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For educational purposes, medical residents often have to pass through many departments, which place different requirements on them. They are informed about the upcoming departments by an annual training schedule which keeps the individual departments’ service level as constant as possible. Due to poor planning and uncertain events, deviations in the schedule can occur. These deviations affect the service level in the departments, as well as the training progress and satisfaction of the residents. This article analyzes the impact of priorities on residents’ annual planning based on department assignments to combat uncertainty that might result in departmental changes. We present a novel two-stage formulation that combines residents’ tactical planning with duty and daily scheduling's operational level. We determine an analytical bound for the problem that is superior to the LP bound. Additionally, we approximate a bound based on the solution approach using the objective value of the deterministic solution of an instance and the absences in each scenario. In a computational study, we analyze the performance of various bounds, our solution approach, and the effects of additional priorities in residents’ annual planning. We show that additional priorities can significantly reduce the number of unexpected department assignments. Finally, we derive a practical number of priorities from the results.

We develop a neural network (NN) metamodeller for efficiently approximating the throughput of different finite-buffer multi-server tandem lines (with varying service rates, number of stations, buffers, and servers). The resulting NN serves as a quick performance evaluation tool and is subsequently used for optimising the tandem-line layout. Specifically, we discuss the optimal allocation of buffer places and optimising service rates where service rates at machines are associated with costs. Our NN metamodelling approach is new as we integrate (biased) analytical queuing knowledge into the training data. The setup and training of the NN metamodeller are discussed in the paper. In particular, we discuss the integration of analytical results from queuing theory. Our numerical studies corroborate the common belief that adding analytical knowledge (in this case from queueing theory) significantly improves the ensuing NN's prediction power. The framework developed in this paper demonstrates how analytical system knowledge can be integrated with data science in performance evaluation and optimisation. Our message is that even basic NNs, combined with formulae available from OR theory, offer invaluable improvements for building metamodellers in simulation optimisation.

Objectives Helicopter Emergency Medical Services (HEMS) throughout Europe are generally on scene within 10–15 minutes. In Norway, however, with its 13 HEMS bases, only 75% of the population can currently be reached within half an hour. We estimate the number of HEMS bases needed to reach the full Norwegian population within 10–15 minutes, and discuss implications regarding cost effectiveness. Methods Using geographic location and population characteristics from Norway’s 428 municipalities as input to the Maximal Covering Location Problem–a mathematical location optimization model–we estimate the number of HEMS bases required along with accompanying personnel and healthcare costs. We estimate the minimum number of lives that would have to be saved to achieve a net social benefit of zero. Results To reach 99% or 100% of the Norwegian population by HEMS within 15 minutes 78 or 104 bases are needed, respectively. The incremental need for personnel going from 20 to 15 minutes for 99/100% of the population is 602/728, with an accompanying incremental cost of 228/276 million EURO per year. A yearly total of 280/339 additional lives would have to be saved to obtain a net social benefit of zero. Then, the HEMS-system as a whole would be cost effective although the least efficient bases still would not be. Conclusions Reducing Norwegian HEMS response times to 10–15 minutes requires a drastic increase in the number of HEMS bases needed. Choice of ethical philosophy (utilitarianism or egalitarianism) determines when the expansion might be considered cost effective.

In this paper, we introduce the multiple Traveling Salesman Problem with Drone Stations (mTSP-DS), which is an extension to the classical multiple Traveling Salesman Problem (mTSP). In the mTSP-DS, we have a depot, a set of trucks, and some packet stations that host a given number of autonomous vehicles (drones or robots). The trucks start their mission from the depot and can supply some packet stations, which can then launch and operate drones/robots to serve customers. The goal is to serve all customers either by truck or by drones/robots while minimizing the makespan. We formulate the mTSP-DS as a mixed integer linear programming (MILP) model to solve small instances. To address larger instances, we first introduce two variants of a decomposition-based matheuristic. Afterwards, we suggest a third approach that is based on populating a solution pool with several restarts of an iterated local search metaheuristic, which is followed by determining the best combination of tours using a set-partitioning model. To verify the performance of our algorithms, we conducted extensive computational experiments. According to the numerical results, we observe that the use of drone stations leads to considerable savings in delivery time compared to traditional mTSP solutions. Furthermore, we investigated the energy consumption of trucks and drones. Indeed, depending on the energy consumption coefficients of trucks and drones as well as on the distance covered by drones, the mTSP-DS can also achieve energy savings in comparison to mTSP solutions.

Why are both A-1${\mathbf{A}}{-1}$ and (I-A)-1${(\mathbf{I}-\mathbf{A})}{-1}$ used in life cycle assessment (LCA) matrix computations? This is a question that, in our experience of teaching LCA, students often wonder about and struggle with. A brief survey of the literature suggests that the question can also confuse experienced LCA practitioners. Here, we seek to unify the computational structures of the two LCA approaches to achieve greater clarity and consistency, especially to make them easier to teach. We first show how small but crucial differences in the set-up of the two approaches lead to the use of A$\mathbf{A}$ versus I-A$\mathbf{I}-\mathbf{A}$. Then, we discuss the options to unify the presentations in a coherent way. We do not prescribe one way or the other. A larger point we hope to stress is the importance of unification, which may have both pedagogical and methodological benefits.

We introduce and study a class of optimization problems we call replenishment problems with fixed turnover times: a very natural model that has received little attention in the literature. Clients with capacity for storing a certain commodity are located at various places; at each client the commodity depletes within a certain time, the turnover time, which is constant but can vary between locations. Clients should never run empty. The natural feature that makes this problem interesting is that we may schedule a replenishment (well) before a client becomes empty, but then the next replenishment will be due earlier also. This added workload needs to be balanced against the cost of routing vehicles to do the replenishments. In this paper, we focus on the aspect of minimizing routing costs. However, the framework of recurring tasks, in which the next job of a task must be done within a fixed amount of time after the previous one is much more general and gives an adequate model for many practical situations. Note that our problem has an infinite time horizon. However, it can be fully characterized by a compact input, containing only the location of each client and a turnover time. This makes determining its computational complexity highly challenging and indeed it remains essentially unresolved. We study the problem for two objectives: min–avg minimizes the average tour cost and min–max minimizes the maximum tour cost over all days. For min–max we derive a logarithmic factor approximation for the problem on general metrics and a 6-approximation for the problem on trees, for which we have a proof of NP-hardness. For min–avg we present a logarithmic factor approximation on general metrics, a 2-approximation for trees, and a pseudopolynomial time algorithm for the line. Many intriguing problems remain open.

Concerns about greenhouse gas emissions and government regulations foster the use of electric vehicles. Several recently published articles study the use of electric vehicles (EVs) in node-routing problems. In contrast, this article considers EVs in the context of arc routing while also addressing practically relevant aspects that have not been addressed sufficiently so far. These include dynamic charging of EVs while driving, speed-dependent energy consumption, and nonlinear charging functions that depend on the battery’s state of charge and the charging time. A generic way of dealing with these aspects is introduced through the concept of an energy-indexed graph, which is used to derive an integer linear programming formulation and a solution framework based on branch and cut. Efficient construction heuristics and a local search for approximately solving large-scale instances are proposed. A computational study is performed on realistic problem instances. Besides analyzing the performance of all proposed methods, the obtained results also provide insights into strategic decisions related to the battery size and the amount of charging facilities.

We consider the distributed scheduling problem on parallel machines with the central objective of maximizing the number of on-time jobs. Jobs are self-interested utility-maximizers that can choose the machines they are processed on and are exclusively interested in reducing their own private objective function. Each machine processes the jobs according to a local policy. We discuss Nash equilibria in the resulting schedules and perform a thorough analysis of the resulting (absolute) prices of anarchy for various parallel machine environments, utilities of the agents, and local policies of the machines. We show that local policies that are based on simple sorting-based procedures like shortest processing time first (SPT) and earliest due date first (EDD) lead to big losses in welfare compared to the global optimum. However, when employing Moore-Hodgson’s algorithm as a local policy, we can prove a price of anarchy of ( 2 m − 1 ) / m for identical machines and a price of anarchy of 2 for related and unrelated parallel machines. Moreover, we show how these results can be used to prove approximation ratios for greedy scheduling algorithms. This paper is the first to prove approximation ratios for two greedy scheduling procedures, turning them from simple heuristics into actual approximation ratios with a provable approximation ratio.

Inspired by a real-life case in the Brussels Capital Region, Belgium, this paper provides a Memetic Algorithm with Sequential Split procedure (MASS) for solving a large variety of waste collection problems with multiple depots, a restricted vehicle fleet at each depot, multiple (intermediate) processing facilities, capacity restrictions per processing facility and partial pick-ups. MASS first generates satisfactory initial solutions which are feasible w.r.t. the shift duration and the vehicle capacity using a novel procedure in which (1) a giant tour is split into vehicle routes, (2) intermediate processing facilities are introduced and (3) waste pick-ups can be split further if profitable. Second, MASS improves these solutions through local search. New test instances are created, which are used to evaluate the performance of MASS's components. We show that MASS provides high-quality feasible solutions by comparing MASS with an exact approach on a small example. Furthermore, MASS is tested on existing instances for the multiple-depot vehicle routing problem (MDVRP), (multi-depot) vehicle routing problem with intermediate facilities ((MD)VRPIF) and the multi-depot vehicle routing problem with inter-depot routes (MDVRPI). MASS shows competitive results for the MDVRP, the VRPIF and the MDVRPI. For the MDVRPIF, MASS obtains better results than those currently found in the literature. To assess its practical value, MASS is used to solve a real-life waste collection problem in the Brussels Capital Region in which alternative scenarios for municipal bio-waste collection and treatment are compared.

A fortification game (FG) is a three-level, two-player hierarchical game, also known as defender-attacker-defender game, in which at the uppermost level, the defender selects some assets to be protected from potential malicious attacks. At the middle level, the attacker solves an interdiction game by depreciating unprotected assets, i.e., reducing the values of such assets for the defender, while at the innermost level the defender solves a recourse problem over the surviving or partially damaged assets. Fortification games have applications in various important areas, such as military operations, design of survivable networks, protection of facilities or power grid protection. In this work, we present an exact solution algorithm for FGs, in which the recourse problems correspond to (possibly NP-hard) combinatorial optimization problems. The algorithm is based on a new generic mixed-integer linear programming reformulation in the natural space of fortification variables. Our new model makes use of fortification cuts that measure the contribution of a given fortification strategy to the objective function value. These cuts are generated when needed by solving separation problems, which correspond to (modified) middle-level interdiction games. We design a branch-and-cut-based solution algorithm based on fortification cuts, their strengthened versions and other speed-up techniques. We present a computational study using the knapsack fortification game and the shortest path fortification game. For the latter one, we include a comparison with a state-of-the-art solution method from the literature. Our algorithm outperforms this method and allows us to solve previously unsolved instances with up to 330 386 nodes and 1 202 458 arcs to optimality.

The objective function of an optimisation model is the main driver for obtaining optimal values for decision variables. An objective function that does not well represent an inventory or production-inventory setting might then mislead the decision maker. There are two well-established frameworks for constructing the objective function of inventory or production-inventory models in an economic context; namely the Net Present Value approach and the average cost/profit approach. In recent years, a variant of the Net Present Value approach has been introduced and used by researchers which is actually a combination of the two main approaches. The researchers, however, provide little justification for this approach and its analytical foundation. In this research, we compare this approach with the two known approaches both analytically and numerically. The results of our study show that, under some circumstances, the new approach significantly deviates from the other two in terms of the optimal values for the decision variables and objective function.

Landside operations in air cargo terminals consist of many freight forwarders (FFWs) delivering and picking up cargo at the capacity-constrained loading docks at the airport's ground handlers' (GHs) facilities. To improve the operations of the terminal and take advantage of their geographical proximity a small set of FFWs can build a coalition to consolidate stochastically-arriving shipments and share truck fleet capacity while other FFWs continue bringing cargo to the terminal in a non-cooperative manner. Results from a detailed discrete-event simulation model of the cargo landside operations in Amsterdam Aiport showed that all operational policies had trade-offs in terms of the average shipment cycle time of coalition FFWs, the average shipment cycle time of non-coalition FFWs, and the total distance traveled by the coalition fleet, suggesting that horizontal cooperation in this context was not always beneficial, contrary to what previous studies on horizontal cooperation have found. Since dock capacity constitutes a significant constraint on operations in air cargo hubs, this paper also investigates the effect of dock capacity utilization and horizontal cooperation on the performance of consolidation policies implemented by the coalition. Thus, we built a general model of the air cargo terminal to analyze the effects caused by dock capacity utilization without the added complexity of landside operations at Amsterdam Airport to investigate whether the results hold for more general scenarios. Results from the general simulation model suggest that, in scenarios where dock and truck capacity become serious constraints, the average shipment cycle times of non-coalition FFWs are reduced at the expense of an increase in the cycle times of FFWs who constitute the coalition. A good balance among all the performance measures considered in this study is reached by following a policy that takes advantage of consolidating shipments based on individual visits to GH.

In this article, we examine how an Operational Research (OR) modeling approach can help in identifying how structural components in the supply process of a food product subject to a small probability of almost immediate failure affects the amount of waste arising at the retailer. This process can be viewed as the cumulative effect of various possible causes, including (apparent) product flaws and breakage. This category of waste, in contrast to products that are removed based on reaching their best before or use-by date, are also having little potential for redistribtion, and may thus be most targeted in future waste reduction legislative initiatives. We develop some relatively easy to calculate measures to help a retailer with identifying the financial implications of waste production in relation to some supply source characteristics, the financial motivation of its supplier to tackle item deterioration at the retailer level, and how this is affected by the level of logistics collaboration. We also discuss how the model can help in deriving the relative benefit of technological, logistical, supplier selection, and marketing strategies available to the retailer to meet future legislative waste reduction targets, and derive conclusions with respect to the design of legislative instruments.

Eco-efficiency is generally defined as the ratio of an economic and an environmental variable. This interpretation is also cited in connection to its most popular implementation, known as the "BASF eco-efficiency portfolio analysis". There is, however, something strange about this. A ratio is easily visualized as a slope, but BASF's method is working with a distance, which can be formulated as a weighted sum, not as a ratio. Upon closer analysis, it further shows that the two variables receive equal weight. These findings are contradicting the ISO 14045 standard and the perception in mainstream literature. We discuss the relevance of this shift of viewpoint. We also discuss some of the extensions, namely, the socio-efficiency analysis and the SEEbalance. We finally investigate the recent changes that were introduced in the eco-efficiency method, including an eco-efficiency index, and conclude that these changes have been reported in an incomplete way, or in documents that are difficult to trace. Effectively, this means that the most popular way to calculate and visualize eco-efficiency is unverifiable, impeding its status as a science-based method for sustainable industry support. We end by sketching the path forward.

Biofuel systems may represent a promising strategy to combat climate change by replacing fossil fuels in electricity generation and transportation. First-generation biofuels from sugar and starch crops for ethanol (a gasoline substitute) and from oilseed crops for biodiesel (a petroleum diesel substitute) have come under increasing levels of scrutiny due to the uncertainty associated with the estimation of climate change impacts of biofuels, such as due to indirect effects on land use. This analysis estimates the magnitude of some uncertainty sources: i) crop/feedstock, ii) life cycle assessment (LCA) modelling approach, iii) land-use change (LUC), and iv) greenhouse gas (GHG) metrics. The metrics used for characterising the different GHGs (global warming potential-GWP and global temperature change potential-GTP at different time horizons) appeared not to play a significant role in explaining the variance in the carbon footprint of biofuels, as opposed to the crop/feedstock used, the inclusion/exclusion of LUC considerations, and the LCA modelling approach (p

We establish sufficient conditions for differentiability of the expected cost collected over a discrete-time Markov chain until it enters a given set. The parameter with respect to which differentiability is analysed may simultaneously affect the Markov chain and the set defining the stopping criterion. The general statements on differentiability lead to unbiased gradient estimators.

In a recent paper, Sadhukhan et al. (2021) describe “the mathematics of life cycle sustainability assessment”. This is an ambitious task for a 12-page paper, given that a previous text on the mathematics of life cycle assessment (Heijungs and Suh, 2002) took 250 pages, for a smaller subject, and that another paper (Heijungs et al., 2013) which was more modest in announcing an approach “toward” the mathematics of life cycle sustainability assessment was already 12 pages. Of course, a paper from 2021 can build on and refer to such previous works, and thereby be more concise. The curious fact is, however, that Sadhukhan et al. (2021) do not refer to and neither build on those previous publications. They even ignore other related works that were published in the Journal of Cleaner Production, including Gwak et al. (2003), Suh and Huppes (2005), Heijungs and Suh (2006) and Islam et al. (2016).

This work deals with the weighted excesses of players in cooperative games which are obtained by summing up all the weighted excesses of all coalitions to which they belong. We first show that lexicographically minimizing the individual weighted excesses of players gives the same minimal weighted excess for every player. Moreover, we show that the associated payoff vector is the corresponding least square value. Second, we show that minimizing the variance of the players' weighted excesses on the preimputation set, again yields the corresponding least square value. Third, we show that these results give rise to lower and upper bounds for the core payoff vectors and, using these bounds, we define the weighted super core as a polyhedron that contains the core. It turns out that the least square values can be seen as a center of this weighted super core, giving a third new characterization of the least square values. Finally, these lower and upper bounds for the core inspire us to introduce a new solution for cooperative TU games that has a strong similarity with the Shapley value.

Over the past years, an increasing number of scholarly papers have used the planetary boundaries (PBs) within life cycle assessment (LCA) to determine if the life cycle impacts of a product system fit within those PBs and thereby establish the absolute sustainability of the product system. This type of LCA is nowadays coined as LCA-based Absolute Environmental Sustainability Assessment (AESA). “Absolute” thereby refers to methods enabling the comparison of environmental impacts of products, companies, nations, and so on, with an assigned share of environmental carrying capacity for various impact categories. A recent review of LCA-based AESA methods and their applications characterized 47 studies “according to their intended application, impact categories, basis of carrying capacity estimates, spatial differentiation of environmental model and principles for assigning carrying capacity.” However, the review and the majority of studies reviewed did not, or only to a limited extent, discuss potential temporal issues of assigning carrying capacity to product systems. Several of the carrying capacity estimates have a time dimension while LCA results lack a time dimension. In this article, we show that assigning PBs to product systems is only technically possible when adopting several fundamental though unrealistic assumptions, and conclude that even product LCA-based AESA is relative. This should not withhold scholars from developing approaches applying the PBs in LCA, but it should prevent them from claiming and using the term “absolute.”.

We investigate a new approach to compute the gradients of artificial neural networks (ANNs), based on the so-called push-out likelihood ratio method. Unlike the widely used backpropagation (BP) method that requires continuity of the loss function and the activation function, our approach bypasses this requirement by injecting artificial noises into the signals passed along the neurons. We show how this approach has a similar computational complexity as BP, and moreover is more advantageous in terms of removing the backward recursion and eliciting transparent formulas. We also formalize the connection between BP, a pivotal technique for training ANNs, and infinitesimal perturbation analysis, a classic path-wise derivative estimation approach, so that both our new proposed methods and BP can be better understood in the context of stochastic gradient estimation. Our approach allows efficient training for ANNs with more flexibility on the loss and activation functions, and shows empirical improvements on the robustness of ANNs under adversarial attacks and corruptions of natural noises. Summary of Contribution: Stochastic gradient estimation has been studied actively in simulation for decades and becomes more important in the era of machine learning and artificial intelligence. The stochastic gradient descent is a standard technique for training the artificial neural networks (ANNs), a pivotal problem in deep learning. The most popular stochastic gradient estimation technique is the backpropagation method. We find that the backpropagation method lies in the family of infinitesimal perturbation analysis, a path-wise gradient estimation technique in simulation. Moreover, we develop a new likelihood ratio-based method, another popular family of gradient estimation technique in simulation, for training more general ANNs, and demonstrate that the new training method can improve the robustness of the ANN.

Water consumption, energy use, and carbon emission are three related key anthropogenic impacts on the natural environment. China is the largest carbon emitter and energy consumer, with the serious unevenly distributed water resources. Therefore, investigating the water–energy–carbon (WEC) nexus is important for China's environmental footprint reduction. This study explores the relation between water utilization, energy consumption, and carbon emission in China, based on a multiregional input–output (MRIO) analysis. The WEC nexus is discussed comprehensively in consideration of the utilization of water and energy and the emission of carbon, as well as the trade to and from and the consumption activities in different sectors and provinces. Results show that water, energy, and carbon present significant consistency in production and consumption processes. Sectors with higher consumption coefficients dominate the transfer of virtual WEC. Although virtual WEC mainly transfers from less developed regions to relatively developed regions, Category 1 (i.e., WEC all import) and category 2 (i.e., WEC disaccord) present opposite results to and category 3 (i.e., WEC all export) provinces in terms of W–E and W–C nexus. The net water and energy transfers are significantly positively correlated in category 1 provinces, whereas both sides are negatively correlated in category 2 and 3 provinces. This phenomenon also exists in the relationship between net water and carbon transfers. The virtual water, as well as energy and carbon export pressures are dispersed in these export provinces. Findings of this study are expected to assist the government in decreasing the environmental footprints and achieve sustainable development in China.

We study an Inventory Routing Problem at the tactical planning level, where the initial inventory levels at the supplier and at the customers are decision variables and not given data. Since the total inventory level is constant over time, the final inventory levels are equal to the initial ones, making this problem periodic. We propose a class of matheuristics, in which a route-based formulation of the problem is solved to optimality with a given subset of routes. Our goal is to show how to design effective subsets of routes. For some of them, we prove effectiveness in the worst case, i.e., we provide a finite worst-case performance bound for the corresponding matheuristic. Moreover, we show they are also effective on average, in a large set of instances, when some additional routes are added to this subset of routes. These solutions significantly dominate, both in terms of cost and computational time, the best solutions obtained by applying a branch-and-cut algorithm we design to solve a flow–based formulation of the problem.

Inspired by an automated teller machine (ATM) cash replenishment problem involving population coverage requirements (PCRs) in the Netherlands, we propose the vehicle tour problem with minimum coverage requirements. In this problem, a set of minimum-cost routes is constructed subject to constraints on the duration of each route and the population coverage of the replenished ATMs. A compact formulation incorporating a family of valid inequalities and an efficient tour-splitting metaheuristic are proposed and tested on 77 instances derived from real-life data involving up to 98 ATMs and 237,604 citizens and on 144 newly generated synthetic instances. Our results for the real-life instances indicate significant cost differences in replenishing ATMs for seven major Dutch cities when the PCRs vary. Additionally, we illustrate the impact of different PCRs on the ATM replenishment costs for seven major cities in the Netherlands by presenting an aggregated cost evaluation of 11 PCRs involving 1,003,519 citizens, 338 ATMs, and 19 cash distribution vehicles.

We consider budget feasible mechanisms for procurement auctions with additive valuation functions. For the divisible case, where agents can be allocated fractionally, there exists an optimal mechanism with approximation guarantee e/ (e- 1 ) under the small bidder assumption. We study the divisible case without the small bidder assumption, but assume that the true costs of the agents are bounded by the budget. This setting lends itself to modeling economic situations in which the goods represent time and the agents’ true costs are not necessarily small compared to the budget. Non-trivially, we give a mechanism with an approximation guarantee of 2.62, improving the result of 3 for the indivisible case. Additionally, we give a lower bound on the approximation guarantee of 1.25. We then study the problem in more competitive markets and assume that the agents’ value over cost efficiencies are bounded by some θ≥ 1. For θ≤ 2, we give a mechanism with an approximation guarantee of 2 and a lower bound of 1.18. Finally, we extend these results to settings with different agent types with a linear capped valuation function for each type.

This article presents a prediction model of the optimal dual variables for the cutting stock problem. For this purpose, we first analyze the influence of different attributes on the optimal dual variables within an instance for the cutting stock problem. We apply and compare our predictions in a stabilization technique for column generation. In most studies, the parameters for stabilized column generation are determined by numerical tests, that is, the same problem is solved several times with different settings. We develop two learning algorithms that predict the best algorithm configuration based on the predicted optimal dual variables and thus omit the numerical study. Our extensive computational study shows the tradeoff between the learning algorithms using full and sparse instance information. We show that both algorithms can efficiently predict the optimal dual variables and dominate the common update mechanism in a generic stabilized column generation approach. Although the learning algorithm with full instance information is applicable when one has to solve the problem mainly for a fixed set of items, the algorithm with sparse instance information is applicable when there is more variability in the number of items between the different instances. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2023.1277 .

The growing water scarcity due to international trade poses a serious threat to global sustainability. Given the intensified international trade throughout the Belt and Road Initiative (BRI), this paper tracks the virtual water trade and water footprint of BRI countries in 2005–2015. By conducting a multi-model assessment, we observe a substantial increase in BRI's water footprint after taking water scarcity into account. Globally the BRI acts as a net exporter of virtual water, while the export volume experiences a decreasing trend. Noticeable transitions in nations' role (net exporters vs. net importers) are found between the BRI and global scales, but also between with and without considering water scarcity. Overall economic and population growth is major drivers of scarcity-weighted water footprint for BRI nations, as opposed to the promotion of water-use efficiency and production structure that can reduce water scarcity. Improving international trade and strengthening cooperation on water resources management deserve priority in alleviating the water scarcity of BRI.

We study the computation and efficiency of pure Nash equilibria in combinatorial congestion games, where the strategies of each player i are given by the binary vectors of a polytope $$P_i$$ P i . Our main goal is to understand which structural properties of such polytopal congestion games enable us to derive an efficient equilibrium selection procedure to compute pure Nash equilibria with attractive social cost approximation guarantees. To this aim, we identify two general properties of the underlying aggregation polytope$$P_N = \sum _i P_i$$ P N = ∑ i P i which are sufficient for our results to go through, namely the integer decomposition property (IDP) and the box-totally dual integrality property (box-TDI). Our main results for polytopal congestion games satisfying IDP and box-TDI are as follows: (i) we show that pure Nash equilibria can be computed in polynomial time. In fact, we obtain this result through a general framework for separable convex function minimization, which might be of independent interest. (ii) We bound the inefficiency of these equilibria and show that this provides a tight bound on the price of stability. (iii) We also prove that these results extend to strong equilibria for the “bottleneck variant” of polytopal congestion games. Examples of polytopal congestion games satisfying IDP and box-TDI include common source network congestion games, symmetric totally unimodular congestion games, non-symmetric matroid congestion games and symmetric matroid intersection congestion games (in particular, r-arborescences and strongly base-orderable matroids).

To ensure the correct functioning of district heating networks and minimize critical failures, utilities allocate every year a significant part of their budget to maintenance operations. In the present work we describe a risk-based approach implemented to tackle the problem of designing optimal multi-year maintenance campaigns, applied to the Italian city of Brescia, showing how data-driven techniques can help decision makers assess the long terms impacts of budget allocations.

This paper presents a column-and-constraint generation algorithm for two-stage stochastic programming problems. A distinctive feature of the algorithm is that it does not assume fixed recourse and as a consequence the values and dimensions of the recourse matrix can be uncertain. The proposed algorithm contains multi-cut (partial) Benders decomposition and the deterministic equivalent model as special cases and can be used to trade-off computational speed and memory requirements. The algorithm outperforms multi-cut (partial) Benders decomposition in computational time and the deterministic equivalent model in memory requirements for a maintenance location routing problem. In addition, for instances with a large number of scenarios, the algorithm outperforms the deterministic equivalent model in both computational time and memory requirements. Furthermore, we present an adaptive relative tolerance for instances for which the solution time of the master problem is the bottleneck and the slave problems can be solved relatively efficiently. The adaptive relative tolerance is large in early iterations and converges to zero for the final iteration(s) of the algorithm. The combination of this relative adaptive tolerance with the proposed algorithm decreases the computational time of our instances even further.

In this paper, we will shed light on when to pack and use 3D-printers in disaster response operations. For that, we introduce a new type of problem, which we call the two-stage stochastic 3D-printing knapsack problem. We provide a two-stage stochastic programming formulation for this problem, for which both the first and the second stage are NP-hard integer linear programs. We reformulate this formulation to an equivalent integer linear program, which can be efficiently solved by standard solvers. Our numerical results illustrate that for most situations using a 3D-printer is beneficial. Only in extreme circumstances, where the quality of printed items is extremely low, the size of the 3D-printer is extremely large compared to the knapsack size, when there is no time to print the items, or when demand for items is low, packing no 3D-printers is the best option.

The large arcsine exponential dispersion model (LAEDM) is a class of three-parameter distributions on the non-negative integers. These distributions show the specific characteristics of being leptokurtic, zero-inflated, overdispersed, and skewed to the right. Therefore, these distributions are well suited to fit count data with these properties. Furthermore, recent studies in actuarial sciences argue for the consideration of such distributions in the computation of risk factors. In this paper, we provide a thorough analysis of the LAEDM by deriving (a) the mean value parameterization of the LAEDM; (b) exact expressions for its probability mass function at (Formula presented.) ; (c) a simple bound for these probabilities that is sharp for large n; (d) a simulation algorithm for sampling from LAEDM. We have implemented the LAEDM for statistical modeling of various real count data sets. We assess its fitting performance by comparing it with the performances of traditional counting models. We use a simulation algorithm for computing tail probabilities of the aggregated claim size in an insurance risk model.

In this paper, we propose a fast and scalable, yet effective, metaheuristic called FILO to solve large-scale instances of the Capacitated Vehicle Routing Problem. Our approach consists of a main iterative part, based on the Iterated Local Search paradigm, which employs a carefully designed combination of existing acceleration techniques, as well as novel strategies to keep the optimization localized, controlled, and tailored to the current instance and solution. A Simulated Annealing-based neighbor acceptance criterion is used to obtain a continuous diversification, to ensure the exploration of different regions of the search space. Results on extensively studied benchmark instances from the literature, supported by a thorough analysis of the algorithm’s main components, show the effectiveness of the proposed design choices, making FILO highly competitive with existing state-of-the-art algorithms, both in terms of computing time and solution quality. Finally, guidelines for possible efficient implementations, algorithm source code, and a library of reusable components are open-sourced to allow reproduction of our results and promote further investigations.

Weighted flow time is a fundamental and very well-studied objective function in scheduling. In this paper, we study the setting of a single machine with preemptions.The input consists of a set of jobs, characterized by their processing times, release times, and weights and we want to compute a (possibly preemptive) schedule for them. The objective is to minimize the sum of the weighted flow times of the jobs, where the flow time of a job is the time between its release date and its completion time.It had been a long-standing open problem to find a polynomial time O(1)-approximation algorithm for this setting. In a recent break-through result, Batra, Garg, and Kumar (FOCS 2018) found such an algorithm if the input data are polynomially bounded integers, and Feige, Kulkarni, and Li (SODA 2019) presented a black-box reduction to this setting. The resulting approximation ratio is a (not explicitly stated) constant which is at least 10000. In this paper we improve this ratio to 2+ε. The algorithm by Batra, Garg, and Kumar (FOCS 2018) reduces the problem to Demand MultiCut on trees and solves the resulting instances via LP-rounding and a dynamic program. Instead, we first reduce the problem to a (different) geometric problem while losing only a factor 1+ε, and then solve its resulting instances up to a factor of 2+ε by a dynamic program. In particular, our reduction ensures certain structural properties, thanks to which we do not need LP-rounding methods.We believe that our result makes substantial progress towards finding a PTAS for weighted flow time on a single machine.

Matching with preferences has great potential to coordinate the efficient allocation of scarce resources in organizations when monetary transfers are not available and thus can provide a powerful design principle for information systems. Unfortunately, it is well known that it is impossible to combine all three properties of truthfulness, efficiency, and fairness (i.e., envy freeness) in matching with preferences. Established mechanisms are either efficient or envy free, and the efficiency loss in envy-free mechanisms is substantial. We focus on a widespread representative of a matching problem: course assignment where students have preferences for courses and organizers have priorities over students. An important feature in course assignment is that a course has both a maximum capacity and a minimum required quota. This is also a requirement in many other matching applications, such as school choice, hospital-residents matching, or the assignment of workers to jobs. We introduce Extended Seat Prioritized Clinch and Trade with a widened Range of guarantees (RESPCT), a mechanism that respects minimum quotas and is truthful, efficient, and has low levels of envy. The reduction in envy is significant and is due to two remarkably effective heuristics. We follow a design science approach and provide analytical and experimental results based on field data from a large-scale course assignment application. These results have led to a policy change, and the proposed assignment system is now being used to match hundreds of students every semester.

In this article we deal with the main critical issues of using electric vehicles in urban transport given the battery related limitations on driving range, and the network layout related limitations on the number of recharging stations. In this context, we seek the optimal routing plans together with the optimal locations of recharging stations for electric vehicle fleets through the Electric Vehicle Location Routing Problem with Intermediate Nodes (ELRP-IN) we propose. The ELRP-IN we formulate as a mathematical program considers the actual characteristics of battery discharging and recovering the braking energy. Energy consumption and recovery are determined through vehicle motion dynamics in conjunction with the 3-dimensional feature of the road geometry, passengers'/customers' demands on getting on and off, and the pre-defined speed profiles, where the graph corresponding to the road network is extended with the explicit consideration of intersections. By alternating the objectives adopted in the ELRP-IN formulation, we discuss through a number of numerical experiments involving real case instances the effects of both the objective functions and the parameters, including the consumption and the gain of energy, cost, traveled distance, and travel time, on the routing plans. Highlighting the finding that energy is not recovered in all the sections with descending grade, we reveal the direct effect of the elevation on the energy consumption, and hence on the location of a recharging station, where we discuss as well the limitation on energy recovery.

In this paper, we introduce a new, single-component model for maintenance optimization under time-varying costs, specifically oriented at offshore wind turbine maintenance. We extend the standard age replacement policy (ARP), block replacement policy (BRP) and modified block replacement policy (MBRP) to address time-varying costs. We prove that an optimal maintenance policy under time-varying costs is a time-dependent ARP policy. Via a discretization of time, the optimal time-dependent ARP can be found using a linear programming formulation. We also present mixed integer linear programming models for parameter optimization of BRP and MBRP. We present a business case and apply our policies for maintenance planning of a wind turbine gearbox and show that we can achieve savings up-to 23%.

Introduction Many methodological papers report a comparison of methods for LCA, for instance comparing different impact assessment systems, or developing streamlined methods. A popular way to do so is by studying the differences of results for a number of products. We refer to such studies as quasi-empirical meta-comparisons. Review of existing approaches A scan of the literature reveals that many different methods and indicators are employed: contribution analyses, Pearson correlations, Spearman correlations, regression, significance tests, neural networks, etc. Critical discussion We critically examine the current practice and conclude that some of the widely used methods are associated with important deficits. A new approach Inspired by the critical analysis, we develop a new approach for meta-comparative LCA, based on directional statistics. We apply it to several real-world test cases, and analyze its performance vis-à-vis traditional regression-based approaches. Conclusion The method on the basis of directional statistics withstands the tests of changing the scale and unit of the training data. As such, it holds a promise for improved method comparisons.

In the Unsplittable Flow on a Path problem (UFP) we are given a path with edge capacities, and a set of tasks where each task is characterized by a subpath, a demand, and a weight. The goal is to select a subset of tasks of maximum total weight such that the total demand of the selected tasks using each edge e is at most the capacity of e. The problem admits a QPTAS [Bansal, Chakrabarti, Epstein, Schieber, STOC'06; Batra, Garg, Kumar, Mömke, Wiese, SODA'15]. After a long sequence of improvements [Bansal, Friggstad, Khandekar, Salavatipour, SODA'09; Bonsma, Schulz, Wiese, FOCS'11; Anagnostopoulos, Grandoni, Leonardi, Wiese, SODA'14; Grandoni, Mömke, Wiese, Zhou, STOC'18], the best known polynomial time approximation algorithm for UFP has an approximation ratio of 1+1/(e+1) + epsilon < 1.269 [Grandoni, Mömke, Wiese, SODA'22]. It has been an open question whether this problem admits a PTAS. In this paper, we solve this open question and present a polynomial time (1 + epsilon)-approximation algorithm for UFP.

Cooperative games with a permission structure are useful tools for analyzing the impact of hierarchical structures on allocation problems in Economics and Operations Research. In this paper, we propose a generalization of the local disjunctive and the local conjunctive permission approaches called the k-local permission approach. In this approach, every player needs permission from a certain number of its predecessors to cooperate in a coalition. The special case where every player needs permission from at least one of, respectively all, its predecessors coincides with the local disjunctive, respectively local conjunctive, approach in the literature. We de ne and characterize a corresponding k-local permission value. After that, we apply this value to de ne a new class of power measures for directed graphs. We axiomatize these power measures, and apply some of them to two classical networks in the literature.

This paper analyzes the allocation of the total toll collected in a highway among its segments. Based on different toll charging rules, we propose the Segments Equal Sharing method, the Exits Equal Sharing method, and the Entrances Equal Sharing method. We provide axioms and characterize these methods used to distribute the toll. Besides, we show how these methods can be obtained by applying the Shapley value to associated coalitional transferable utility games.

Dairy farms are systems with multiple dependent variables whose practices influence their economic and environmental performances. Decisions made and actions taken to improve environmental performances of dairy farms carry the risk of decreasing farm profitability. Correlations among multiple variables must therefore be considered to reliably assess risks of improving environmental performances of farms. We applied copula models to a dataset of conventional dairy farms surveyed in France to decscribe relationships among their characteristics, such as forage dry matter (DM) production, milk production, and greenhouse gas (GHG) emissions. By modeling relationships among farm characteristics, copula models can identify the characteristics’ joint distributions, unlike other statistical methods. For dairy farms, copula models are useful for estimating probabilities of reaching a milk production goal or not exceeding a regulatory emission limit as a function of forage production. For instance, when a farm produced at least 4,500 kg DM/livestock unit/year of maize silage, the probability of producing at least 7,000 l milk/cow/year was 75%, while the probability of emitting less than 7,000 kg CO2 eq./farm/year (a value close to the mean of 6669 kg CO2 eq./farm/year for all of the farms) was 48%. When the same amount of grass from pasture was produced, these probabilities changed to 48% and 78%, respectively (i.e., decreased probability of reaching a production goal, but increased probability of not exceeding an emission threshold). Farmers must make trade-offs, since increased milk production goals are likely to increase GHG emissions per farm and/or reduce GHG emission intensities per l of milk, but are less likely to be reached for a given amount of forage DM. By providing information about relationships among farm characteristics that other statistical approaches cannot, copula models are useful for investigating these trade-offs.

This paper deals with the problem of modelling complex transaction cost structures within portfolio management models in an efficient and effective way. We consider a general structure of transaction costs, where the applied commissions depend on the range of traded monetary amount and we use this general structure within a portfolio optimization problem with rebalancing decisions in response to new market conditions. The presence of transaction costs reduces the fund’s capital and should be properly accounted for to avoid substantial costs that impact on portfolio performance. In this paper we present a mixed integer model equipped with a specialized Branch and Bound method that exploits the specific formulation of the trading operations. Computational experiments, carried out on transaction cost structures offered by real-life traders, have shown the effectiveness of the proposed model and the computational efficiency of the solution approach.

In the Inventory Routing Problem, customer demand is satisfied from inventory which is replenished with capacitated vehicles. The objective is to minimize total routing and inventory holding cost over a time horizon. If the customers are located relatively close to each other, one has the opportunity to satisfy the demand of a customer by inventory stored at another nearby customer. In the optimization of the customer replenishments, this option can be included to lower total costs. This is for example the case for ATMs in urban areas where an ATM-user that wants to withdraw money could be redirected to another ATM. To the best of our knowledge, the possibility of redirecting end-users is new to the operations research literature and has not been implemented, but is being considered, in the industry. We formulate the Inventory Routing Problem with Demand Moves in which demand of a customer can (partially) be satisfied by the inventory of a nearby customer at a service cost depending on the quantity and the distance. We propose a branch-price-and-cut solution approach which is evaluated on problem instances from the literature. Cost improvements over the classical IRP of up to 10% are observed with average savings around 3%.

Efficiently handling last-mile deliveries becomes more and more important nowadays. Using drones to support classical vehicles allows improving delivery schedules as long as efficient solution methods to plan last-mile deliveries with drones are available. We study exact solution approaches for some variants of the traveling salesman problem with drone (TSP-D) in which a truck and a drone are teamed up to serve a set of customers. This combination of truck and drone can exploit the benefits of both vehicle types: the truck has a large capacity but usually low travel speed in urban areas; the drone is faster and not restricted to street networks, but its range and carrying capacity are limited. We propose a compact mixed-integer linear program (MILP) for several TSP-D variants that is based on timely synchronizing truck and drone flows; such an MILP is easy to implement but nevertheless leads to competitive results compared with the state-of-the-art MILPs. Furthermore, we introduce dynamic programming recursions to model several TSP-D variants. We show how these dynamic programming recursions can be exploited in an exact branch-and-price approach based on a set partitioning formulation using ng-route relaxation and a three-level hierarchical branching. The proposed branch-and-price can solve instances with up to 39 customers to optimality outperforming the state-of-the-art by more than doubling the manageable instance size. Finally, we analyze different scenarios and show that even a single drone can significantly reduce a route’s completion time when the drone is sufficiently fast.

A recent study on alternative road materials concluded that the cost associated with noise-related health impacts would favour one type of material. In the analysis, the noise of road and vehicles was allocated fully to the road. If we would only allocate a part to the road and the rest to the vehicles, an opposite conclusion could be drawn. We therefore argue for a closer study of this allocation problem, and for the use of sensitivity analyses as long as no good solution has been found.

Influence maximization aims at identifying a limited set of key individuals in a (social) network which spreads information based on some propagation model and maximizes the number of individuals reached. We show that influence maximization based on the probabilistic independent cascade model can be modeled as a stochastic maximal covering location problem. A reformulation based on Benders decomposition is proposed and a relation between obtained Benders optimality cuts and submodular cuts for correspondingly defined subsets is established. We introduce preprocessing tests, which allow us to remove variables from the model and develop efficient algorithms for the separation of Benders cuts. Both aspects are shown to be crucial ingredients of the developed branch-and-cut algorithm since real-life social network instances may be very large. In a computational study, the considered variants of this branch-and-cut algorithm outperform the state-of-the-art approach for influence maximization by orders of magnitude.