Stochastic Last-Mile Delivery with Crowd-Shipping and Mobile Depots

2021 ◽  
Author(s):  
Kianoush Mousavi ◽  
Merve Bodur ◽  
Matthew J. Roorda
Keyword(s):  
Stochastic Model ◽  
Value At Risk ◽  
Deterministic Model ◽  
Computational Study ◽  
Branch And Cut ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Solution Algorithms ◽  
Last Mile ◽  
Last Mile Delivery

This paper proposes a two-tier last-mile delivery model that optimally selects mobile depot locations in advance of full information about the availability of crowd-shippers and then transfers packages to crowd-shippers for the final shipment to the customers. Uncertainty in crowd-shipper availability is incorporated by modeling the problem as a two-stage stochastic integer program. Enhanced decomposition solution algorithms including branch-and-cut and cut-and-project frameworks are developed. A risk-averse approach is compared against a risk-neutral approach by assessing conditional-value-at-risk. A detailed computational study based on the City of Toronto is conducted. The deterministic version of the model outperforms a capacitated vehicle routing problem on average by 20%. For the stochastic model, decomposition algorithms usually discover near-optimal solutions within two hours for instances up to a size of 30 mobile depot locations, 40 customers, and 120 crowd-shippers. The cut-and-project approach outperforms the branch-and-cut approach by up to 85% in the risk-averse setting in certain instances. The stochastic model provides solutions that are 3.35%–6.08% better than the deterministic model, and the improvements are magnified with increased uncertainty in crowd-shipper availability. A risk-averse approach leads the operator to send more mobile depots or postpone customer deliveries to reduce the risk of high penalties for nondelivery.

scholarly journals A Risk-Averse Shelter Location and Evacuation Routing Assignment Problem in an Uncertain Environment

2019 ◽  
Vol 16 (20) ◽  
pp. 4007
Author(s):  
Bian Liang ◽  
Dapeng Yang ◽  
Xinghong Qin ◽  
Teresa Tinta
Keyword(s):  
Value At Risk ◽  
Computational Study ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Chance Constraint ◽  
Risk Averse ◽  
Evacuation Time ◽  
First Case ◽  
Non Linear

Disasters such as hurricanes, earthquakes and floods continue to have devastating socioeconomic impacts and endanger millions of lives. Shelters are safe zones that protect victims from possible damage, and evacuation routes are the paths from disaster zones toward shelter areas. To enable the timely evacuation of disaster zones, decisions regarding shelter location and routing assignment (i.e., traffic assignment) should be considered simultaneously. In this work, we propose a risk-averse stochastic programming model with a chance constraint that takes into account the uncertainty in the demand of disaster sites while minimizing the total evacuation time. The total evacuation time reflects the efficacy of emergency management from a system optimal (SO) perspective. A conditional value-at-risk (CVaR) is incorporated into the objective function to account for risk measures in the presence of uncertain post-disaster demand. We resolve the non-linear travel time function of traffic flow by employing a second-order cone programming (SOCP) approach and linearizing the non-linear chance constraints into a new mixed-integer linear programming (MILP) reformulation so that the problem can be directly solved by state-of-the-art optimization solvers. We illustrate the application of our model using two case studies. The first case study is used to demonstrate the difference between a risk-neutral model and our proposed model. An extensive computational study provides practical insight into the proposed modeling approach using another case study concerning the Black Saturday bushfire in Australia.

scholarly journals Risk-Averse Multi-Stage Stochastic Programming to Optimizing Vaccine Allocation and Treatment Logistics for Effective Epidemic Response

2021 ◽  
Author(s):  
Xuecheng Yin ◽  
Esra Buyuktahtakin
Keyword(s):  
Value At Risk ◽  
Virus Disease ◽  
Risk Measure ◽  
Adverse Outcomes ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Expected Number ◽  
Multi Stage ◽  
Stochastic Mixed Integer Programming

Existing compartmental-logistics models in epidemics control are limited in terms of optimizing the allocation of vaccines and treatment resources under a risk-averse objective. In this paper, we present a data-driven, mean-risk, multi-stage, stochastic epidemics-vaccination-logistics model that evaluates various disease growth scenarios under the Conditional Value-at-Risk (CVaR) risk measure to optimize the distribution of treatment centers, resources, and vaccines, while minimizing the total expected number of infections, deaths, and close contacts of infected people under a limited budget. We integrate a new ring vaccination compartment into a Susceptible-Infected-Treated-Recovered-Funeral-Burial epidemics-logistics model. Our formulation involves uncertainty both in the vaccine supply and the disease transmission rate. Here, we also consider the risk of experiencing scenarios that lead to adverse outcomes in terms of the number of infected and dead people due to the epidemic. Combining the risk-neutral objective with a risk measure allows for a trade-off between the weighted expected impact of the outbreak and the expected risks associated with experiencing extremely disastrous scenarios. We incorporate human mobility into the model and develop a new method to estimate the migration rate between each region when data on migration rates is not available. We apply our multi-stage stochastic mixed-integer programming model to the case of controlling the 2018-2020 Ebola Virus Disease (EVD) in the Democratic Republic of the Congo (DRC) using real data. Our results show that increasing the risk-aversion by emphasizing potentially disastrous outbreak scenarios reduces the expected risk related to adverse scenarios at the price of the increased expected number of infections and deaths over all possible scenarios. We also find that isolating and treating infected individuals are the most efficient ways to slow the transmission of the disease, while vaccination is supplementary to primary interventions on reducing the number of infections. Furthermore, our analysis indicates that vaccine acceptance rates affect the optimal vaccine allocation only at the initial stages of the vaccine rollout under a tight vaccine supply.

Coordinating Supply Chain with Buy-Back Contracts in the Presence of Risk Aversion

2018 ◽  
Vol 35 (02) ◽  
pp. 1840008 ◽  
Author(s):  
Chunlin Luo ◽  
Xin Tian ◽  
Xiaobing Mao ◽  
Qiang Cai
Keyword(s):  
Supply Chain ◽  
Risk Aversion ◽  
Value At Risk ◽  
Performance Measure ◽  
Expected Profit ◽  
Conditional Value At Risk ◽  
Allocation Rule ◽  
Risk Averse ◽  
Buy Back ◽  
The Impact

This paper addresses the operational decisions and coordination of the supply chain in the presence of risk aversion, where the risk averse retailer’s performance is measured by a combination of the expected profit and conditional value-at-risk (CVaR). Such performance measure reflects the desire of the retailer to maximize the expected profit on one hand and to control the downside risk of the profit on the other hand. The impact of risk aversion on the supply chain’s decision and performance is also explored. To overcome the inefficiency due to the double marginalization and the aggravation resulting from risk aversion, we investigate the buy-back contract to coordinate the supply chain. Such contract can largely increase the supply chain’s profit, especially when the retailer is more risk averse. Lastly, we extend such risk measure to the widely-used business model nowadays — platform selling model, and explore the impact of the allocation rule on the manufacturer’s decision.

Optimal Option Purchasing Decisions for the Risk-Averse Retailer with Shortage Cost

2019 ◽  
Vol 36 (02) ◽  
pp. 1940005 ◽  
Author(s):  
Xin-Sheng Xu ◽  
Felix T. S. Chan
Keyword(s):  
Confidence Level ◽  
Value At Risk ◽  
Expected Profit ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Purchasing Decisions ◽  
Shortage Cost ◽  
High Return ◽  
Potential Risks ◽  
Purchase Quantity

To hedge against potential risks, this paper introduces the conditional value-at-risk (CVaR) measure into the option purchasing for the risk-averse retailer with shortage cost. We introduce two models for the risk-averse retailer to select the optimal option purchase quantity. It is found that both two optimal option purchase quantities to two models can be decreasing in the retail price and increasing in the option executing price under certain conditions. This is different from the optimal option purchase quantity for a risk-neutral retailer to maximize the expected profit. It is found that both two optimal option purchase quantities may be increasing or decreasing in the confidence level, which implies a retailer who becomes more risk-averse may purchase more or fewer options to hedge against potential risks. Under both two optimal option purchase quantities, it is proven that the retailer’s expected profit is decreasing in the confidence level. This confirms the fact that high return implies high risk while low risk comes with low return.

SUPPLY CHAIN COORDINATION WITH CVaR CRITERION

2009 ◽  
Vol 26 (01) ◽  
pp. 135-160 ◽  
Author(s):  
LEI YANG ◽  
MINGHUI XU ◽  
GANG YU ◽  
HANQIN ZHANG
Keyword(s):  
Supply Chain ◽  
Value At Risk ◽  
Supply Chain Coordination ◽  
Revenue Sharing ◽  
Retail Price ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Mild Conditions ◽  
Quantity Flexibility ◽  
Buy Back

We study the coordination of supply chains with a risk-neutral supplier and a risk-averse retailer. Different from the downside risk setting, in a conditional value-at-risk (CVaR) framework, we show that the supply chain can be coordinated with the revenue-sharing, buy-back, two-part tariff and quantity flexibility contracts. Furthermore the revenue-sharing contracts are still equivalent to the buy-back contracts when the retail price is fixed. At the same time, it is shown that the risk-averse retailer of the coordinated supply chain can increase its profit by raising its risk-averse degree under mild conditions.

scholarly journals Single-stage gradient-based stellarator coil design: stochastic optimization

2021 ◽  
Author(s):  
Florian Wechsung ◽  
Andrew Giuliani ◽  
M. Landreman ◽  
Antoine J Cerfon ◽  
Georg Stadler
Keyword(s):  
Stochastic Optimization ◽  
Value At Risk ◽  
Optimization Problems ◽  
Numerical Study ◽  
Single Stage ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Coil Design ◽  
Risk Neutral ◽  
Gradient Based

Abstract We extend the single-stage stellarator coil design approach for quasi-symmetry on axis from [Giuliani et al, 2020] to additionally take into account coil manufacturing errors. By modeling coil errors independently from the coil discretization, we have the flexibility to consider realistic forms of coil errors. The corresponding stochastic optimization problems are formulated using a risk-neutral approach and risk-averse approaches. We present an efficient, gradient-based descent algorithm which relies on analytical derivatives to solve these problems. In a comprehensive numerical study, we compare the coil designs resulting from deterministic and risk-neutral stochastic optimization and find that the risk-neutral formulation results in more robust configurations and reduces the number of local minima of the optimization problem. We also compare deterministic and risk-neutral approaches in terms of quasi-symmetry on and away from the magnetic axis, and in terms of the confinement of particles released close to the axis. Finally, we show that for the optimization problems we consider, a risk-averse objective using the Conditional Value-at-Risk leads to results which are similar to the risk-neutral objective.

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