Ride-hailing services have expanded the role of shared mobility in passenger transportation systems, creating new markets and creative planning solutions for major urban centers. In this paper, we consider their use for the first-mile or last-mile passenger transportation in coordination with a mass transit service to provide a seamless multimodal transportation experience for the user. A system that provides passengers with predictable information on travel and waiting times in their commutes is immensely valuable. We envision that the passengers will inform the system of their desired travel and arrival windows so that the system can jointly optimize the schedules of passengers. The problem we study balances minimizing travel time and the number of trips taken by the last-mile vehicles, so that long-term planning, maintenance, and environmental impact are all taken into account. We focus on the case where the last-mile service aggregates passengers by destination. We show that this problem is NP-hard, and propose a decision diagram-based branch-and-price decomposition model that can solve instances of real-world size (10,000 passengers spread over an hour, 50 last-mile destinations, 600 last-mile vehicles) in computational time ( 1 minute) that is orders-of-magnitude faster than other methods appearing in the literature. Our experiments also indicate that aggregating passengers by destination on the last-mile service provides high-quality solutions to more general settings.

Statistical parity metrics have been widely studied and endorsed in the AI community as a means of achieving fairness, but they suffer from at least two weaknesses. They disregard the actual welfare consequences of decisions and may therefore fail to achieve the kind of fairness that is desired for disadvantaged groups. In addition, they are often incompatible with each other, and there is no convincing justification for selecting one rather than another. This paper explores whether a broader conception of social justice, based on optimizing a social welfare function (SWF), can be useful for assessing various definitions of parity. We focus on the well-known alpha fairness SWF, which has been defended by axiomatic and bargaining arguments over a period of 70 years. We analyze the optimal solution and show that it can justify demographic parity or equalized odds under certain conditions, but frequently requires a departure from these types of parity. In addition, we find that predictive rate parity is of limited usefulness. These results suggest that optimization theory can shed light on the intensely discussed question of how to achieve group fairness in AI.

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes.

Natural fractures in wells from oil-rich shale of the Upper Xiaganchaigou Formation in Qaidam Basin, the largest Cenozoic sedimentary basin in the Tibetan Plateau, vary systematically by stratigraphic position, allowing reconstruction of fracture generation processes during regional tectonic deformation. Compacted fractures, layerbounded fractures, and low-angle (or bed-parallel) fractures were widely identified in oil-rich shale cores obtained from vertical wells. The layer-bounded fractures can be subdivided into two sets: one prevalent in lightcolored (low gamma-ray) stiff layers and arrested by dark-colored (high gamma-ray) compliant layers, the other set primarily confined to the dark-colored compliant layers. The strikes of layer-bounded fractures, revealed by horizontal well FMI logs, are dominantly N60 degrees-80 degrees E and N10 degrees-30 degrees E within the light and dark intervals respectively. These strikes are consistent with natural hydraulic fracturing of the light layers during the Oligocene and the dark layers during the Middle Miocene-Holocene, based on a regional anticlockwise rotation of the compressional strain orientation. The abutment of layer-bounded fractures against low-angle (or bed-parallel) fractures in dark layers implies that the low-angle fractures were hydraulically fractured under a vertical least compressive stress during the Early Miocene, which produced the most intense tectonic compression. Layerbounded fractures generally remain unmineralized in the dark layers but were mineralized in the light layers, suggesting that fractures confined in light layers would not decrease the sealing capacity of the shale oil system and fractures confined in dark layers can increase the pore space of shale oil storage. The Oligocene and Early Miocene fractures represented mechanical flaws that affected the initiation of Middle Miocene-Holocene fractures, implying that all natural fractures may alter hydraulic fracture stimulations to some extent.

We revisit the question initially raised by Yuji Ijiri about the notion of fairness in accounting. We argue that the fairness question was important then and remains relevant today. First we situate Ijiri's question in relevant debates in the history of accounting thoughts and in contemporary debates. Then we develop a framework of fair flow of information for accounting practices. To do so, we draw upon deontological ethical theory and the generalization principle, in particular. We invite a counter-example from the game-theoretic phenomenon of signal jamming to challenge the generalization principle. By addressing the challenge, we further clarify the appropriate uses of the generalization principle.

This chapter develops the elementary theory of logic-based Benders decomposition (LBBD), beginning with the essential concept of inference duality. It formally states the LBBD algorithm and proves finite convergence when certain variables have finite domains, a condition normally satisfied in practice. It shows how classical Benders decomposition is a special case, and suggests some alternative perspectives on LBBD that provide additional insight. It then details how to exploit the common situation in which the Benders subproblem decouples into smaller problems. The chapter concludes with some practical guidelines for implementing an efficient LBBD algorothm.

Effective logic-based cuts are essential to the success of logic-based Benders decomposition, and this chapter shows how they can be designed to exploit problem structure. The most popular cuts used in practice are strengthened nogood cuts and analytical cuts. Nogood cuts are based on optimal values returned from the Benders subproblem, and several algorithms that strengthen them are presented. Analytical cuts are derived from an analysis of subproblem structure. The chapter presents a class of generic analytical cuts, followed by in-depth studies of domain-specific cuts for scheduling, vehicle routing, and packing problems, as demonstrations of how strong cuts can be fashioned. It concludes by showing how cuts can be obtained directly from a proof of optimality when it is available from the subproblem solver.

Introduction MERL Last Mile Problem Set At a Glance The size of the unzipped dataset is ~5.3MB The dataset contains the instances used in the manuscript "Seamless Multimodal Transportation Scheduling" by Raghunathan, Bergman, Hooker, Serra, and Kobori (see Citation section). Files in the unzipped folder: ./README.md express_500_10: Folder with instances. express_750_10: Folder with instances. express_1250_25: Folder with instances. express_1875_25: Folder with instances. ProblemObjectiveInformation.xlsx: Provides information on each problem instance including the optimal solution. regular_1000_10: Folder with instances. regular_1500_10: Folder with instances. regular_2000_10: Folder with instances. regular_2500_25: Folder with instances. regular_3750_25: Folder with instances. regular_5000_25: Folder with instances. regular_5000_50: Folder with instances. regular_7500_50: Folder with instances. regular_10000_50: Folder with instances. The instances of this problem set are organized in folders with names following the pattern regular_NP_ND and express_NP_ND, where NP and ND are the number of passengers and the number of destinations in the instances of the corresponding folder. Folders that begin with "regular" have uniform mass transportation service for all origins. Folders that begin with "express" have better mass transportation service for certain origins, as described below. Other Details In each folder, we have files with names following the patterns merl_lastmile_demand_NP_ND_TW_I.txt, merl_lastmile_arrivals_NP_ND.txt, and merl_lastmile_network_NP_ND.txt, where NP and ND are the number of passengers and the number of destinations as before. In addition, TW is the size of the time window (in minutes) and I is the number of the instance (from 1 to 5). Every instance corresponds to a combination of the passenger demands in each file that begins with "merl_lastmile_demand" along with the mass transportation services in the file that begin with "merl_lastmile_arrivals" and the last mile routes to each destination in the file that begins with "merl_last_mile_network". Those latter two files are unique in each folder and they can differ from the corresponding files in other folders that describe instances with the same number of destinations ND. Each file that begins with "merl_lastmile_demand" has the following structure. The first line contains the number N of mass transportation stations used as origin for the passengers. These stations are numbered from 1 to N. The second line contains the number M of locations used as last mile destinations for the passengers. These locations are numbered from 1 to M. The third line contains the number P of passengers. The next P lines describe the relevant information of each passenger as 4 integer numbers: their station of origin, last mile destination, earliest time for arrival at destination, and latest time for arrival at destination. Please note that those times are given in integer units that are multiples of 30 seconds. Each file that begins with "merl_lastmile_arrivals" has the following structure. The first line containts the number N of mass transportation stations used as origin for the passengers. These stations are numbered from 1 to N. The remaining lines describe transportation legs taking each passenger from their station of original to the alighting terminal in which they should board for their last mile trip. Each line describes a mass transit leg as 3 integer numbers: the station of origin, the departure time from the state of origin, and the arrival time at the alighting terminal. In practice, you can assume that all legs with the same arrival time correspond to a single mass transportation service. In the folders that begin with "express", the departure time for certain stations of origin is a very large negative number. That implies that, in practice, that mass transportation service does not serve the corresponding station. Please note that those times are given in integer units that are multiples of 30 seconds. Each file that begins with "merl_lastmile_network" has the following structure. The first line contains the number M of locations used as last mile destinations for the passengers. These locations are numbered from 1 to M. The second line contains the number L of time units for loading and unloading of passengers in the last mile service. This time should be added after the conclusion of every operation of loading or unloading passengers in the last mile service. The third line contains the number R of routes used for last mile service. Those routes are numbers from 0 to R-1. The remaining lines describe those routes by providing the times, relative to departure from the alighting terminal, that it takes for a given route to be in different locations. Each line describes that as 3 integer numbers: the last mile route in use, the last mile location, and the time relative to departure for reaching that location. Every route begins and ends at the alighting terminal, which is denoted as 0. The first line for each route has a time 0 at the alighting terminal and the last line for each route has the time to arrive back at the alighting terminal. Please note that those times as well as the duration L are given in integer units that are multiples of 30 seconds. Certain parameters of the experiments are not described in those files, such as the number and capacity of last mile vehicles. The coefficient alpha that is used to balance between minimizing passenger travel time and number of trips using last mile vehicles is also not given. The values described for those parameters are tested with all instances. Citation If you use LastMile-TestSet in your research, please cite our paper:@misc{raghunathan2022seamless, title={Seamless Multimodal Transportation Scheduling}, author={Arvind U Raghunathan and David Bergman and John Hooker and Thiago Serra and Shingo Kobori}, year={2022}, eprint={1807.09676}, archivePrefix={arXiv}, primaryClass={math.OC} } Copyright and License The LastMile-TestSet dataset is released under CC-BY-SA-4.0 license. All data:Created by Mitsubishi Electric Research Laboratories (MERL), 2020,2023 SPDX-License-Identifier: CC-BY-SA-4.0

This volume describes progress in understanding brittle structures in deep and ultra-deep (>4 km to > 7 km) sedimentary basins. Under deep conditions in sandstone, carbonate rocks, shale, and other rocks, fluid charge and resource recovery are sensitive to faults and opening-mode fractures. In China, work is in progress on deep, deformed, and tectonically active basins including drilling of wells expected to exceed 10 km in depth. Papers describing fractures in horizontal wells indicate locally highly clustered spatial arrangements. Orientation patterns record protracted superposed deformation. Despite deep settings, open fractures are abundant, and wide (>1 mm) fractures with varying amounts of sealing calcite are common. Differences in cement abundances are due to the diagenetic history of fractures, not their origins (e.g., tectonic loading or elevated pore fluid pressure). In carbonate rocks, solution enhanced strike-slip faults and fractures with cavernous porosity are present, and in sandstone enigmatic enhanced host-rock porosity halos a few mm wide locally surround sealed fractures. Owing to differences in thermal exposure due to recent (>6 Ma to present) rapid deep burial (in some cases >2000 m) and locally low geothermal gradients, some fractures at great depths are less diagenetically altered than those at shallower depths in the North American Cordillera. Contrasts in diagenesis may affect fracture size, spatial arrangement, and connectivity.

A small instance exemplifying the structure used in the paper is provided in the data folder. The collection of instances used in the paper and their description can be found in the website for the MERL Last Mile Problem Set.

The coefficient of variation (CV), or ratio of a population standard deviation to mean, can distinguish regular spacing (CV < 1) or clustering (CV > 1) from random sequences (CV = 1) in 1D spatial or time-series data. This technique is commonly applied to fracture spacing, with qualitative interpretations of the significance of the regularity or clusteredness. Here we use Monte Carlo simulations to derive robust confidence intervals for distinguishing 1D patterns from random signals using CV. Our simulations show that CV is negatively skewed for small fracture populations. We also present a new alternative statistic, CV', which is unbiased and retains the capability of CV to distinguish nonrandomness in 1D sequences.

Fracture networks play a significant role in controlling fluid flow in carbonate reservoirs. Here we have utilized a modern and rigorous technique known as normalized correlation count (NCC) to investigate the 1D spatial arrangement and size distribution of conductive opening-mode fractures in the Asmari Formation, a naturally fractured carbonate reservoir in the Zagros Fold and Thrust Belt. To overcome subsurface sampling limitations, here we integrate data from a subsurface fault-related fold called the Gachsaran anticline, and from adjacent outcrops. The Oligo-Miocene Asmari Formation is composed of three units with different lithology, thickness, and stratal geometry. Subsurface and outcrop data from the Asmari Formation have different patterns of spatial arrangements. While the fractures from outcrop anticlines show indistinguishable from random arrangements, the subsurface scanlines from the Gachsaran anticline have various clustering patterns, from self-organized regularly-spaced fracture clustering in the backlimb to externally-imposed clustering in the forelimb. The NW-SE striking fracture set in outcrops and subsurface show clustering. Aperture-size data for all fracture sets are best-fit by log-normal distributions, but sampling biases against the smallest apertures may obscure a power-law aperture-size distribution. Forcing the power-law fit to aperture-size distribution indicates steeper slopes in the backlimb and gentler slopes in the forelimb, which reflect lower and higher strain, respectively. This is consistent with higher tendency of clustering in the forelimb of the anticline which correlates with higher productivity index. Our results demonstrate the ability of NCC to identify hierarchical fracture clusters as well as to distinguish between self-organized and extrinsic organization. The results of quantitative analysis of fracture clustering and patterns in the Asmari Formation provides valuable insights that can aid in the refinement of Discrete Fracture Network (DFN) models and help make informed decisions regarding fractured reservoir development and production.

This chapter presents several variations and special cases of logic-based Benders decomposition (LBBD). The most important variation is branch and check, which solves the master problem only once. Other variations include enumerative methods, multilevel decomposition, and dynamic variable partitioning. Special cases include stochastic and robust LBBD and combinatorial Benders cuts for mixed integer programming. The chapter shows how a subproblem relaxation can be included in the master problem, often an essential part of successful implementations. It concludes with a discussion of automating LBBD in an off-the-shelf solver, and the pros and cons of doing so.

Optimization models typically seek to maximize overall benefit or minimize total cost. Yet fairness is an important element of many practical decisions, and it is much less obvious how to express it mathematically. We provide a critical survey of various schemes that have been proposed for formulating ethics-related criteria, including those that integrate efficiency and fairness concerns. The survey covers inequality measures, Rawlsian maximin and leximax criteria, convex combinations of fairness and efficiency, alpha fairness and proportional fairness (also known as the Nash bargaining solution), Kalai-Smorodinsky bargaining, and recently proposed utility-threshold and fairness-threshold schemes for combining utilitarian with maximin or leximax criteria. The paper also examines group parity metrics that are popular in machine learning. We present what appears to be the best practical approach to formulating each criterion in a linear, nonlinear, or mixed integer programming model. We also survey axiomatic and bargaining derivations of fairness criteria from the social choice literature while taking into account interpersonal comparability of utilities. Finally, we cite relevant philosophical and ethical literature where appropriate.

This talk introduces a concept of stochastic binary decision diagrams (stochastic BDDs). A BDD is a graphical representation of a Boolean function. Deterministic BDDs are well known in computer science, and weighted BDDs (in which arcs have costs) have been successfully applied to discrete optimization. We extend the concept to stochastic BDDs by associating each arc of the BDD with a probability as well as a control and a cost. Each control at a given node of the BDD results in several possible outcomes, each with a specified probability. We show that relaxation techniques that have been used for deterministic BDDs can be extended to stochastic BDDs. In particular, we develop sufficient conditions under which a node merger operation applied during top-down compilation yields a relaxed BDD of any desired size. This results in a general and completely novel method for deriving optimization bounds for stochastic dynamic programming models in which controls are state-dependent. We report computational experience with a stochastic maximum clique (maximum independent set) problem.

In this chapter, we address the problem of humanizing business when we must interact with intelligent robots and other AI systems, rather than real people, on a daily basis. There is a strong tendency to anthropomorphize pets and other animals that carries over to smart machines, leading us to replace human relationships with something less sophisticated and subtle. As a result, we argue, humanizing machines actually tends to dehumanize the workplace. We take an anthropological approach to this phenomenon that teaches three important lessons. One is that Western cultures have a particularly strong tendency to anthropomorphize machines, due to what Max Weber called the disenchantment of nature. Another is that humans have long interacted with intelligent nonhuman beings, such as domesticated work animals, without anthropomorphizing them. Finally, we can take a cue from these interactions to create analogous relationships with robots by neither humanizing nor objectifying them, but by relating to them in a manner that suits their capabilities. In particular, we can avoid anthropomorphism by involving workers in the training of AI systems, much as our ancestors trained domesticated animals, and by introducing ritual activities involving robots that clarify their ethical status and guide our interaction with them.

The primary role of cutting planes is to separate fractional solutions of the linear programming relaxation, which results in tighter bounds for pruning the search tree and reducing its size. Bounding, however, has an indirect impact on the size of the search tree. Cutting planes can also reduce backtracking by excluding inconsistent partial assignments that occur in the course of branching, which directly reduces the tree size. A partial assignment is inconsistent with a constraint set when it cannot be extended to a full feasible assignment. The constraint programming community has studied consistency extensively and used it as an effective tool for the reduction of backtracking. We extend this approach to integer programming by defining concepts of consistency that are useful in a branch-and-bound context. We present a theoretical framework for studying these concepts, their connection with the convex hull and their power to exclude infeasible partial assignments. We introduce a new class of cutting planes that target achieving consistency rather than improving dual bounds. Computational experiments on both synthetic and benchmark instances show that the new class of cutting planes can significantly outperform classical cutting planes, such as disjunctive cuts, by reducing the size of the search tree and the solution time. More broadly, we suggest that consistency concepts offer a new perspective on integer programming that can lead to a better understanding of what makes cutting planes work when used in branch-and-bound search.

We introduce stochastic decision diagrams (SDDs) as a generalization of deterministic decision diagrams, which in recent years have been used to solve a variety of discrete optimization and constraint satisfaction problems. SDDs allow one to extend the relaxation techniques of deterministic diagrams to stochastic dynamic programming problems in which optimal controls are state-dependent. In particular, we develop sufficient conditions under which node merger operations applied during top-down compilation of the SDD yield a valid relaxed SDD whose size can be limited as desired. The relaxed SDD provides bounds on the optimal value that can be used to evaluate the quality of solutions obtained heuristically or to accelerate the search for an optimal solution. This results in a general and completely novel method for obtaining optimization bounds for stochastic dynamic programming, and the only method that can be applied to the original state space. We report computational experience on stochastic maximum clique (equivalently, maximum independent set) problem instances.

We apply logic-based Benders decomposition (LBBD) to two-stage stochastic planning and scheduling problems in which the second stage is a scheduling task. We solve the master problem with mixed integer/linear programming and the subproblem with constraint programming. As Benders cuts, we use simple no-good cuts as well as analytic logic-based cuts we develop for this application. We find that LBBD is computationally superior to the integer L-shaped method. In particular, a branch-and-check variant of LBBD can be faster by several orders of magnitude, allowing significantly larger instances to be solved. This is due primarily to computational overhead incurred by the integer L-shaped method while generating classic Benders cuts from a continuous relaxation of an integer programming subproblem. To our knowledge, this is the first application of LBBD to two-stage stochastic optimization with a scheduling second-stage problem and the first comparison of LBBD with the integer L-shaped method. The results suggest that LBBD could be a promising approach to other stochastic and robust optimization problems with integer or combinatorial recourse. Summary of Contribution: We study an important class of optimization problems, namely, two-stage stochastic programs with integer recourse, which are known to be extremely difficult to solve in general. We focus on an application in which the second-stage problem is a scheduling problem, a first in the literature to the best of our knowledge. Our study exemplifies how one can exploit the combinatorial structure of the scheduling problem to derive novel analytic Benders cuts and use them within a branch-and-check algorithm. The proposed algorithm solves instances that are intractable for commercial solvers and state-of-the-art decomposition-based methods, such as the integer L-shaped method. We believe that our study will inspire further research in the use of hybrid logic-based optimization methods for solving stochastic combinatorial optimization problems.