Anticipative Dynamic Slotting for Attended Home Deliveries

Attended home delivery requires offering narrow delivery time slots for online booking. Given a fixed fleet of delivery vehicles and uncertainty about the value of potential future customers, retailers have to decide about the offered delivery time slots for each individual order. To this end, dynamic slotting techniques compare the reward from accepting an order to the opportunity cost of not reserving the required delivery capacity for later orders. However, exactly computing this opportunity cost means solving a complex vehicle routing and scheduling problem. In this paper, we propose and evaluate several dynamic slotting approaches that rely on an anticipatory, simulation-based preparation phase ahead of the order horizon to approximate opportunity cost. Our approaches differ in their reliance on outcomes from the preparation phase (anticipation) versus decision making on request arrival (flexibility). For the preparation phase, we create anticipatory schedules by solving the Team Orienteering Problem with Multiple Time Windows. From stochastic demand streams and problem instance characteristics, we apply learning models to flexibly estimate the effort of accepting and delivering an order request. In an extensive computational study, we explore the behavior of the proposed solution approaches. Simulating scenarios of different sizes shows that all approaches require only negligible run times within the order horizon. Finally, an empirical scenario demonstrates the concept of estimating demand model parameters from sales observations and highlights the applicability of the proposed approaches in practice.

GNOME: A Dynamic Dispatch and Investment Optimisation Model of the European Natural Gas Network and Its Suppliers

As indigenous production declines, the European gas market is becoming increasingly dependent on imports. This poses energy security questions for a number of countries, particularly in the north-east of Europe. A suite of mathematical models of the European natural gas network has been borne from these concerns and has traditionally been used to assess supply disruption scenarios. The literature reveals that most existing European gas network models are insufficiently specified to analyse changes in supply and demand dynamics, appraise proposed infrastructure investments, and assess the impacts of supply disruption scenarios over a range of time horizons. Furthermore, those that are suited to these applications are typically proprietary and therefore publicly unavailable. This offers an opportunity to present a new model. The Gas Network Optimisation Model for Europe (GNOME) is a dynamic, highly granular mixed-integer linear optimisation model of the European natural gas network and its exogenous suppliers. GNOME represents demand and supply for all EU-27 Member States except Cyprus, Luxembourg, and Malta. The UK, Norway, Switzerland, Belarus, Ukraine, and Turkey are also included. Russia, the Southern Corridor suppliers, Qatar, North Africa, Nigeria, and the Americas are modelled as supply-only regions. GNOME satisfies gas demand in each country by generating a cost-minimal mix of indigenous gas production, pipeline flows, LNG imports, and storage use. If demand cannot be met using existing infrastructure, GNOME will generate a cost-optimal investment strategy of pipeline, LNG regasification, and gas storage capacity additions. The model solves on a monthly basis, from 2025 to 2040, in 5-year steps. The capabilities of GNOME are demonstrated by tasking it to analyse the impacts of a failure to complete the upcoming Nord Stream 2 pipeline between Russia and Germany. The complete formulation of GNOME including input files, equations, and source code is provided.

Consumer Optimization and a First-Order PDE with a Non-Smooth System

We study a first-order nonlinear partial differential equation and present a necessary and sufficient condition for the global existence of its solution in a non-smooth environment. Using this result, we prove a local existence theorem for a solution to this differential equation. Moreover, we present two applications of this result. The first concerns an inverse problem called the integrability problem in microeconomic theory and the second concerns an extension of Frobenius’ theorem.

Secretary Problem: Graphs, Matroids and Greedoids

In the paper, the generalisation of the well-known “secretary problem” is considered. The aim of the paper is to give a generalised model in such a way that the chosen set of the possible best k elements have to be independent of all previously rejected elements. The independence is formulated using the theory of greedoids and in their special cases—matroids and antimatroids. Examples of some special cases of greedoids (uniform, graphical matroids and binary trees) are considered. Applications in cloud computing are discussed.