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In this paper, we consider a project-based organization that deals with an assignment problem in which a set of projects must be assigned to a group of project managers. This assignment is done based on the relative contributions of projects to the organizational mission and a matching score between each pair of a project and a project manager. We assume that some projects are deterministic, and the organization has signed their corresponding contracts while others are stochastic, i.e. the organization has submitted bids for these projects and may or may not win them in the future. Furthermore, we consider a finite planning horizon and presume a predetermined start time for each deterministic and stochastic project. We develop two models including a multi-stage stochastic integer programming model and a stochastic dynamic programming model to solve the problem. The latter shows better performance for small-size and less complex instances whereas the former gives better performance for more complex instances. We also developed a heuristic algorithm to solve large-size and more complex instances. Computational results indicate that the developed heuristic algorithm can reach near-optimal solutions in reasonable CPU run times and dominates the two other solution approaches particularly for large-size instances. [ABSTRACT FROM AUTHOR]

During an investigation using Forensic Investigative Genetic Genealogy, which is a novel approach for solving violent crimes and identifying human remains, reference testing—when law enforcement requests a DNA sample from a person in a partially constructed family tree—is sometimes used when an investigation has stalled. Because the people considered for a reference test have not opted in to allow law enforcement to use their DNA profile in this way, reference testing is viewed by many as an invasion of privacy and by some as unethical. We generalize an existing mathematical optimization model of the genealogy process by incorporating the option of reference testing. Using simulated versions of 17 DNA Doe Project cases, we find that reference testing can solve cases more quickly (although many reference tests are required to substantially hasten the investigative process), but only rarely (<1%) solves cases that cannot otherwise be solved. Through a mixture of mathematical and computational analysis, we find that the most desirable people to test are at the bottom of a path descending from an ancestral couple that is most likely to be related to the target. We also characterize the rare cases where reference testing is necessary for solving the case: when there is only one descending path from an ancestral couple, which precludes the possibility of identifying an intersection (e.g., marriage) between two descendants of two different ancestral couples. [ABSTRACT FROM AUTHOR]

We revisit a service provider's problem to match supply and demand via an online appointment system such as a doctor in the health care sector. We identify in a survey that an extensive set of available appointments leads to significantly less demand because customers infer a lower quality of the service, as part of an observational learning process. We capture the quality inference effect in a multinomial logit framework and present a Markov decision process for solving the problem of releasing available slots of the appointment system to optimality aiming at maximizing the expected profits. We further evaluate several simple decision rules and provide management insights on which rule to apply under different generic scenarios. Different from current literature, offering all available appointments may lead to suboptimal results when accounting for the quality inference effect. The profit-maximizing strategy then is to offer a subset of the available appointments. [ABSTRACT FROM AUTHOR]

Coconut plantations throughout the Asia–Pacific region are generally characterised by the presence of low-productivity senile palms over the age of 60, which have negative impacts on farming communities, coconut processors, and the wider economy. In Fiji, despite numerous senile coconut replacement programs, 60% of coconut palms are considered senile. The purpose of this study is to provide preliminary estimates of the financial viability of a market-based approach to senile coconut palm replacement in Fiji by utilising the palms as a feedstock, for the manufacture of rotary peeled veneer, along with plantation pine and mahogany. A mathematical model capable of supporting deterministic and stochastic dynamic optimisation was developed with an objective function to maximise the gross margin of marketable veneer manufacture per hour ( G M p z ) by procuring the optimal allocation of logs throughout the landscape. The majority of facility location and log processing scale scenarios evaluated found that utilising large volumes of senile coconut palms for the manufacture of veneer was optimal, whilst veneering mills situated near the coconut plantations in Vanua Levu were found to maximise G M p z . Overall, the results indicate that a coconut veneer and engineered wood product (EWP) value chain could present a financially viable opportunity to support large-scale senile coconut palm replacement in Fiji. [ABSTRACT FROM AUTHOR]

Some nonprofit organizations (NPOs) manage a complex workforce composed of a mix of volunteers, part-time workers, and full-time workers. We study the NPO's finite-horizon staffing problem to determine the optimal initial staff planning decisions and per period optimal hiring and assignment decisions given a budget, capacity constraints, and an uncertain supply of volunteers and part-time workers. Our main goal is to solve this problem in a way that is effective and easy to implement while obtaining interesting managerial insights. To this end, we first demonstrate that the optimal staffing policies are computationally challenging to identify in general. However, we demonstrate that a prioritization assignment policy and a hire-up-to policy for part-time workers can be conveniently applied and are close to optimal. These policies are, in fact, optimal under staff scarcity and staff sufficiency. In our numerical analysis, we study the value and impact of the general optimal solution that considers flexibility and turnover of part-time workers versus the prioritization assignment policy and a constant hire-up-to policy that omit flexibility and turnover behaviors. We further suggest two easy-to-implement heuristics and theoretically analyze them and run a numerical performance study. We observe that both heuristics have low relative optimality gaps. Finally, we extend our analysis by studying how the optimal policy varies under three different practical considerations: a concave social value objective, nonzero volunteer costs, and dynamic volunteer behaviors. This paper was accepted by Jayashankar Swaminathan, operations management. Funding: This work was supported by the Comunidad de Madrid [Grant EPUC3M12], the Ministerio de Ciencia e Innovación [Grant PID2021-127657NA-I00], and the Ramon y Cajal Fellowship [RYC2020-029303-I]. Supplemental Material: The data files and online appendices are available at https://doi.org/10.1287/mnsc.2023.4923. [ABSTRACT FROM AUTHOR]

Introduction: Considering the perishability and substitutability of products are among the most significant challenges in the design and optimization of decision-making in Vendor Managed Inventory (VMI) systems. This challenge becomes more pronounced when there is uncertainty in product demand. Therefore, the primary objective of this research is to present a stochastic dynamic programming approach for optimal control of decisions in VMI systems with dynamic demand uncertainty, optimizing the ordering levels and inventory of perishable products in a two-tier network including vendors and buyers. Methods: After defining the problem of interest in developing VMI systems, considering demand uncertainty and product perishability, the problem is formulated in a multi-period modeling framework, and a stochastic dynamic programming (SDP) approach is used for its formulation. In the proposed SDP model, the objective function is to maximize expected profit by taking into account various costs such as ordering and holding, where the holding cost is dependent on the remaining product life; meaning that as the product approaches its expiration date, the holding cost increases. The proposed SDP model is executed in a recursive manner, and MATLAB software is used for its implementation. Each step of the SDP model is a simpler linear optimization model that is efficiently solved using the CPLEX solver. Results and discussion (Findings): Numerical results demonstrate the computational effectiveness of the SDP method in solving this problem. Using this approach, it is possible to control different costs in a VMI system and make optimal decisions at different stages under any state, thereby improving profit at the end of the time periods. Product substitution in the event of a shortage ensures that, firstly, in the case of a shortage at one center and the supplier's inability to replenish, the center offers its excess inventory to prevent the shortage. Secondly, if the inventory in a distribution center approaches its expiration date, spoilage is prevented. Therefore, the substitution capability generally leads to a reduction in shortage costs and spoilage costs. Results related to product shelf life indicate that by considering the remaining shelf life of products in a VMI-based inventory control system, information between the distribution and supply layers can be used to reduce prices, transfer inventory to another center, and even change inventory control policies to not only prevent product spoilage but also reduce shortage and reordering costs. To model this feature, a full shelf life is initially defined for each newly supplied product, and then a set of periods is defined. For each planning period, if the product is not delivered to the end customer (remains in inventory), one period/day is deducted from the initially defined shelf life, and over time, it moves from a fresh state to the category of older products, which are subject to price reductions. Furthermore, comparing the proposed model with substitution capability in the case of a shortage to the case where a shortage is not considered, it is observed that there is a 10.5% improvement in profit. Conclusion: In the management of modern VMI systems, considering the dynamism in demand behavior and the associated uncertainty is very important and can significantly affect the profitability of enterprises. This importance is doubled when the system in question is managed for the inventory control of perishable products. The SDP approach, by considering potential scenarios of demand uncertainty, enabling substitution, and ultimately paying attention to product shelf life, provides optimal decisions in different situations and not only reduces the risk of decision-making but also leads to a noticeable improvement in final profit compared to nominal quantity models and classical optimization models in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we develop a framework to analyze stochastic dynamic optimization problems in discrete time. We obtain new results about the existence and uniqueness of solutions to the Bellman equation through a notion of Banach contractions that generalizes known results for Banach and local contractions. We apply the results obtained to an endogenous growth model and compare our approach with other well‐known methods, such as the weighted contraction method, countable local contractions, and the Q‐transform. [ABSTRACT FROM AUTHOR]

We deal with the problem of managing a project or a complex operational process by controlling the execution pace of the activities it comprises. We consider a setting in which these activities are clearly defined, are subject to precedence constraints, and progress randomly. We formulate a discrete-time, infinite-horizon Markov decision process in which the manager reviews progress in each period and decides which activities to expedite to balance expediting costs with delay costs. We derive structural properties for this dynamic project expediting problem. These enable us then to devise exact solution methods that we show to reduce computational burden significantly. We illustrate how our method generalizes and can be used to tackle a wide range of so-called stochastic shortest-path problems that are characterized by an intuitive property and can capture other applications, including medical decision-making and disease-modeling problems. Moreover, we also deal with the state identification issue for our problem, which is a challenging task in and of itself, owing to precedence constraints. We complement our analytical results with numerical experiments, demonstrating that both our solution and state identification methods significantly outperform extant methods for a supply chain example and for various randomly generated instances. This paper was accepted by Chung Piaw Teo, optimization. Funding: R. Mogre acknowledges support from the U.S.-UK Fulbright Commission and the Lloyd's Tercentenary Research Foundation through the Fulbright-Lloyd's Scholar Award, which allowed him to spend an extended period of time at Massachusetts Institute of Technology. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2023.4876. [ABSTRACT FROM AUTHOR]

Introduction: Considering the perishability and substitutability of products are among the most significant challenges in the design and optimization of decision-making in Vendor Managed Inventory (VMI) systems. This challenge becomes more pronounced when there is uncertainty in product demand. Therefore, the primary objective of this research is to present a stochastic dynamic programming approach for optimal control of decisions in VMI systems with dynamic demand uncertainty, optimizing the ordering levels and inventory of perishable products in a two-tier network including vendors and buyers.Methods: After defining the problem of interest in developing VMI systems, considering demand uncertainty and product perishability, the problem is formulated in a multi-period modeling framework, and a stochastic dynamic programming (SDP) approach is used for its formulation. In the proposed SDP model, the objective function is to maximize expected profit by taking into account various costs such as ordering and holding, where the holding cost is dependent on the remaining product life; meaning that as the product approaches its expiration date, the holding cost increases. The proposed SDP model is executed in a recursive manner, and MATLAB software is used for its implementation. Each step of the SDP model is a simpler linear optimization model that is efficiently solved using the CPLEX solver.Results and discussion (Findings): Numerical results demonstrate the computational effectiveness of the SDP method in solving this problem. Using this approach, it is possible to control different costs in a VMI system and make optimal decisions at different stages under any state, thereby improving profit at the end of the time periods.Product substitution in the event of a shortage ensures that, firstly, in the case of a shortage at one center and the supplier's inability to replenish, the center offers its excess inventory to prevent the shortage. Secondly, if the inventory in a distribution center approaches its expiration date, spoilage is prevented. Therefore, the substitution capability generally leads to a reduction in shortage costs and spoilage costs. Results related to product shelf life indicate that by considering the remaining shelf life of products in a VMI-based inventory control system, information between the distribution and supply layers can be used to reduce prices, transfer inventory to another center, and even change inventory control policies to not only prevent product spoilage but also reduce shortage and reordering costs. To model this feature, a full shelf life is initially defined for each newly supplied product, and then a set of periods is defined. For each planning period, if the product is not delivered to the end customer (remains in inventory), one period/day is deducted from the initially defined shelf life, and over time, it moves from a fresh state to the category of older products, which are subject to price reductions. Furthermore, comparing the proposed model with substitution capability in the case of a shortage to the case where a shortage is not considered, it is observed that there is a 10.5% improvement in profit.Conclusion: In the management of modern VMI systems, considering the dynamism in demand behavior and the associated uncertainty is very important and can significantly affect the profitability of enterprises. This importance is doubled when the system in question is managed for the inventory control of perishable products. The SDP approach, by considering potential scenarios of demand uncertainty, enabling substitution, and ultimately paying attention to product shelf life, provides optimal decisions in different situations and not only reduces the risk of decision-making but also leads to a noticeable improvement in final profit compared to nominal quantity models and classical optimization models in the literature.

We revisit an approximate stochastic dynamic programming method that we proposed earlier for the optimization of multireservoir problems. The method exploited the convexity properties of the value function to sample the reservoir level space based on the local curvature of the value function, which is estimated by the difference between a lower and an upper bounds (error bound). Unlike the previous approach in which the state space is exhaustively partitioned into full dimensional simplices whose vertices formed a discrete grid over which the value function was approximated, here we propose instead a new randomized approach for selecting the grid points from a small number of randomly sampled simplices from which an error bound is estimated. Results of numerical experiments on three literature test problems and simulated midterm reservoir optimization problems illustrate the advantages of the randomized approach which can solve models of higher dimensions than with the exhaustive approach. [ABSTRACT FROM AUTHOR]

The pace and scale of environmental change represent major challenges to many organisms. Animals that move long distances, such as migratory birds, are especially vulnerable to change since they need chains of intact habitat along their migratory routes. Estimating the resilience of such species to environmental changes assists in targeting conservation efforts. We developed a migration modeling framework to predict past (1960s), present (2010s), and future (2060s) optimal migration strategies across five shorebird species (Scolopacidae) within the East Asian-Australasian Flyway, which has seen major habitat deterioration and loss over the last century, and compared these predictions to empirical tracks from the present. Our model captured the migration strategies of the five species and identified the changes in migrations needed to respond to habitat deterioration and climate change. Notably, the larger species, with single or few major stopover sites, need to establish new migration routes and strategies, while smaller species can buffer habitat loss by redistributing their stopover areas to novel or less-used sites. Comparing model predictions with empirical tracks also indicates that larger species with the stronger need for adaptations continue to migrate closer to the optimal routes of the past, before habitat deterioration accelerated. Our study not only quantifies the vulnerability of species in the face of global change but also explicitly reveals the extent of adaptations required to sustain their migrations. This modeling framework provides a tool for conservation planning that can accommodate the future needs of migratory species. [ABSTRACT FROM AUTHOR]

Introduction: Human-induced environmental change is driving a global redistribution of biodiversity, resulting in shifting prey and predation landscapes. These shifting landscapes can lead to changes in behavior, health, and vital rates, with potential implications for population dynamics. Methods: In the present study, a state-dependent life-history theory model was developed to investigate the individual- and population-level responses of Australian fur seals (Arctocephalus pusillus doriferus) to changes in prey availability and at-sea mortality risk. Results: Rates of pregnancy, pup nursing, and abortion were unaffected by prey availability in the simulated population. Likewise, on-land and at-sea durations were largely unaffected by prey availability, with more pronounced affects for nonreproductive and pregnant females than for lactating females. There was a strong influence of prey availability on the proportion of females that were concurrently pregnant and lactating, largely due to an increase in pup abandonments under low prey availability scenarios. This effect on pup abandonments also had flow on effects for pup recruitment. Increasing at-sea mortality risk resulted in greater offspring losses due to maternal death. The combined impact of prey availability and at-sea mortality risk on the number of simulated female offspring reaching sexual maturity was substantial. Discussion: Consequently, our results suggest high vulnerability of the Australian fur seal population to shifting prey and predation landscapes. These results indicate a need for continued monitoring of Australian fur seal pup production and population dynamics in the face of rapid environmental change. [ABSTRACT FROM AUTHOR]

Collective animal behaviour is a subfield of behavioural ecology, making extensive use of its tools of observation, experimental manipulation and model building. However, a fundamental behavioural ecology approach, the application of optimality theory, has been comparatively neglected in collective animal behaviour. This article seeks to address this imbalance, by outlining an evolutionary theory framework for the discipline. The application of optimality theory to collective animal behaviour requires a number of questions to be addressed. First, what is the correct quantity to optimize? This can be achieved via a combination of considering the organisms' life history, alongside tools such as statistical decision theory and stochastic dynamic programming. Second, what mechanism is appropriate for optimal behaviour? This involves ensuring that models are self-consistent rather than assuming parameter values. Third, at what level of selection does optimization act? Selection acts on the individual except in very particular circumstances, yet collective animal behaviour phenomena are group level, thus introducing a risk of confusing at what level adaptive properties emerge. This article presents examples under each of the three questions, as well as discussing mismatches between theory and observation. In doing so, it is hoped that collective animal behaviour fully inherits the tools and philosophy of its parent discipline of behavioural ecology. • We undertake a review of collective animal behaviour using Tinbergen's four questions. • We thus identify a lack of optimality theory in collective animal behaviour. • We propose three new questions for optimality theory in collective animal behaviour. • Using these questions we review the literature for successes and missed opportunities. [ABSTRACT FROM AUTHOR]

This paper proposes a deep learning approach for solving optimal stopping problems and high-dimensional American-style options pricing problems. Through state-space partition, the method does not require recalculation of the structure of networks when the price of the asset changes, which makes tracking valuation more efficient. This paper also offers theoretical proof for the existence of a deep learning network that can determine the optimal stopping time via state-space partition. We present convergence proofs for the estimators and also test the method on Bermuda max-call options as examples. [ABSTRACT FROM AUTHOR]

This study delves into the realm of green credit policy, a recognized solution for harmonizing financial growth with environmental progress. It highlights the pivotal role of credit-granting orientation in determining the effectiveness of green credit. Introducing a dual-track mechanism that combines industry and enterprise activity orientation, the study provides novel insights into green credit granting. Based on theoretical modeling and simulation analysis, the study explores how different granting orientations in green credit impact enterprise economic and environmental performance using stochastic dynamic programming. The results underscore that industry-oriented granting constrains eco-innovation capital investment and credit fund inflow, while activity-oriented granting leads to reduced carbon emissions and enhanced enterprise value. A dual-track green credit approach demonstrates a superior balance between the two orientations, delivering higher carbon emission reduction effects than industry-oriented granting and more sustainable impacts on enterprise value than activity-oriented granting. Ultimately, the study advocates for differentiating green credit into two orientation types and leveraging eco-innovation activities as credit allocation criteria to enhance the efficiency of green credit operations. [Display omitted] [ABSTRACT FROM AUTHOR]

We use stochastic dynamic programming to design and solve an extended structural setting for which the illiquidity of the firm's assets under liquidation is interpreted as an intangible corporate security. This asset tends to reduce bond values, augment yield spreads, and, thus, partially explain the credit-spread puzzle. To assess our construction, we provide a sensitivity analysis of the values of corporate securities with respect to the illiquidity parameter. [ABSTRACT FROM AUTHOR]

Shellfish aquaculture producers in coastal systems are facing uncertain future growing conditions as climate change alters weather patterns and raises sea level. We examined expected mid-century (2059-2068) changes in aquaculture profitability from recent conditions by integrating models of climate change, estuarine hydrodynamics and biogeochemistry, oyster growth, oyster mortality, and economics, using the Chesapeake Bay, USA as a case study. We developed an economic stochastic dynamic programming (SDP) approach that generates optimal grower behavior to maximize profits under uncertainty by dynamically choosing planting density, replanting and mitigation use, in response to changing oyster stock status and water quality conditions. Separate models were developed for bottom culture largely serving the cannery market, and container culture largely serving the half-shell market, to reflect different production costs, market prices, and oyster growth and survival. The coupled hydrodynamic-biogeochemical and oyster ecology models projected high spatial variability in oyster growth and mortality with the most favorable growing conditions in the lower north and upper mid bay, where mortality is lowest, and the upper south bay, where growth is highest. Climate change by late mid-century generated modest water quality changes and virtually no mortality rate changes. Nonetheless, our modeling revealed that even if growers made optimal management choices under uncertainty, the majority of modeled sites would see a decline in profitability under climate change, primarily due to potential reductions in food availability. Bottom culture was more resilient to the future climate at most sites, being less sensitive to small changes in growth than container culture. Information on how aquaculture conditions currently vary in space was more important for profitability than future climate forecasts. Our stochastic dynamic programming approach tailored grower behavior to each site and unfolding annual conditions, including highly targeted and cost-effective mitigation adjustments to boost oyster survival or growth., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

Container slot allocation represents a critical operational decision-making challenge within the liner shipping industry, which necessitates making decisions on the transportation of loaded containers and the repositioning of empty ones under stochastic demand. We study novel dynamic allocation policy that leverage sequentially-revealed demand information to determine the slot allocation decision for both loaded and empty containers at each stage. In this paper, we develop a stochastic dynamic programming (DP) model to optimize the slot allocation decision for maximizing the expected total revenue over the planning horizon. To solve this model, we design an efficient allocation policy that makes slot allocations at each stage based on current empty container stocks, realized demand, and the mean demand at future stages. Comprehensive numerical experiments on both synthetic and realistic data demonstrate substantial revenue improvement of our approach over the commonly-used benchmark policies in practice and literature. • We develop a stochastic dynamic program for container slot allocation with empty container repositioning under stochastic demand. • We design a dynamic allocation policy that sequentially determines the slot allocation decision based on the realized information at each stage. • A series of numerical experiments are carried out to show that our approach can outperform the benchmark policies used in practice and literature. [ABSTRACT FROM AUTHOR]

When performing operation of the energy system in a building, it is difficult to accurately represent the uncertain long-term objectives in the short-term window, and the correlation between long-term objectives. This work investigates a strategic modelling framework for representing long-term incentives during short-term operational planning for an energy system within flexible buildings. Multi-stage backwards Stochastic Dynamic Programming (SDP) is used to decompose the yearly operational problem into smaller stages, and create long-term cost curves that captures the cost of adjusting long-term price signals, which in this work considers seasonal thermal energy storage and recurring monthly capacity-based grid tariff costs. The proposed method is analyzed for a flexible realistic Norwegian building located in Southern Norway, where the influence both price signals have on long-term operational performance is analyzed. Results show that the framework strategically optimizes the long-term seasonal storage together with the recurring monthly grid tariff, complementing each other by using the seasonal storage to reduce peak costs during winter. With both seasonal storage and monthly demand charge, yearly operational costs are reduced by 4.3% compared to only accounting for the grid tariff. Additionally, the operational performance achieved only a 0.9% higher cost compared to yearly simulation with perfect information. • We apply Stochastic Dynamic Programming for operational planning of the building. • We look at long-term operation of seasonal thermal energy storage in buildings. • We analyze the strategy between seasonal storage and a capacity-based grid tariff. • We present a method to consider price signals with different activation periods. • We show how seasonal storage reduce peak import during winter months. [ABSTRACT FROM AUTHOR]