model. To solve this new problem, we design an efficient iterative optimization algorithm that asymptotically converges to the optimal solution. To this end, a linear optimization (LO) problem is formulated, based on the trust-region approach, to find a "good" feasible solution and approximate the problem from below. Another LO problem is designed using piecewise linear relaxations to approximate the optimization problem from above. Then, we develop a new branching method to tighten the optimality gap. Numerical experiments show the effectiveness of our method on a published, non-trivial, parking choice model

LiBiT algorithm to solve static pricing problems under mixed multinomial logit demand

Price differentiation is a common strategy for many operators. We study a static multiproduct price optimization problem with demand given by a continuous mixed multinomial logit model. To solve this new problem, we design an efficient iterative optimization algorithm that asymptotically converges to the optimal solution. To this end, a linear optimization (LO) problem is formulated, based on the trust-region approach, to find a "good" feasible solution and approximate the problem from below. Another LO problem is designed using piecewise linear relaxations to approximate the optimization problem from above. Then, we develop a new branching method to tighten the optimality gap

An Adaptive Large Neighborhood Search Heuristic for Last-Mile Deliveries Under Stochastic Customer Availability and Multiple Visits

Attended Home Delivery, where customer attendance at home is required, is an essential last-mile delivery challenge, e.g., for valuable, perishable, or oversized items. Logistics service providers are often faced no-show customers. In this paper, we consider the delivery problem in which customers can be revisited on the same day by a courier in the case of a failed first delivery attempt. Specifically, customer presence uncertainty is considered in a two-stage stochastic program, where penalties are introduced as recourse actions for failed deliveries. We build on the notion of a customer availability profile defined as a profile containing historical time-varying probability information of successful deliveries. We tackle this stochastic program by developing an efficient parallelized Adaptive Large Neighborhood Search algorithm. Our results show that by achieving a right balance between increasing the hit rate and reducing travel cost, logistics service providers can realize costs savings as high as 32% if they plan for second visits on the same day