Risk-neutral Solution Research Articles

An operational scheduling framework for Electric Vehicle Battery Swapping Station under demand uncertainty

This paper proposes a novel mathematical optimization model aimed at incorporating demand response strategies in the operational scheduling problem of Electric Vehicle (EV) Battery Swapping Stations (BSS). The primary goal of the model is to minimize the operational costs while accounting for intricacies arising from diverse charging modes, variations in battery capacities, charger availability, different states of charges (SOC) of incoming discharged batteries, time-of-use power prices, power constraints and fluctuating customer demand patterns. Furthermore, the model takes into consideration the effect of faster charging modes on battery health to ensure a sustainable operation. The proposed model is further extended to incorporate the effect of swapping demand uncertainty on the operational decision-making of the BSS, and a two-stage stochastic optimization model with a recourse approach is proposed. The proposed stochastic optimization model is tested with relevant case studies, and the results demonstrate the efficacy of the model in providing a risk-neutral solution by determining the optimal demand satisfaction pattern and calculating the number of additional batteries needed to minimize demand shortfalls across all scenarios. The proposed scheduling framework holds the promise of improving both the efficiency of the BSS operations and customer satisfaction, paving the way for accelerated EV adoption.

A risk-averse solution for the prescribed burning problem

Hazard reduction is a complex task involving important efforts to prevent and mitigate the consequences of disasters. Many countries around the world have experienced devastating wildfires in recent decades and risk reduction strategies are now more important than ever. Reducing contiguous areas of high fuel load through prescribed burning is a fuel management strategy for reducing wildfire hazard. Unfortunately, this has an impact on the habitat of fauna and thus constrains a prescribed burning schedule which is also subject to uncertainty. To address this problem a mathematical programming model is proposed for scheduling prescribed burns on treatment units on a landscape over a planning horizon. The model takes into account the uncertainty related to the conditions for performing the scheduled prescribed burns as well as several criteria related to the safety and quality of the habitat. This multiobjective stochastic problem is modelled from a risk-averse perspective whose aim is to minimize the worst achievement of the criteria on the different scenarios considered. This model is applied to a real case study in Andalusia (Spain) comparing the solutions achieved with the risk-neutral solution provided by the simple weighted aggregated average. The results obtained show that our proposed approach outperforms the risk-neutral solution in worst cases without a significant loss of quality in the global set of scenarios.

Risk-Averse Co-Decision for Lower-Carbon Product Family Configuration and Resilient Supplier Selection

Due to global pandemics, political unrest and natural disasters, the stability of the supply chain is facing the challenge of more uncertain events. Although many scholars have conducted research on improving the resilience of the supply chain, the research on integrating product family configuration and supplier selection (PCSS) under disruption risks is limited. In this paper, the centralized supply chain network, which contains only one major manufacturer and several suppliers, is considered, and one resilience strategy (i.e., the fortified supplier) is used to enhance the resilience level of the selected supply base. Then, an improved stochastic bi-objective mixed integer programming model is proposed to support co-decision for PCSS under disruption risks. Furthermore, considering the above risk-neutral model as a benchmark, a risk-averse mixed integer program with Conditional Value-at-Risk (CVaR) is formulated to achieve maximum potential worst-case profit and minimum expected total greenhouse gases (GHG) emissions. Then, NSGA-II is applied to solve the proposed stochastic bi-objective mixed integer programming model. Taking the electronic dictionary as a case study, the risk-neutral solutions and risk-averse solutions that optimize, respectively, average and worst-case objectives of co-decision are also compared under two different ranges of disruption probability. The sensitivity analysis on the confidence level indicates that fortifying suppliers and controlling market share in co-decision for PCSS can effectively reduce the risk of low-profit/high-cost while minimizing the expected GHG emissions. Meanwhile, the effects of low-probability risk are more likely to be ignored in the risk-neutral solution, and it is necessary to adopt a risk-averse solution to reduce potential worst-case losses.

RISK-AVERSE STOCHASTIC ORIENTEERING PROBLEMS

In this study, we consider risk-averse orienteering problems with stochastic travel times or stochastic rewards. In risk-neutral orienteering problems, the objective is generally to maximize the expected total reward of visited notes. However, due to uncertain travel times or uncertain rewards, the dispersion in total reward collected may be large, which necessitates an approach that minimizes the dispersion (risk) in addition to maximizing the expected total reward. To handle this, for the orienteering problems with stochastic travel times or stochastic rewards, we suggest two different formulations with an objective of coherent measures of risk. For both problems, we conduct an experimental study using two different coherent measures of risk, which have been extensively used in the literature, and compare the results. The computational results show that, in both models suggested and under both risk measures used, the decision maker is able to obtain a tour with expected total reward being close to the expected total reward of risk-neutral solution, however with a significant decrease in the standard deviation of total reward.

Risk management optimization framework for the optimal deployment of carbon capture and storage system under uncertainty

In order to meet the CO2 reduction target and realize cleaner production, large emission sources have two options: investing in carbon capture and storage (CCS) system and/or paying surcharge for carbon tax. CCS system requires industry to make huge investment in infrastructure and the cost of making improper decisions on CCS is substantial. Many factors can impact the successful deployment of commercial-scale CCS, including significant uncertainty regarding carbon policy, technology and engineering performance. In this study, a two-stage stochastic mixed-integer linear programming (MILP) model is formulated to explore the relationship between these two reduction options by minimizing expected total cost (ETC) for CO2 reduction, considering carbon tax uncertainty. Furthermore, to assess the risk imposed by the uncertainty, three financial risk metrics are introduced for risk management and each metric is formulated as secondary objective to ETC in a multi-objective optimization model with two objectives. The trade-offs between the economic and risk objectives are obtained via the ε-constraint method. At last, a case of power plants in Northeast China is studied. Results show that the risk-neutral solution may confront high risk or even be infeasible in some extreme scenarios, and the carbon tax price of no less than $ 50/t is recommended for policy-makers. In risk-management cases, to control the risk, variability index metric is reduced from $ 40 × 108 to $ 0, probability financial metric is reduced from 0.20 to 0.12 and downside risk metric is reduced from $ 27.09 × 108 to $ 13.38 × 108 at the expense of increasing ETC.

Pemodelan Rantai Suplai Berbasis Economic Production Quantity dengan Menerapkan Kredit Perdagangan Dua Eselon

<p><em>Implementation of the supply chain is felt more important and very useful in today’s era of industrialization. But in the process of supply chain encountered various risks that may affect the flow of the supply chain so it can not run smoothly, such as interference or imperfectness in transportations. This research was made to propose a mathematical model for a supply chain under the effect of unexpected disruptions in transport. Supplier/manufacturer offers the retailer a trade credit period t<sub>1</sub> , then the retailer offers the customer a credit with a period of t<sub>2</sub> and finally the retailer receives the revenue from t<sub>2</sub> ke T + t<sub>2</sub> , where T is the cycle time at the retailer. Under this situation, the three cases such as T ≤ t<sub>1</sub> ≤ T + t<sub>2</sub> , T ≤ T + t<sub>1</sub> ≤ t<sub>2</sub>, and t<sub>1</sub> ≤ t<sub>2</sub> are discussed. An EPQ (Economic Production Quantity) based model is established and retailer’s optimal replenishment policy is obtained through mathematical theorems. From the results of testing on several cases, the best solution for the two procedures has been obtained, namely between risk neutral and risk averse solutions based on the level or number of items damaged/defective. If the number of items damaged is 2 units, then solution risk neutral is far better than the risk averse solution, whereas if the number of items is damaged </em> <em>3 units, then the risk averse solution is far better than the risk neutral solution.</em></p><p class="HowToCite"> </p>

Time-consistent, risk-averse dynamic pricing

Many industries use dynamic pricing on an operational level to maximize revenue from selling a fixed capacity over a finite horizon. Classical risk-neutral approaches do not accommodate the risk aversion often encountered in practice. When risk aversion is considered, time-consistency becomes an important issue. In this paper, we use a dynamic coherent risk-measure to ensure that decisions are actually implemented and only depend on states that may realize in the future. In particular, we use the risk measure Conditional Value-at-Risk (CVaR), which recently became popular in areas like finance, energy or supply chain management.A result is that the risk-averse dynamic pricing problem can be transformed to a classical, risk-neutral problem. To do so, a surprisingly simple modification of the selling probabilities suffices. Thus, all structural properties carry over. Moreover, we show that the risk-averse and the risk-neutral solution of the original problem are proportional under certain conditions, that is, their optimal decision variable and objective values are proportional, respectively. In a small numerical study, we evaluate the risk vs. revenue trade-off and compare the new approach with existing approaches from literature.This has straightforward implications for practice. On the one hand, it shows that existing dynamic pricing algorithms and systems can be kept in place and easily incorporate risk aversion. On the other hand, our results help to understand many risk-averse decision makers who often use “conservative” estimates of selling probabilities or discount optimal prices.

Risk management policies for dynamic capacity control

Consider a dynamic decision making model under risk with a fixed planning horizon, namely the dynamic capacity control model. The model describes a firm, operating in a monopolistic setting and selling a range of products consuming a single resource. Demand for each product is time-dependent and modeled by a random variable. The firm controls the revenue stream by allowing or denying customer requests for product classes. We investigate risk-sensitive policies in this setting, for which risk concerns are important for many non-repetitive events and short-time considerations.Numerically analysing several risk-averse capacity control policies in terms of standard deviation and conditional-value-at-risk, our results show that only a slight modification of the risk-neutral solution is needed to apply a risk-averse policy. In particular, risk-averse policies which decision rules are functions depending only on the marginal values of the risk-neutral policy perform well. From a practical perspective, the advantage is that a decision maker does not need to compute any risk-averse dynamic program. Risk sensitivity can be easily achieved by implementing risk-averse functional decision rules based on a risk-neutral solution.

Replenishment policies considering trade credit and logistics risk

This paper develops an inventory model with non-instantaneous delivery under trade credit and logistics risk. The objective is to determine the optimal replenishment policy for a retailer, given uncertainty in a supply chain due to unforeseeable disruption or various types of defect (e.g. shipping damage, missing parts, misplaced products and/or disasters such as earthquake or hurricane). We provide two solution procedures from the perspective of risk-neutral and risk-averse, respectively. For the risk-neutral solution, the retailer determines the cycle time to minimize the expected total cost. For the risk-averse solution, the model limits the solution space to the set of cycle times, which guarantees an upper bound of defective products under contingency. This risk management operations research technology is very useful in the case of a low-probability high-consequence contingency event. We conclude with computational examples that lead to a comparison of these two solution procedures.

A multi-product risk-averse newsvendor with exponential utility function

We consider a multi-product newsvendor using an exponential utility function. We first establish a few basic properties for the newsvendor regarding the convexity of the model and monotonicity of the impact of risk aversion on the solution. When the product demands are independent and the ratio of the degree of risk aversion to the number of products is sufficiently small, we obtain closed-form approximations of the optimal order quantities. The approximations are as easy to compute as the risk-neutral solution. We prove that when this ratio approaches zero, the risk-averse solution converges to the corresponding risk-neutral solution. When the product demands are positively (negatively) correlated, we show that risk aversion leads to lower (higher) optimal order quantities than the solution with independent demands. Using a numerical study, we examine convergence rates of the approximations and thoroughly study the interplay of demand correlation and risk aversion. The numerical study confirms our analytical results and further shows that an increased risk aversion does not always lead to lower order quantities, when demands are strongly negatively correlated.

Evaluating Treatment Protocols Using Data Combination

In real-life, individuals are often assigned by external planners to binary treatments. Taste-based allocation by planners would make such assignments productively inefficient in that the expected returns to treatment for the marginal treatment recipient would vary across covariates and be larger for discriminated groups. This cannot be directly tested if a planner observes more covariates than the researcher, because then the marginal treatment recipient is not identified. We present (i) a partial identification approach to detecting such inefficiency which is robust to selection on unobservables and (ii) a novel way of point-identifying counterfactual distributions needed to calculate treatment returns by combining observational datasets with experimental estimates. Our methods can also be used to (partially) infer risk-preferences of the planner, which can rationalize the observed data. The most risk neutral solution may be obtained via maximizing entropy. We illustrate our methods using survival data from the Coronary Artery Surgery Study which combined experimental and observational components. Such data combination can be useful even when outcome distributions are partially known. Collecting such data is no harder than running field experiments and its use is analogous to using validation data for measurement error analysis. Our methods apply when individuals cannot alter their potential treatment outcomes in response to the planner's actions, unlike in the case of law enforcement.

Optimal decisions when balancing expected profit and conditional value-at-risk in newsvendor models

This paper investigates a risk-averse inventory model by balancing the expected profit and conditional value-at-risk (CVaR) in a newsvendor model setting. We find out that: i) The optimal order quantity is increasing in the shortage cost for both the CVaR only criterion and the tradeoff objective. ii) For the case of zero shortage cost, the optimal order quantity to the CVaR criterion or tradeoff objective is increasing in the selling price, respectively. However, it may not be monotonic in the selling price when incorporating a substantial shortage cost. Moreover, it may be larger or less than the risk-neutral solution. iii) Under the tradeoff objective function, although the optimal order quantity for the model without shortage cost is increasing in the weight put on the expected profit, this property may not be true in general for the model with a substantial shortage cost. Some numerical examples are conducted to verify our results and observations.

A Multiproduct Risk-Averse Newsvendor with Law-Invariant Coherent Measures of Risk

We consider a multiproduct risk-averse newsvendor under the law-invariant coherent measures of risk. We first establish several fundamental properties of the model regarding the convexity of the problem, the symmetry of the solution, and the impact of risk aversion. Specifically, we show that for identical products with independent demands, increased risk aversion leads to decreased orders. For a large but finite number of heterogeneous products with independent demands, we derive closed-form approximations for the optimal order quantities. The approximations are as simple to compute as the classical risk-neutral solutions. We also show that the risk-neutral solution is asymptotically optimal as the number of products tends to be infinity, and thus risk aversion has no impact in the limit. For a risk-averse newsvendor with dependent demands, we show that positively (negatively) dependent demands lead to lower (higher) optimal order quantities than independent demands. Using a numerical study, we examine the convergence rates of the approximations and develop additional insights into the interplay between dependent demands and risk aversion.

Pareto efficient income taxation with stochastic abilities

This paper studies Pareto efficient income taxation in an economy with finitely-lived individuals whose income generating abilities evolve according to a two-state Markov process. The study yields three main results. First, when individuals are risk neutral, in any period the only individuals whose earnings are distorted are those who currently are and have always been low ability. In addition, the degree to which these perpetual low ability types have their earnings distorted decreases over time, converging to zero if the time horizon is long enough. Second, the earnings distortions are continuous with respect to the degree of risk aversion at the risk neutral solution. Third, Pareto efficient income tax systems can be time consistent even when the degree of correlation in ability types is large. The condition for time consistency suggests a novel theoretical reason why the classic equity–efficiency trade off may be steeper in a dynamic environment than previously thought.

A risk-sensitive approach to total productive maintenance

While risk-sensitive (RS) approaches for designing plans of total productive maintenance are critical in manufacturing systems, there is little in the literature by way of theoretical modeling. Developing such plans often requires the solution of a discrete-time stochastic control-optimization problem. Renewal theory and Markov decision processes (MDPs) are commonly employed tools for solving the underlying problem. The literature on preventive maintenance, for the most part, focuses on minimizing the expected net cost, and disregards issues related to minimizing risks. RS maintenance managers employ safety factors to modify the risk-neutral solution in an attempt to heuristically accommodate elements of risk in their decision making. In this paper, our efforts are directed toward developing a formal theory for developing RS preventive-maintenance plans. We employ the Markowitz paradigm in which one seeks to optimize a function of the expected cost and its variance. In particular, we present (i) a result for an RS approach in the setting of renewal processes and (ii) a result for solving an RS MDP. We also provide computational results to demonstrate the efficacy of these results. Finally, the theory developed here is of sufficiently general nature that can be applied to problems in other relevant domains.