Optimizing e-waste recycling networks under uncertain environment: a fourth-party logistics perspective

After a large-scale disaster, the emergency commodity should be distributed to relief centers. However, the initial commodity distribution may be unbalanced due to the incomplete information and uncertain environment. It is necessary to rebalance the emergency commodity among relief centers. Traffic congestion is an important factor to delay delivery of the commodity. Neither the commodity rebalancing nor traffic congestion is considered in previous studies. In this study, a two-stage stochastic optimization model is proposed to manage the commodity rebalancing, where uncertainties of demand and supply are considered. The goals are to minimize the expected total weighted unmet demand in the first stage and minimize the total transportation time in the second stage. Finally, a numerical analysis is conducted for a randomly generated instance; the results illustrate the effectiveness of the proposed model in the commodity rebalancing over the transportation network with traffic congestion.

In this paper, a Casualty Collection Points (CCPs) location problem is formulated as a two-stage robust stochastic optimization model in an uncertain environment. In this modelling approach, the network design decisions are integrated with the multi-period response operational decisions where the number of casualties with different levels of injuries coming from the affected areas is uncertain. Furthermore, the transportation capacity for the evacuation of casualties to CCPs and hospitals is also uncertain. To solve this complex problem, a robust sample average approximation method with the feasibility restoration technique is proposed, and its efficiency is examined through a statistical validation procedure. We then evaluate the proposed methodology in the backdrop of a hypothetical case of Bhopal gas tragedy (with the same hazard propagation profile) at the present day. We also report the solution robustness and model robustness of 144 instances of the case-study to show the proficiency of our proposed solution approach. Results analysis reveals that our modelling approach enables the decision makers to design a humanitarian logistic network in which not only the proximity and accessibility to CCPs are improved, but also the number of lives lost is decreased. Moreover, it is shown that the proposed robust stochastic optimization approach converges rapidly and more efficiently. We hope that our methodology will encourage urban city planners to pre-identify CCP locations, and, in the event of a disaster, help them decide on the subset of these CCPs that could be rapidly mobilised for disaster response.

To address the uncertainties caused by the penetration of intermittent renewable energy, most ISOs/RTOs perform day-ahead and look-ahead reliability unit commitment (RUC) runs, ensuring sufficient generation capacity available in real time to accommodate the uncertainties. Two-stage stochastic optimization models have been studied extensively to strengthen the RUC runs, while multi-stage stochastic optimization models were barely studied. In this paper, we investigate the unit commitment and economic dispatch decision differences generated by these two approaches considering the load uncertainties in the system. The stochasticity is represented by a set of scenarios for the two-stage model and a scenario tree for the multi-stage case.

Dynamic pooled capacity deployment for urban parcel logistics

Portfolios of renewable electricity sources are interesting risk-management mechanisms for trading in electricity contract markets. When formed by players belonging to different companies, their stability relies on the way the benefit generated by the optimal portfolio is allocated. The challenge of finding a fair and efficient allocation can be mathematically formulated in terms of finding the Core of a cooperative game, which in turn is stated as an optimization problem with a set of constraints that exponentially grows with the number of participants, quickly becoming computationally intractable. Moreover, the right-hand-side of each constraint relies on a given coalition value, which in our case is obtained by a two-stage stochastic optimization model. This paper presents an efficient methodology based on mixed —linear programming and Benders decomposition to find the Nucleolus share of large-scale renewable portfolios. Case studies are presented with data from the Brazilian power system.

Decisions for a variable renewable resource generator’s commitment in the energy market are typically made in advance when little information is obtainable about wind availability and market prices. Much research has been published recommending various frameworks for addressing this issue. However, these frameworks are limited as they do not consider all markets a producer can participate in. Moreover, current stochastic programming models do not allow for uncertainty data to be updated as more accurate information becomes available. This work proposes two decision-making frameworks for a wind energy generator participating in day-ahead, intraday, reserve, and balancing markets. The first framework is a two-stage stochastic convex optimization approach, where both scenario-independent and scenario-dependent decisions are made concurrently. The second framework is a series of four two-stage stochastic optimization models wherein the results from each model feed into each subsequent model allowing for scenarios to be updated as more information becomes available to the decision-maker. In the simulation experiments, the multi-phase framework performs better than the single-phase in every run, and results in an average profit increase of 7%. The proposed optimization frameworks aid in better decision-making while addressing uncertainty related to variable resource generators and maximize the return on investment.

The interdependence between natural gas and electric power systems is becoming increasingly tight, as the share of natural gas-fired units increases. Within this context, this paper addresses the coordinated expansion planning of natural gas and power systems. We analyze the tradeoff of building natural gas-related facilities (e.g., natural gas pipelines and natural gas-fired generation units) versus electric-power-related facilities (e.g., transmission lines and other generation units). We use a two-stage stochastic optimization model that provides an appropriate balance between accuracy and computational tractability and represents uncertainty pertaining to electricity and natural gas demands. We show the importance of representing uncertainty by computing the value of stochastic solution, which is significant. We analyze the functioning of the model through a small example and a case study based on the IEEE 118-bus system. Computational results confirm the need for detailed representation of both the natural gas and power systems to achieve investment decisions that are well coordinated and optimal.

An Integrated Practice Unit (IPU) is a new approach to outpatient care in which a co-located multidisciplinary team of clinicians, technicians, and staff provide treatment in a single patient visit. This article presents a new integer programming model for an extended open shop problem with application to clinic appointment scheduling for IPUs. The advantages of the new model are discussed and several valid inequalities are introduced to tighten the linear programming relaxation. The objective of the problem is to minimize a combination of makespan and total job processing time, or in terms of an IPU, to minimize a combination of closing time and total patient waiting time. Feasible solutions are obtained with a two-step heuristic, which also provides a lower bound that is used to judge solution quality. Next, a two-stage stochastic optimization model is presented for a joint pain IPU. The expected value solution is used to generate two different patient arrival templates. Extensive computations are performed to evaluate the solutions obtained with these templates and several others found in the literature. Comparisons with the expected value solution and the wait-and-see solution are also included. For the templates derived from the expected value solution, the results show that the average gap between the feasible solution and lower bound provided by the two-step heuristic is 2% for 14 patients. They also show that either of the two templates derived from the expected value solution is a good candidate for assigning appointment times when either the clinic closing time or the patient waiting time is the more important consideration. Sensitivity analysis confirmed that the optimality gap and clinic statistics are stable for marginal changes in key resources.

Optimal planning of mobile emergency generators of resilient distribution system

SUMMARY & CONCLUSIONSThis paper develops a two-stage stochastic optimization model to optimize the reliability thresholds for options like reuse, recycling, and remanufacturing in order to minimize the total cost of producing and providing warranty service for a product family. The major uncertainty of remanufacturing decision-making comes from the periodical product demand and quality of returned resources after various usage processes. We assume discrete demand scenarios for each time period and developed a simulation program to estimate the Remaining Useful Life (RUL) of returned resources. The two-stage optimization model can incorporate stage dependency into the decision making so that the remanufacturing decisions will not be myopic.A case study on a product family with different end-of-life options is conducted to illustrate the efficacy of the optimization model. The result shows that the proposed model can help optimize joint manufacturing and remanufacturing decisions considering uncertain demand and usage profiles. With the optimized multi-stage decisions, the manufacture could save the total cost in producing and providing warranty service compared with a fixed manufacturing policy.

This paper proposes a two-stage stochastic optimization model for proactive planning and reactive operation of resilient power systems under transmission line disruptions. The model, formulated using Generalized Disjunctive Programming (GDP), minimizes total cost, including investment, operation, and resilience penalties, while ensuring load satisfaction under uncertainty. First-stage decisions include line hardening, line addition, and installation of distributed generators or batteries, whereas second-stage decisions include line switching and generator re-dispatch. To improve computational efficiency, two solution strategies are proposed: (i) critical line identification, which focuses on lines whose failures cause major operational issues, and (ii) a scenario reduction-based decomposition algorithm, which gradually adds disruption scenarios instead of solving all at once. Case studies of systems with different scales show that the proposed decomposition algorithm performs more efficiently than Big-M and Hull reformulations. The positive Value of the Stochastic Solution (VSS) further demonstrates that considering disruption scenarios leads to more resilient and cost-effective planning solutions.

This paper presents a two-phase mathematical framework for efficient power network damage assessment using unmanned aerial vehicle (UAV). In the first phase, a two-stage stochastic integer programming optimization model is presented for damage assessment in which the first stage determines the optimal UAV locations anticipating an arrival of an extreme weather event, and the second stage is to adjust the UAV locations, if necessary, when the arrival time of the predicted extreme weather becomes closer with updated information. UAV paths to scan the power network are generated in the second phase to minimize operating costs and final damage assessment completion time of the UAVs. Computational techniques are developed to help reduce the solution time. Numerical experiments show that the proposed stochastic model outperforms the deterministic counterpart in terms of the total UAV pre-positioning setup cost. Additionally, sensitivity analysis discovered the relations among damage assessment time, UAV pre-positioning setup cost, and operating cost.

Urban integrated energy system stochastic robust optimization scheduling under multiple uncertainties

Stochastic optimization models for a bike-sharing problem with transshipment

The current recycling networks of the waste electronic products in China are analyzed from the view of the layout of the recycling center and the structure of recycling channel. The optimization model of an e-waste recycling network is established according to our national actual condition, and solved with simulated data. The results show that setting up detecting centers dispersedly can reduce the transportation amount of the waste electronic products and reduce transportation costs, and the relative concentration of recycling processing center can achieve economies of scale and lower the total cost.