Designing a Resilient and Sustainable Logistics Network under Epidemic Disruptions and Demand Uncertainty

To face the new challenges caused by modern industry, logistics operations managers need to focus more on integrating sustainability goals, adapt to unexpected disruptions and find new strategies and models for logistics management. The COVID-19 pandemic has proven that unforeseen fragilities, negatively affecting the supply chain performance, can arise rapidly, and logistics systems may confront unprecedented vulnerabilities regarding network structure disruption and high demand fluctuations. The existing studies on a resilient logistics network design did not sufficiently consider sustainability aspects. In fact, they mainly addressed the independent planning of decision-making problems with economic objectives. To fill this research gap, this paper concentrates on the design of resilient and sustainable logistics networks under epidemic disruption and demand uncertainty. A two-stage stochastic mixed integer programming model is proposed to integrate key decisions of location–allocation, inventory and routing planning. Moreover, epidemic disruptions and demand uncertainty are incorporated through plausible scenarios using a Monte Carlo simulation. In addition, two resiliency strategies, namely, capacity augmentation and logistics collaboration, are included into the basic model in order to improve the resilience and the sustainability of a logistics chain network. Finally, numerical examples are presented to validate the proposed approach, evaluate the performance of the different design models and provide managerial insights. The obtained results show that the integration of two design strategies improves resilience and sustainability.

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

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.

Parallelizing Subgradient Methods for the Lagrangian Dual in Stochastic Mixed-Integer Programming

The dual decomposition of stochastic mixed-integer programs can be solved by the projected subgradient algorithm. We show how to make this algorithm more amenable to parallelization in a master-worker model by describing two approaches, which can be combined in a natural way. The first approach partitions the scenarios into batches and makes separate use of subgradient information for each batch. The second approach drops the requirement that evaluation of function and subgradient information is synchronized across the scenarios. We provide convergence analysis of both methods. We also evaluate their performance on two families of problems from SIPLIB on a single server with 32 single-core worker processes, demonstrating that when the number of workers is high relative to the number of scenarios, these two approaches (and their synthesis) can significantly reduce running time.

A Multistage Stochastic Programming Approach to the Optimal Surveillance and Control of the Emerald Ash Borer in Cities

Emerald ash borer (EAB), a wood-boring insect native to Asia and invading North America, has killed untold millions of high-value ash trees that shade streets, homes, and parks and caused significant economic damage in cities of the United States. Local actions to reduce damage include surveillance to find EAB and control to slow its spread. We present a multistage stochastic mixed-integer programming (M-SMIP) model for the optimization of surveillance, treatment, and removal of ash trees in cities. Decision-dependent uncertainty is modeled by representing surveillance decisions and the realizations of the uncertain infestation parameter contingent on surveillance as branches in the M-SMIP scenario tree. The objective is to allocate resources to surveillance and control over space and time to maximize public benefits. We develop a new cutting-plane algorithm to strengthen the M-SMIP formulation and facilitate an optimal solution. We calibrate and validate our model of ash dynamics using seven years of observational data and apply the optimization model to a possible infestation in Burnsville, Minnesota. Proposed cutting planes improve the solution time by an average of seven times over solving the original M-SMIP model without cutting planes. Our comparative analysis shows that the M-SMIP model outperforms six different heuristic approaches proposed for the management of EAB. Results from optimally solving our M-SMIP model imply that under a belief of infestation, it is critical to apply surveillance immediately to locate EAB and then prioritize treatment of minimally infested trees followed by removal of highly infested trees. Summary of Contributions: Emerald ash borer (EAB) is one of the most damaging invasive species ever to reach the United States, damaging millions of ash trees. Much of the economic impact of EAB occurs in cities, where high-value ash trees grow in abundance along streets and in yards and parks. This paper addresses the joint optimization of surveillance and control of the emerald ash borer invasion, which is a novel application for the INFORMS society because, to our knowledge, this specific problem of EAB management has not been published before in any OR/MS journals. We develop a new multi-stage stochastic mixed-integer programming (MSS-MIP) formulation, and we apply our model to surveillance and control of EAB in cities. Our MSS-MIP model aims to help city managers maximize the net benefits of their healthy ash trees by determining the optimal timing and target population for surveying, treating, and removing infested ash trees while taking into account the spatio-temporal stochastic growth of the EAB infestation. We develop a new cutting plane methodology motivated by our problem, which could also be applied to other stochastic MIPs. Our cutting plane approach provides significant computational benefit in solving the problem. Specifically, proposed cutting planes improve the solution time by an average of seven times over solving the original M-SMIP model without cutting planes. We calibrate and validate our model using seven years of ash infestation observations in forests near Toledo, Ohio. We then apply our model to an urban forest in Burnsville, Minnesota, that is threatened by EAB. Our results provide insights into the optimal timing and location of EAB surveillance and control strategies.

Salvage harvest planning for spruce budworm outbreak using multistage stochastic programming

Forest supply chain planning must deal with many natural disturbance uncertainties such as fires, insects, and windthrow. One important consideration is wood infestation by invasive insects, as it causes environmental and economic harm. An example of invasive insects in Eastern Canada is the spruce budworm (Choristoneura fumiferana (Clemens)), which is the most destructive insect in North America’s conifer stands. In 2017, more than 5 million ha of forest were defoliated by spruce budworm in Quebec. Repeated defoliation causes tree mortality, reduction of growth rates, and reduced lumber quality. Consequently, different wood qualities with greatly varied values are found in the forest. Changes in the outbreak intensity impact wood values throughout the forest. One of the common actions to mitigate the economic and environmental damages is salvage harvesting. However, because of the large uncertainties and lack of detailed information, it is a difficult problem to model. We propose a multistage stochastic mixed-integer programming model for harvest scheduling under various outbreak intensities. The objective is to maximize revenues of wood value minus logistic costs while satisfying demand for wood in the industry. The results show that when there is an outbreak throughout the forest, the priority for salvage harvesting is to focus on forest areas with the lowest level of infestation.

Semi-liner Shipping Service Design

Semi-liner shipping transports various types of cargo, such as containers, break-bulk cargo, and heavy-lift project cargo, between different ports. Similar to liner shipping, semi-liner shipping publishes shipping routes for customers’ reference. However, it does not strictly follow the published route and usually makes some adjustments for each ship voyage by adding some port calls to transport more cargo considering the excess ship capacity. This study first proposes the semi-liner shipping service design (SLSSD) problem that aims to maximize the shipping profit by determining a shipping route subject to the potential adjustments. The proposed SLSSD problem is subsequently formulated as a two-stage stochastic mixed integer programming model with integer recourse variables. The first stage determines the visit sequence of a set of compulsory ports under shipping demand uncertainty. The second stage decides whether to add or remove some ports in the route in view of the realized shipping demand for each ship voyage. To effectively solve the model, two decomposition methods are developed, namely, the stage decomposition method and the scenario decomposition method, that decompose the problem by stage and demand scenario, respectively. In addition, two novel acceleration techniques are also provided to expedite the scenario decomposition method. Numerical experiments reveal satisfactory efficiency of these two methods to solve the semi-liner shipping service design problem, especially the scenario decomposition method, which is generally better than the stage decomposition method and can be thousands of times faster than the classic branch-and-cut algorithm.

Two-Stage Stochastic Mixed-Integer Programming with Chance Constraints for Extended Aircraft Arrival Management

The extended aircraft arrival management problem, as an extension of the classic aircraft landing problem, seeks to preschedule aircraft on a destination airport a few hours before their planned landing times. A two-stage stochastic mixed-integer programming model enriched by chance constraints is proposed in this paper. The first-stage optimization problem determines an aircraft sequence and target times over a reference point in the terminal area, called initial approach fix (IAF), so as to minimize the landing sequence length. Actual times over the IAF are assumed to deviate randomly from target times following known probability distributions. In the second stage, actual times over the IAF are assumed to be revealed, and landing times are to be determined in view of minimizing a time-deviation impact cost function. A Benders reformulation is proposed, and acceleration techniques to Benders decomposition are sketched. Extensive results on realistic instances from Paris Charles-de-Gaulle airport show the benefit of two-stage stochastic and chance-constrained programming over a deterministic policy.