The patient path scheduling problem studied in this work is inspired by a real-world case from a large comprehensive hospital in China, where patients must visit multiple medical departments, requiring efficient scheduling of their examination paths. We introduce a new large-scale patient path scheduling problem that minimizes patient non-treatment time, reflecting the perspective of patient satisfaction. We consider the time patients spend walking between departments and waiting for treatment outside the departments, as well as environmental factors that may influence patients’ waiting experience. We first present a mixed integer programming model and solve it via the Gurobi optimization solver. To address large-scale benchmark instances with up to 1000 patients and 6 types of examinations, we propose an effective neighborhood reduction based local search algorithm. The algorithm distinguishes itself by employing an original neighborhood reduction strategy to avoid unpromising neighboring solutions and a dedicated rollback strategy to intensify the search. Computational results on 60 benchmark instances demonstrate that our algorithm is competitive compared to the Gurobi solver and three greedy algorithms used in real-world hospital settings. The key components of the algorithm are analyzed to understand its behavior. Moreover, we show how hospitals can leverage this study under different patient numbers, demonstrating that our approach is particularly beneficial in large-scale settings.
For surgery duration prediction, it has been shown that integrating human judgment into algorithmic prediction models results in a higher accuracy than machine learning based approaches can achieve alone. However, since humans are a scarce resource in healthcare, their involvement in surgery duration prediction has high opportunity costs as their time could be spent more effectively on patient care and other medical tasks. This raises the question of how these costs should influence human involvement in tasks where algorithms perform reasonably well at minimal cost. This paper introduces a framework for selectively integrating human judgment based on the costs of human involvement and prediction uncertainty, which is captured using algorithmic meta features. Our framework identifies instances in surgery duration prediction where human judgment should be integrated in algorithmic predictions and those where it should not. We evaluate our framework using a data set containing 70,610 surgeries from a large university hospital. We observe that while always integrating human judgment leads to an overall higher accuracy than never integrating human judgment, employing the framework can lead to an even higher accuracy with lower human workload. In our case study planning costs could be reduced by 27
Efficient resource leveling is a critical challenge in ship refit and maintenance planning, where fluctuating labor demand leads to costly subcontracting, overtime, and risks of project delay. To address this issue, this paper presents a continuous-time mixed-integer linear programming approach to Rough Cut Capacity Planning (RCCP) for tactical project planning, which integrates resource leveling by treating work package execution intensities as decision variables. The model allows greater flexibility in execution intensities and enforces a single-peaked resource usage profile, in which demand rises to a peak and then declines, thereby reducing repeated hiring and rehiring while assessing impacts on overall project duration. Computational experiments on specially generated instances show that allowing reduced coupling between resource-specific intensities improves workload leveling by up to 35.16 ε -constraint analysis quantifies the trade-off between project duration and resource stability for instances with extended horizons. The analysis considers three factors: the total project duration, the variation of workload between periods, and whether or not the workload profile is unimodal.
Sustainable energy technologies and efficient energy usage are important drivers for reducing greenhouse gas emissions. The manufacturing industry, with its high energy consumption, is particularly important. Integrated energy-oriented production planning becomes essential with the adoption of on-site renewable energy technologies such as photovoltaics, wind power, hydropower, and energy storage systems. However, energy-oriented planning approaches, particularly in terms of lot-sizing, are limited. Hence, we present a novel energy-oriented dynamic lot-sizing model for multiple products in a capacity-restricted production system. Decentralized renewable energy sources supply energy, which can be stored temporarily in an energy storage system. Connections to the national power grid and energy trading are included, assuming that power generation and energy prices are known. The model aims to minimize inventory, setup, and energy costs. Numerical results highlight the superiority of our model in terms of solvability over a model formulation based on the PLSP presented by Liao and Gicquel (2024). Furthermore, we explore strategies to improve the lower and upper bounds of the monolithic model. The proposed hybrid matheuristic, which combines a Fix-and-Optimize heuristic with local branching, achieves high solution quality. Comparisons with traditional (consecutive) planning approaches underscore the benefits of energy-oriented lot-sizing, including better utilization of renewable energy and cost reductions of up to 19
This paper revisits the classical newsvendor problem with unreliable suppliers, examining both risk-neutral and risk-averse formulations. We study multi-sourcing decisions under yield uncertainty, distinguishing between all-or-nothing (AON) suppliers, who either deliver fully or fail completely, and suppliers offering fractional delivery guarantees (FDGs) that ensure partial fulfillment under disruption. For the risk-neutral case, we show that the supplier ranking rule proposed previously, based on effective cost, is not optimal. Instead, we prove a cost-ordered dominance property: suppliers are considered in nondecreasing unit procurement cost (a higher-cost supplier cannot be active if a lower-cost supplier is inactive), while disruption risk affects the optimal quantities and the activation thresholds within this structure. Fractional guarantees generate nonlinear and potentially unimodal patterns in order quantities and service levels, leading to different activation behavior compared with AON models. In the risk-averse case, we extend the mean–variance formulation and demonstrate that an earlier study omitted part of the profit variability, resulting in an underestimation of risk. We derive the complete mean–variance expression and introduce a simplified weighted-variance formulation that captures risk more accurately while remaining computationally efficient. The results show that minimizing weighted variance activates all suppliers when stockout penalties are present, whereas minimizing full variance offers greater protection when reliability is low. Overall, our study offers clearer guidance for supplier selection and ordering decisions under uncertainty and risk aversion, providing new analytical and numerical insights into risk-averse supplier portfolio management.
The provision of technician-based after-sales field services, such as installing, repairing, or maintaining consumer goods, requires operational planning to schedule and route skilled technicians under various operational constraints and objectives. From a methodological perspective, these operational planning problems belong to the class of Technician Routing and Scheduling Problems (TRSPs). To address the high heterogeneity of the TRSP literature, we conduct a model-based literature review that structures the literature at the modeling level rather than solely at the problem level. The survey is based on a taxonomy, which allows us to represent a static-deterministic TRSP as a specific configuration of core routing constraints, service- and technician-related constraints, and objectives. The taxonomy also covers stochastic-dynamic TRSPs, which are additionally characterized by sequential decision-making and uncertainty, and are becoming increasingly relevant in both research and practice due to the progress in mobile communication technology. Drawing on the taxonomy-based literature classification, we identify real-world TRSP configurations that are underrepresented in the scientific literature. These include, e.g., TRSPs combining teaming with synchronization as well as TRSPs involving demand management decisions by the provider.
This paper addresses the issue of nursing workload imbalances in healthcare environments with highly stochastic patient demand. The core objective is to explore the effects of shift design and scheduling decisions on nursing workload in emergency departments, utilizing the German University Hospital Augsburg as a case study. By introducing a mixed-integer optimization model, we provide a method to balance hourly workload over a typical one-month scheduling horizon, measured as an acuity-adjusted patient-to-nurse ratio, where acuity is represented at the level of care activities rather than individual patients. Our model accounts for real-world parameters including staff details, qualifications, work preferences, and extensive patient data. We further explore the potential impact of various shift designs on the desired target level of workforce balance and care quality. The results provide actionable insights into strategic staffing decisions, their effects on nursing workload, and potential solutions to healthcare staffing challenges. The findings also form the basis for future research in workforce optimization in healthcare.
This paper addresses the two-machine blocking flow shop scheduling problem with a learning effect, aiming to minimize the makespan. Under certain conditions, we show that the problem can be reduced to a polynomially solvable case and further reduced to an equivalent single-machine scheduling problem. We derive dominance rules and theoretical lower bounds. For small instances, we develop a mixed-integer programming (MIP) formulation and a constraint programming model. In addition, a warm-start strategy is designed and effectively used to initialize the MIP. For large instances involving up to 300 jobs, we design a beam search algorithm enhanced with a variable neighborhood descent improvement phase. Extensive computational experiments are reported, including comparisons with a well-established metaheuristic from the literature.
Applications for optimization with uncertain data in practice often feature a possibility to reduce the uncertainty at a given query cost, e.g., by conducting measurements, surveys, or paying a third party in advance to limit the deviations. We model such situations by a class of decision-dependent robust optimization problems in which the uncertainty set can be modified elementwise at a cost. In our framework, uncertain cost coefficients lie in bounded intervals and the optimizer chooses a query vector that shrinks each interval towards a hedging point, possibly down to a single value. We refer to this overall modeling paradigm with decision-dependent uncertainty sets as optimization under elementwise controllable uncertainty (OCU). We study two different problem settings – one with known and one with unknown hedging points – in more detail, in which we handle the remaining uncertainty by the paradigm of robust optimization. For both settings, we draw connections to the existing literature, provide bounds on the optimal objective value, and give a single-level non-linear reformulation. Furthermore, we state assumptions under which the three- respectively four-level problem can be solved as a single-level mixed-integer linear program. Finally, we formalize the phenomenon of budget deflection, where a parameter is queried solely to control the uncertainty for other parameters. We provide examples illustrating when budget deflection can occur and identify modeling choices under which it is provably excluded.
Recognizing that investors’ risk preferences evolve in response to dynamically changing market conditions, which are often unobservable and exhibit regime-switching behavior, this paper addresses multi-period mean-variance (MMV) portfolio optimization with market-regime-dependent risk parameters and partially observed market information. The model incorporates a regime-switching framework represented by hidden Markov models (HMM) with Gaussian emission probabilities. This approach mirrors financial practice, where continuously observable variables, such as the Volatility Index (VIX), are used as proxies for underlying market information. HMM not only provides a tractable method for updating risk aversion and model parameters in an online learning fashion, but it also integrates seamlessly into the MMV solution framework. In the decision phase, we derive closed-form solutions for the MMV model in two scenarios: one with only risky assets and another that includes a risk-free asset. The proposed policies generalize several classical policies as special cases. Using real market data, we compare our model with alternatives that either ignore the regime-switching structure or assume constant risk aversion. Our experiments demonstrate that the proposed model consistently outperforms these benchmarks, highlighting the importance of incorporating dynamic market conditions and evolving risk preferences into practical portfolio management.
The apparel industry has long struggled with profit losses from stockouts of popular items and excess inventory of unsold ones. Quick Response (QR) offers a remedy by allowing retailers to place firm orders closer to the selling season and to delay commitments to variants such as colors, sizes, or styles of a generic design. In this paper, we present an analytical model to study the ordering and production planning of apparel variants in the context of QR. We model a retailer’s and a supplier’s decision-making problems using dynamic programming formulations and show that both optimization problems are concave. Our analysis shows that the retailer consistently benefits from QR by reducing mismatch costs across variants, while the impact on the supplier is mixed. Numerical experiments demonstrate that QR improves their profitability when expedited production is not much costlier than regular production, when wholesale prices are relatively high, when demand correlation across variants tends to be negative, or when demand forecasts become more accurate. Finally, we examine a minimum order quantity arrangement and find that, within a range of baseline order quantities, both parties achieve higher profits than under the traditional practice.
The Triangle Scheduling (TS) Problem, defined by Dürr et al. (J Sched 21:305–312, 2018. https://doi.org/10.1007/s10951-017-0533-1 ), is a geometric model for non-preemptive scheduling of jobs with different criticality levels on a single machine. The jobs have a criticality equal to the worst-case execution time and are scheduled off-line. In this article, we describe, implement and analyze the Bintree algorithm on TS, which is an algorithm based on a binary tree construction. It has O(nlog (n)) runtime and its approximation ratio is between 1.35 and 2ln (2) ≈ 1.386 . Bintree is, therefore, the first polynomial-time approximation algorithm for TS with an approximation ratio below 1.5. We also explore Bintree’s relation to a previously defined algorithm, Greedy, and a potential hybrid algorithm that runs both and chooses the shorter schedule, which we suspect to be better than either algorithm by itself. We analyze the behavior of Bintree on small values of input sizes formalizing its quadratic integer programming model.
The following questions, which are of fundamental importance for data envelopment analysis (DEA) and, to some extent, for efficiency measurement in general, are examined: Is DEA a general “multiple-criteria evaluation methodology” or a specific methodology for analysing the efficiency of production processes? What performance measures are original to any efficiency analysis? What assumptions are essential for a reasonable benchmarking when applying the DEA methodology? These questions have not yet been answered conclusively. The article provides some answers by systematically examining DEA’s foundations as a kind of multidimensional cost-benefit analysis within a general framework of decision and production theory. The findings enable propositions to be derived that contribute to advancing the DEA methodology and to its meaningful and useful empirical and practical application. For instance, it justifies how pollutants and disposability properties can be treated in DEA.
We develop novel heuristics for the single-leg seat inventory control problem using robust optimization. Our starting point is the bounded, continuous knapsack formulation of the single-leg problem. We show how a modification of the classical knapsack problem brings the uncertain parameter (demand) to both the objective function and the constraints. We derive robust counterparts of this model based on different measures of robustness and uncertainty sets. The robust optimal capacity allocation is then modified heuristically to prevent under-utilization of capacity. The modified capacity allocation yields new nested booking limit policies for the single-leg revenue management problem with independent demand. For the choice-based demand model in revenue management, the same robust models—with minimal change—provide the optimal time each choice set should be offered. The performance of the new heuristic is shown to be effective in simulations, with good worst-case guarantees and low computational complexity.
Internet-of-Things-enabled systems that monitor usage and inventory are the latest technological advancement in demand forecasting and inventory control. Unlike traditional systems that record sales via cash registers or RFID technology at the point-of-sale, these novel systems can track product usage via smart, connected devices at the point-of-consumption, i.e., directly at the end user. This usage data promises to be a valuable basis for smart, automated replenishment services. We study such a service in the context of commercial coffee machines through collaboration with a large manufacturer in the coffee industry. Our data set contains information on more than 75 million drinks recorded since late 2017 by nearly 6,500 IoT-enabled coffee machines for commercial customers such as office kitchens, restaurants, and gas stations. The nature of the problem and data at the point-of-consumption warrants the development of synergetic models for demand forecasting, inventory control, and correction of inventory record inaccuracy. The resulting models are distinct from the state-of-the-art approach at the point-of-sale as they are uniquely integrated and involve an alternative strategy to mitigate inventory record inaccuracies. Overall, we contrast different approaches to manage smart replenishment systems, test their forecasting, inventory control, and inaccuracy correction performance, and pave the path to implementation in the field. Our findings suggest important implications for manufacturers who wish to engage in direct relationships with the end users of their products.
This paper addresses a critical gap in circular economy (CE) research by introducing a novel methodological framework that integrates Network Data Envelopment Analysis (NDEA) with a chance-constrained programming. The proposed approach captures the interrelated dynamics of economic production and waste treatment subsystems, while accounting for stochastic variables and data uncertainties to provide robust CE efficiency estimates. Using data from 26 European (EU) countries from 2013 to 2020, our results reveal that achieving CE efficiency requires a balanced focus on economic production and waste management. Although strong economic output can support circularity, waste treatment efficiency often plays a decisive role in determining overall CE performance. Moreover, we find that economic size does not necessarily translate into circular efficiency, whilst large economies may face challenges with effective waste management and resource recovery despite their economic status. The proposed approach offers policymakers and practitioners a robust empirical framework to guide CE improvements, particularly in regions where environmental practices lag behind economic achievements. Stronger incentives and regulatory measures are recommended to enhance circular activities within the EU and foster greater circular efficiency across countries.
The paper addresses the efficient and fair allocation of limited healthcare resources to patient groups, with a special focus on the consideration of patients’ age in the allocation decision. At the core of this issue lies the controversially discussed “fair innings argument” which suggests a prioritization of younger patients over older ones. Recently, Adler (J Health Econ 75:102412, 2021) developed a rigorous theoretical framework for the fair innings concept, building on a prioritarian social welfare function. The first goal of the present work is to recast this prioritarian framework to an egalitarian one by employing a social welfare function based on the Gini index. Some theoretical properties related to the “social value of risk reduction” are derived. Secondly, as an example of application, it is shown how the egalitarian framework can be used to set up an optimization model for vaccination policies against epidemics. Third, an alternative for healthcare decision makers who reject the fair innings argument is offered by proposing a variant of the egalitarian model which builds on the idea of “deontic fairness” by Parfit (Equality or priority?, University of Kansas, Lawrence, 1995). Numerical results on a small case study are presented and compared.
Risk parity, an evolving approach in portfolio management that aims to distribute risk equitably among assets, is reshaping traditional views on asset allocation and diversification. This study proposes a novel two-step strategy within the risk parity framework with the primary objective to induce sparsity. In the first step, assets are ranked by defining a three state markov chain based on second order stochastic dominance criterion and top k assets are filtered to match the desired cardinality. The optimal portfolio is then generated using a variance-based risk parity framework for these selected k assets. The proposed strategy is evaluated against a comprehensive suite of benchmarks, including the market index, equally weighted (1/n) portfolios, the traditional risk parity, minimum variance, mean variance, along with their cardinality constrained extensions, and two generalized risk parity frameworks. The analysis spans five levels of cardinality; k=10%, 25% , 50% , 75% and 90% of the total number of assets. A comprehensive empirical investigation is conducted on weekly data of four global datasets, namely, S P Asia 50 (Asia), HangSeng (Hong Kong), FTSE 100 (UK) and BSE 200 (India) and daily data of two global indices, namely, S P 500 and Russell 1000 that highlights the superior out-of-sample performance of the proposed strategy in terms of mean return, Sharpe ratio, Sortino ratio, and Stable tail-adjusted return ratio (STARR) across all datasets. Additionally, analysis on different market phases further demonstrates the robustness of the proposed framework to changing market dynamics. The proposed framework strikes a favorable balance between computational efficiency and out-of-sample performance when compared to the traditional benchmarks and the cardinality-constrained models.
Production routing problems (PRPs) are integrated planning problems that combine vehicle routing and lot-sizing decisions. Given a discrete finite time horizon and a set of customers, the basic PRP consists of deciding for each period if and how much to produce, the inventories at the supplier and the customers, and the vehicle routes. The latter include the decisions on which customers to serve and the quantities delivered. The objective is to minimize the total cost over the planning horizon consisting of production, inventory, and routing cost. In this paper, we consider the PRP with time windows (PRPTW) and propose a branch-price-and-cut (BPC) algorithm for its solution. The BPC relies on a path-based formulation that explicitly specifies which demands are satisfied by which deliveries and employs several families of valid inequalities. The performance of the BPC is assessed in an extensive computational study on existing benchmark instances for the related inventory routing problem with time windows (IRPTW) and newly created instances for the PRPTW. Our BPC outperforms the current state-of-the-art BPC for the IRPTW, closing 62 previously open instances. Finally, we derive managerial insights from our PRPTW instances.
The paper investigates a stochastic-dynamic customer-oriented dial-a-ride problem of a ridepooling provider in a large city. Due to competing mobility services, the ridepooling provider needs to offer the customers short waiting and travel times. New customer requests are inserted to maximize their acceptance probability which depends on the customer’s detour in relation to their direct travel time. The trade-off between current and future customers is included by a “potential” that assesses the attractiveness of a tour for future customers. As we need to compute offers quickly, we introduce several precomputation steps, which are done in the meantime between two customer requests, as well as a clustering and a sampling method to reduce the computational effort and use parallelization. These methods allow to solve instances with larger numbers of customers. Our methods are evaluated in a comprehensive computational study with 2700 instances. The main result is that it is best to weight the interests of the current and the future customers equally. Furthermore, the approach can be used by the provider to steer the system’s performance. Given a desired service level, i.e. an acceptance rate, the provider can use the approach to decide on the required number of vehicles to reach this service level. Besides, the length of the delivery time windows is important to solve the trade-off between a sufficiently high degree of freedom to reinsert accepted customers in favour of new customers and the system’s attractiveness for accepted customers.
