We consider the revenue management problem of finding profit-maximising prices for delivery time slots in the context of attended home delivery. This multi-stage optimal control problem admits a dynamic programming formulation that is intractable for realistic problem sizes due to the so-called "curse of dimensionality". Therefore, we study three approximate dynamic programming algorithms both from a control-theoretical perspective and in a parametric numerical case study. Our numerical analysis is based on real-world data, from which we generate multiple scenarios to stress-test the robustness of the pricing policies to errors in model parameter estimates. Our theoretical analysis and numerical benchmark tests show that one of these algorithms, namely gradient-bounded dynamic programming, dominates the others with respect to computation time and profit-generation capabilities of the delivery slot pricing policies that it generates. Finally, we show that uncertainty in the estimates of the model parameters further increases the profit-generation dominance of this approach.
Same-day delivery for e-commerce has become a popular service. Companies usually offer several time delivery options with the earliest one being next hour delivery. Due to tight delivery deadlines and thin margins, companies often find it challenging to provide efficient same-day delivery services. In this work, we propose a holistic scheme that combines the optimization of routing and pricing for same-day delivery. The proposed approach is able to take into account uncertainty in travel times, a crucial factor for delivery applications in urban environments. We model this problem as a Markov …
We study the dynamic programming approach to revenue management in the context of attended home delivery. We draw on results from dynamic programming theory for Markov decision problems to show that the underlying Bellman operator has a unique fixed point. We then provide a closed-form expression for the resulting fixed point and show that it admits a natural interpretation. Moreover, we also show that -- under certain technical assumptions -- the value function, which has a discrete domain and a continuous codomain, admits a continuous extension, which is a finite-valued, concave function of …
A Pricing-for-Integrality Primal Heuristic for Branch-and-Price: An Application to the Electric Vehicle Routing Problem with Time Windows and Charging Time Slots
Motivated by issues dealing with delivery of emergency medical products during humanitarian disasters, this paper addresses the general problem of delivering perishable items to remote demands accessible only by helicopters or drones. Each drone operates out of platforms that may be move when not in use and each drone has a limited delivery range to service a demand points. Associated with each demand point is a disutility function, or a cost function, with respect to time that reflects preferred delivery clock time for the demanded item, as well as the item's perishability characteristic that…
We develop an asymptotic approximation and bounds for the traveling salesman problem with time slots, i.e. when the time windows of points to visit are a partition of a given time horizon. Although this problem is relevant in several delivery applications, operational research researchers did not pay close attention to it, contrary to the extensively studied general formulation with time windows. Exploiting the specificity of this problem allows to solve more efficiently instances which may be hard to solve by specifically designed algorithms for the traveling salesman problem with time window…
We consider dynamic programming problems with finite, discrete-time horizons and prohibitively high-dimensional, discrete state-spaces for direct computation of the value function from the Bellman equation. For the case that the value function of the dynamic program is concave extensible and submodular in its state-space, we present a new algorithm that computes deterministic upper and stochastic lower bounds of the value function similar to dual dynamic programming. We then show that the proposed algorithm terminates after a finite number of iterations. Finally, we demonstrate the efficacy of…
Price based demand response schemes may significantly improve power system efficiency. Additionally, it is desired that such schemes yield improved power operation, by reducing the peak consumption. This paper proposes the Intraday Block Pricing (IBP) scheme, aiming to promote effective demand response among consumers by charging their electricity usage based on intraday time-slots. To design the prices associated with the proposed scheme, we formulate a bilevel optimization problem that aims to minimize the Peak-to-Average Ratio (PAR) and simultaneously benefit the consumers and the utility c…
University of Nottingham（诺丁汉大学）；University of Nottingham Ningbo China（宁波诺丁汉大学）；The University of Melbourne（墨尔本大学）
Full truckload transportation (FTL) in the form of freight containers represents one of the most important transportation modes in international trade. Due to large volume and scale, in FTL, delivery time is often less critical but cost and service quality are crucial. Therefore, efficiently solving large scale multiple shift FTL problems is becoming more and more important and requires further research. In one of our earlier studies, a set covering model and a three-stage solution method were developed for a multi-shift FTL problem. This paper extends the previous work and presents a signific…
We consider stochastic dynamic programming problems with high-dimensional, discrete state-spaces and finite, discrete-time horizons that prohibit direct computation of the value function from a given Bellman equation for all states and time steps due to the "curse of dimensionality". For the case where the value function of the dynamic program is concave extensible and submodular in its state-space, we present a new algorithm that computes deterministic upper and stochastic lower bounds of the value function in the realm of dual dynamic programming. We show that the proposed algorithm terminat…
We propose a model of incentives for data pricing in large mobile networks, in which an operator wishes to balance the number of connections (active users) of different classes of users in the different cells and at different time instants, in order to ensure them a sufficient quality of service. We assume that each user has a given total demand per day for different types of applications, which he may assign to different time slots and locations, depending on his own mobility, on his preferences and on price discounts proposed by the operator. We show that this can be cast as a bilevel progra…
A Rolling-Space Branch-and-Price Algorithm for the Multi-Compartment Vehicle Routing Problem with Multiple Time Windows
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, USA（佐治亚理工学院H. Milton Stewart工业与系统工程学院）；Department of Operations and Decision Systems, Université Laval（拉瓦尔大学运营管理与决策系统系）
