Recourse Actions Research Articles

Optimizing Fleet Size in Point-to-Point Shared Demand Responsive Transportation Service: A Network Decomposition Approach

With increasing urbanization and the demand for efficient, flexible transportation solutions, demand-responsive transportation services (DTRS) has emerged as a viable alternative to traditional public transit. However, determining the optimal fleet size to balance the investment and operational revenue remains a significant challenge for service providers. In this article, we address the optimization of fleet size in point-to-point shared demand DRTS, which widely operates within many cities. To capture the uncertain passenger demands in the future when planning the fleet size currently, we model this problem with a framework of two-stage stochastic programming with recourse. Fleet sizing decisions are made in the first stage before the uncertain demands are revealed. After the uncertainty is revealed, the second stage involves making additional decisions to maximize operational revenue. The objective is to optimize the total revenue of the first-stage decisions and the expected revenue of the recourse actions. To solve this practical problem, we resort to the Model Predictive Control method (MPC) and propose a network decomposition approach that first converts the transportation network to a nodal tree structure and then develops a Nodal Tree Recourse with Dependent Arc Capacities (NTRDAC) algorithm to obtain the exact value of the expected recourse functions. In the experiments, NTRDAC is able to produce results within seconds for transportation networks with over 30 nodes. In contrast, a commercial solver is only capable of solving networks with up to five nodes. The stability tests show that NTRDAC remains robust as the problem size varies. Lastly, the value of the stochastic solution (VSS) was evaluated, and the results indicate that it consistently outperforms the expected value solutions. Numerical experiments show that the performance of the NTRDAC algorithm is quite encouraging and fit for large-scale practical problems.

Home-based care and center-based care: From being alternatives to being synergistic. Optimization models to support flexible care delivery

The delivery of health care services, especially for patients with chronic conditions and/or requiring cyclical treatment, can be accomplished by resorting to two organizational models: center-based care and home-based care. In developed countries, government pressure to reduce healthcare spending and the COVID-19 pandemic have led to the spread of home-based care. This type of care is proven to outperform the center-based one in terms of cost-effectiveness, patient satisfaction, and adherence to treatment guidelines. However, even for treatments usually suitable to be delivered at home, the patient's health status or other constraints may make it inappropriate to deliver service at the patient's home. This calls for a new organizational model, referred to as flexible care, where home-based and center-based care are not seen as mutually exclusive models but as options that can be activated according to the patient's and provider's needs. This paper presents a novel network-based deterministic optimization model and two matheuristics to address a scheduling problem typically faced by providers adopting a flexible care model. The model considers a provider relying on a treatment room with a fixed number of medical chairs, a fleet of vehicles, and a team of operators. It allows for determining on which days of the planning horizon, in which setting (home or center), and by which operator each patient will be treated. The model takes into account patients’ preferences and considers two objective functions: minimizing provider costs and patients’ travel time. In addition, we propose a two-stage mixed-integer stochastic programming model with recourse actions. This model allows incorporating the uncertainty due to the occurrence of adverse events. Adverse events are sudden changes in the patient's condition randomly happening at a specific point in the planning horizon. These events render the patient unsuitable for home care and require them to be visited at the center from that moment onward. The models have been inspired by a real case and tested on multiple random instances.

Co-optimizing the smart grid and electric public transit bus system

AbstractAs climate change provides impetus for investing in smart cities, with electrified public transit systems, we consider electric public transportation buses in an urban area, which play a role in the power system operations in addition to their typical function of serving public transit demand. Our model considers a social planner, such that the transit authority and the operator of the electricity system co-optimize the power system to minimize the total operational cost of the grid, while satisfying additional transportation constraints on buses. We provide deterministic and stochastic formulations to co-optimize the system. Each stochastic formulation provides a different set of recourse actions to manage the variable renewable energy uncertainty: ramping up/down of the conventional generators, or charging/discharging of the transit fleet. We demonstrate the capabilities of the model and the benefit obtained via a coordinated strategy. We compare the efficacies of these recourse actions to provide additional managerial insights. We analyze the effect of different pricing strategies on the co-optimization. Noting the stress growing electrified fleets with greater battery capacities will eventually impose on a power network, we provide theoretical insights on coupled investment strategies for expansion planning in order to reduce greenhouse gas (GH) emissions. Given the recent momentum towards building smarter cities and electrifying transit systems, our results provide policy directions towards a sustainable future. We test our models using modified MATPOWER case files and verify our results with different sized power networks. This study is motivated by a project with a large transit authority in California.

A Bilevel DEA Model for Efficiency Evaluation and Target Setting with Stochastic Conditions

The effective allocation of limited resources and the establishment of targeted goals play a pivotal role in enhancing the overall efficiency of large enterprises and organizations. To achieve optimal organizational efficiency, managers seek dynamic strategies that adapt to the constraints of limited and uncertain historical data. This paper introduces an evaluation of organizational efficiency through a stochastic framework, employing a bilevel data envelopment analysis (DEA) approach. This decision-making process is centralized within a decision-making unit (DMU) overseeing subordinate decision-making units (subDMUs). Discrete scenarios, each associated with a realization probability, define the uncertain parameters in the bilevel DEA-based model. This stochastic approach allows for recourse actions upon scenario realization leading to an enhanced overall organizational strategy. Decision-makers acting within uncertain and dynamic environments can benefit from this research since it allows the investigation of efficiency assessment under alternative scenarios in the presence of volatility and risk. The potential impact of applying this methodology varies depending on the specific domain. Although, the context of this paper focuses on banking, in general, enhancing resource allocation and target setting under stochasticity, contributes to advancing sustainability across all its three dimensions (economic, environmental, social). As mentioned earlier, the practical application of our approach is demonstrated via a case study in the banking sector.

A Two-Phase Pattern Generation and Production Planning Procedure for the Stochastic Skiving Process

The stochastic skiving stock problem (SSP), a relatively new combinatorial optimization problem, is considered in this paper. The conventional SSP seeks to determine the optimum structure that skives small pieces of different sizes side by side to form as many large items (products) as possible that meet a desired width. This study studies a multiproduct case for the SSP under uncertain demand and waste rate, including products of different widths. This stochastic version of the SSP considers a random demand for each product and a random waste rate during production. A two-stage stochastic programming approach with a recourse action is implemented to study this stochastic N P -hard problem on a large scale. Furthermore, the problem is solved in two phases. In the first phase, the dragonfly algorithm constructs minimal patterns that serve as an input for the next phase. The second phase performs sample-average approximation, solving the stochastic production problem. Results indicate that the two-phase heuristic approach is highly efficient regarding computational run time and provides robust solutions with an optimality gap of 0.3% for the worst-case scenario. In addition, we also compare the performance of the dragonfly algorithm (DA) to the particle swarm optimization (PSO) for pattern generation. Benchmarks indicate that the DA produces more robust minimal pattern sets as the tightness of the problem increases.

Recovery policies for safe exploration of lunar permanently shadowed regions by a solar-powered rover

The success of a multi-kilometre drive by a solar-powered rover at the lunar south pole depends upon careful planning in space and time due to highly dynamic solar illumination conditions. An additional challenge is that the rover may be subject to random faults that can temporarily delay long-range traverses. The majority of existing global spatiotemporal planners assume a deterministic rover-environment model and do not account for random faults. In this paper, we consider a random fault profile with a known, average spatial fault rate. We introduce a methodology to compute recovery policies that maximize the probability of survival of a solar-powered rover from different start states. A recovery policy defines a set of recourse actions to reach a safe location with sufficient battery energy remaining, given the local solar illumination conditions. We solve a stochastic reach-avoid problem using dynamic programming to find an optimal recovery policy. Our focus, in part, is on the implications of state space discretization, which is required in practical implementations. We propose a modified dynamic programming algorithm that conservatively accounts for approximation errors. To demonstrate the benefits of our approach, we compare against existing methods in scenarios where a solar-powered rover seeks to safely exit from permanently shadowed regions in the Cabeus area at the lunar south pole. We also highlight the relevance of our methodology for mission formulation and trade safety analysis by comparing different rover mobility models in simulated recovery drives from the LCROSS impact region.

An Adjustable Scenario Optimisation Approach in Operating PV-Rich Distribution Systems

The embrace of intermittent distributed energy resources (DER) on the demand side increases the concerns around the safe operation of distribution networks. Existing solutions either neglect the available information around the distribution of uncertain parameters or underestimate DER capability in providing real-time recourse actions. In this paper, we propose an adjustable scenario optimisation-based solution approach that maximises the usage of DER generation within the operation horizon, while providing the required level of network security. Our modelling i) guarantees hard constraints satisfaction, ii) allows fast-acting devices, e.g., inverters, to adjust in response to live realisations, and iii) enables the operators to maintain the soft constraints with a required probability using a joint chance-constrained (JCC) program. We reformulate the JCCs using the scenario optimisation approach that directly takes empirical data and provides a pre-specified bound on the risk of constraint violation. To increase the scalability of our proposal, we introduce an approximation of JCCs to be used within the scenario optimisation approach. Through extensive comparisons and simulations, we show that our approach outperforms the conventional scenario optimisation and adjustable robust approaches respectively by 83% and 80% in our experiments.

Integrating stochastic mine planning model with ARDL commodity price forecasting

Commodity price is of paramount importance to mine planning among other stochastic factors such as mining cost and geological uncertainties. Commodity price uncertainty is critical in the determining block values, and it has been incorporated into mine planning by simulation-based methodologies to deal with the effects of price uncertainty during the mining process. In this article, stochastic optimisation was undertaken using parametric minimum cut network flow algorithm for ultimate pit and pushback design, while stochasticity of commodity prices was incorporated into the planning using Autoregressive Distributed Lag (ARDL) simulation model. The push back design and cashflows in two scenarios, namely when the prices are going up and when the prices are going down, were investigated. Moreover, for each scenario, three types of price inputs were considered: (a) actual prices; (b) ARDL forecasted prices; and (c) stochastic prices generated from ARDL forecasted prices. The results of cashflows indicated that when commodity price moving up scenario, the ARDL forecasted prices underestimate the NPV by about 17% and the stochastic minimum cut underestimates the NPV by 72.27% compared to actual price. Similarly, for the price declining scenario, the ARDL forecasted prices underestimated the NPV by about 3% compared to the actual, while the stochastic minimum cut has an NPV value that is 277% of the actual value. Lastly the value of stochastic programming (VSP) was evaluated. The VSP was about 9.2 million dollars when the prices were going up, while the VSP was about 27.1 million dollars, when price was declining. Moreover, declining commodity price produced negative cashflows which indicate need for risk management with a recourse action to evert losses.

Prepositioning can improve the performance of a dynamic stochastic on-demand public bus system

This paper presents the first application of prepositioning in the context of the dynamic stochastic on-demand bus routing problem (DODBRP). The DODBRP is a large-scale dial-a-ride problem that involves bus station assignment and aims to minimize the total user ride time (URT) by simultaneously assigning passengers to alternative stations and determining optimal bus routes.In the DODBRP, transportation requests are introduced dynamically, and buses are dispatched to stations with known requests. This paper investigates the concept of prepositioning, which involves sending buses not only to currently known requests but also to requests that are likely to appear in the future, based on a given probability.To solve this dynamic and stochastic ODBRP, the paper proposes a heuristic algorithm based on variable neighborhood search (VNS). The algorithm considers multiple scenarios to represent different realizations of the stochastic requests.Experimental results demonstrate the superiority of the prepositioning approach over the DODBRP across various levels of forecast accuracy, lengths of time bucket, and probabilities of realization. Furthermore, the paper shows that removing empty stations as a recourse action can further enhance solution quality. Additionally, in situations with low prediction accuracy, increasing the number of scenarios can lead to improved solutions. Finally, a combination of prepositioning, empty station removal, and the insertion of dynamic requests proves to be effective.Overall, the findings of this paper provide valuable insights into the application of prepositioning in the dynamic stochastic on-demand bus routing problem, highlighting its potential for addressing real-world transportation challenges.

An Integer L-shaped algorithm for vehicle routing problem with simultaneous delivery and stochastic pickup

This paper addresses an exact algorithm for vehicle routing problem with simultaneous pickup and delivery in which customer demands to be collected are stochastic. The problem is modeled as a two-stage stochastic programming problem with recourse, in which routing decisions are made based on known delivery demand and deterministic expected pickup demand in the first stage and recourse actions are made in the second stage when stochastic pickup quantities have been revealed. However, failures happen when the load of the vehicle is insufficient to meet the observed pickup demand of a customer. Three recourse policies are proposed to help deal with the failures to proceed with the routing decisions in the first stage. The Integer L-shaped algorithmic framework is used to solve this two-stage stochastic programming problems with recourse. Furthermore, effective lower bounding of the expected recourse cost of partial routes is designed for the three recourse policies, respectively. Computational experiments on the newly generated instances compare the performance of the Integer L-shaped algorithm under the three recourse policies, and the conclusion is validated via numerous simulations. The effectiveness of the proposed lower bounding functionals is confirmed through reduced optimality gaps and lower computing times.

A stochastic optimization algorithm for the supply vessel planning problem under uncertain demand and uncertain weather conditions

The Supply Vessel Planning Problem (SVPP) with stochastic demands and uncertain weather conditions is a transportation problem occurring in offshore oil and gas logistics. A fleet of supply vessels based at an onshore depot delivers supplies to a set of offshore oil platforms in a weekly sailing schedule. However, the schedules are frequently disrupted due to adverse weather conditions and uncertain demand for cargo from the oil platforms. The two sources of uncertainty are generally addressed in separate, most often through the use of two-phased methods, where simulation is combined with an optimization algorithm. The most common approach to incorporate robustness in the constructed schedules is to use a subjective penalized cost for non-robust voyages, with explicit modelling of recourse actions. In contrast, this paper proposes a two-stage stochastic programming algorithm accounting for both uncertain demand and uncertain weather conditions, allowing for the incorporation of the cost of recourse in the objective function. The cost of each solution is approximated through the use of discrete event simulation within a genetic algorithm. For the tested problem instances, the potential benefit from solving the stochastic program over solving the corresponding deterministic version leads to average relative annual cost savings of approximately 12%.

An Adaptive Large Neighborhood Search heuristic for last-mile deliveries under stochastic customer availability and multiple visits

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

Integrating flexibility in open pit mine planning to survive commodity price decline

Historically the mining industry grew substantially across the globe, acquiring new licenses, investing in exploration activities, and opening new mines along with the boom in commodity prices. However, the steady decline in mineral commodities prices significantly affects mineral industry as well as commodity producing nations. Mining risk management is undertaken to mitigate the adverse effects of uncertainties such as price fluctuations using Net Present Value (NPV). In this article risk management of commodity price decline was undertaken by integrating a recourse action with mine planning. The framework was presented in four distinct phases namely commodity price simulation using autoregressive distributed lag forecasting method; formulation of the mathematical stochastic phase design structure of the stochastic graph framework, and parametric solution of the graph problem; estimation and analysis of risk by Value at Risk (Var) and Weibull exceedance of losses concepts respectively, and minimizing the risk by optimizing operating level using the Lagrange model on Cobb-Douglass model. The proposed methodology was applied on an anonymous gold mine and the analysis of potential losses using Gumbel exceedance shows that mine could incur an annual loss of $20 million with a recurrence period of 1 in 1.38 years with a probability of 0.72. The recourse action was identified using the Lagrange model on the Cobb-Douglass model which reduced the cost by about 50% and subsequently the production level. The NPVs for the stochastic minimum cut models after application of the recourse action was 54% of the NPV at full production showing that there is an increase in the value of the project.

A sampling-based matheuristic for the continuous-time stochastic inventory routing problem with time-windows

This article considers a continuous-time variant of the stochastic inventory routing problem. In most of the articles present in the literature related to inventory routing, customers reveal their demands at the end of each period, which is when the inventory level is calculated. In the variant of the problem at hand, the demand that each customer experiences on each period, results in a continuous decrease of the inventory for the customer during the period. This characteristic strongly affects the quantities that can be delivered to each customer and, if the deliveries are not sufficient or arrive too late, they can cause some stock-out situations within the periods. In the inventory routing problem, the vendor manages all the replenishment decisions of the vendees and, therefore, creates delivery plans for a planning horizon, aiming to reduce the routing, consistency, inventory and lost-sales costs. We formulate the problem as a two-stage mathematical program. Customers experience a continuous stochastic demand within each period and present information about inventory level and capacity at each period, as well as the time windows in which deliveries can take place. To solve this problem, we develop a matheuristic solution approach based on an adaptive large neighborhood search algorithm. In addition, we evaluate the impact of applying recourse actions to deal with expected lost sales during the planning horizon. We compare the performance of the algorithm with adapted variants of the multiple scenario approach and the branch and regret algorithms from the literature. Samples based on the stochastic demands are considered in the algorithms, to find robust solutions that can minimize the objective function. We evaluate the solutions by means of a sample average estimator procedure, and we compare the efficiency of the algorithms as well as the impact of different levels of stochasticity.

An integer L-shaped algorithm for the vehicle routing problem with time windows and stochastic demands

This paper addresses the vehicle routing problem with time windows and stochastic demands (VRPTWSD). The problem is modeled as a two-stage stochastic program with recourse, in which routes are designed in the first stage and executed in the second. A failure occurs if the load of the vehicle is insufficient to meet the observed demand of a customer, implying recourse actions to recover feasibility. We consider the classical recourse policy where reactive trips to the depot are made in case of failures and a fixed rule-based recourse policy where, in addition, preventive trips are allowed. These recourse actions delay the vehicle and may cause further failures if the arrival times on the remaining customers of the planned route do not satisfy their time windows. An additional recourse action is used to service the customers whose time windows would be violated in the planned routes. We propose an Integer L-shaped algorithm considering the mentioned recourse actions. To the best of our knowledge, this is the first tailored exact approach for the VRPTWSD. Computational experiments using 112 benchmark instances evaluate the performance of this algorithm as well as the quality of the stochastic problem solutions. The results indicate significant savings in the solutions when using the fixed rule-based policy and round-trip recourse actions instead of the classical policy. Additionally, the algorithm performed better with the fixed rule-based policy, solving to optimality all instances with up to 34 customers, and taking less time on instances that were solved to optimality with both policies.

Flexibility analysis for continuous ibuprofen manufacturing processes

Continuous ibuprofen (a widespread used analgesic drug) manufacturing is full of superiorities and is a fertile field both in industry and academia since it can not only effectively treat rheumatic and other chronic and painful diseases, but also shows great potential in dental diseases. As one of central elements of operability analysis, flexibility analysis is in charge of the quantitative assessment of the capability to guarantee the feasible operation in face of variations on uncertain parameters. In this paper, we focus on the flexibility index calculation for the continuous ibuprofen manufacturing process. We update existing state-of-the-art formulations, which traditionally lead to the max-max-max optimization problem, to approach the calculation of the flexibility index with a favorable manner. Advantages regarding the size of the mathematical model and the computational CPU time of the modified method are examined by four cases. In addition to identifying the flexibility index without any consideration of control variables, we also investigate the effects of different combinations of control variables on the flexibility property to reveal the benefits from taking recourse actions into account. Results from systematic investigations are expected to provide a solid basis for the further control system design and optimal operation of continuous ibuprofen manufacturing.

Adjustable robust approach to increase DG hosting capacity in active distribution systems

We propose a robust coordinated dynamic hosting capacity (HC) evaluation method considering active network management (ANM) techniques in three-phase distribution systems. Our proposed method extends the literature in two main ways. Firstly, by applying the adjustable robust counterpart methodology, we allow fast-acting devices, such as inverters, to take live recourse actions in response to demand and generation uncertainties while not making the unrealistic assumption that they have real-time communication with a central entity. Secondly, we propose a linear uncertainty model capable of handling the strong spatial correlation between PV outputs. We show that our proposed linear model, compared to the existing linearised ellipsoidal uncertainty model, significantly reduces the computational burden while introducing a minor error. We validate the optimality and robustness of our proposed methods via numerical tests on the IEEE 37-node unbalanced three-phase distribution system.

On the Fairness of Causal Algorithmic Recourse

Algorithmic fairness is typically studied from the perspective of predictions. Instead, here we investigate fairness from the perspective of recourse actions suggested to individuals to remedy an unfavourable classification. We propose two new fair-ness criteria at the group and individual level, which—unlike prior work on equalising the average group-wise distance from the decision boundary—explicitly account for causal relationships between features, thereby capturing downstream effects of recourse actions performed in the physical world. We explore how our criteria relate to others, such as counterfactual fairness, and show that fairness of recourse is complementary to fairness of prediction. We study theoretically and empirically how to enforce fair causal recourse by altering the classifier and perform a case study on the Adult dataset. Finally, we discuss whether fairness violations in the data generating process revealed by our criteria may be better addressed by societal interventions as opposed to constraints on the classifier.

Data-driven adjustable robust solution to voltage-regulation problem in PV-rich distribution systems

Adjustable robust counterpart (ARC) methodology has been recently utilised in distribution system operation to allow fast-acting devices, such as PV inverters, to take live recourse actions in response to operating point deviations. Available ARC models are used to obtain the controller parameters based on the worst-case realisations. However, we show that such a strategy might lead to over-conservative results when uncertainty realises away from the worst-case. To close this gap, this paper extends ARC to allow exploiting probabilistic information of uncertainty within the optimisation problem. This results in controller parameters that not only secure the worst-case but also work better in expectation. We formulate our approach as a linear program that minimises the real power curtailment (RPC) and reactive power usage of PV inverters while maintaining network voltages in an acceptable range. In contrast to the conventional ARC, our approach considers a segmented uncertainty set, and assigns a probability to each segment based on historical data. It then optimises to find inverter controller parameters in the form of piecewise affine functions, with each piece associated with one segment in the segmented uncertainty set. In live operation, the controllers use the real-time local measurements and assigned piecewise affine functions to generate real and reactive power set-points for the inverters. The performance of the proposed approach is validated using Monte-Carlo simulations on IEEE 37-bus and 906-bus networks. The simulations show that the proposed approach improves the performance of ARC by 30% to 60% over a variety of experiments.

On sample average approximation for two-stage stochastic programs without relatively complete recourse

We investigate sample average approximation (SAA) for two-stage stochastic programs without relatively complete recourse, i.e., for problems in which there are first-stage feasible solutions that are not guaranteed to have a feasible recourse action. As a feasibility measure of the SAA solution, we consider the “recourse likelihood”, which is the probability that the solution has a feasible recourse action. For $$\epsilon \in (0,1)$$ , we demonstrate that the probability that a SAA solution has recourse likelihood below $$1-\epsilon $$ converges to zero exponentially fast with the sample size. Next, we analyze the rate of convergence of optimal solutions of the SAA to optimal solutions of the true problem for problems with a finite feasible region, such as bounded integer programming problems. For problems with non-finite feasible region, we propose modified “padded” SAA problems and demonstrate in two cases that such problems can yield, with high confidence, solutions that are certain to have a feasible recourse decision. Finally, we conduct a numerical study on a two-stage resource planning problem that illustrates the results, and also suggests there may be room for improvement in some of the theoretical analysis.