Stochastic optimization formulations for reliability unit commitment runs

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.

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.

Urban integrated energy system stochastic robust optimization scheduling under multiple uncertainties

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.

Stochastic optimization models for a bike-sharing problem with transshipment

A two-stage stochastic optimization model for reverse logistics network design under dynamic suppliers’ locations

Purpose The complexity of modern agricultural systems requires resilient, adaptable supply chains to help achieve net-zero emissions. This study presents a two-stage stochastic programming model designed to address these challenges in a sustainable forward-reverse hybrid agricultural supply chain (ASC). Design/methodology/approach The proposed methodology integrates sustainability, resilience and circular economy (CE) principles into a two-stage stochastic optimization model for ASC. The model includes waste valorization (WV) by recycling agricultural waste in composting centers, turning it into valuable resources. It also incorporates resilience strategies, including an inventory buffering policy and a multi-level energy fortification strategy integrating gas, solar panels and gasoline, within a mixed-integer linear programming framework. The model is solved using the General Algebraic Modeling System with the CPLEX solver. A real-world hydroponic agriculture case study and test problems validate the model, with sensitivity analysis to evaluate the impact of key parameters. Findings Integrating clean energy, resource efficiency and waste reuse supports the global goal of net-zero emissions in agriculture. This approach reduces raw material purchasing costs by 24%, enhancing sustainability, while increasing profitability by 15%. It provides a practical, scalable pathway to a low-carbon ASC. Originality/value This study integrates CE principles with stochastic optimization to design a low-carbon, adaptable ASC. A hybrid greenhouse–field combining hydroponic farming and traditional agriculture optimizes resource efficiency, WV and clean energy use, ensuring sustainability and profitability.

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.

Efficient E-waste recycling is key for electronic product manufacturing companies to achieve resource optimization and sustainable development. However, market fluctuations and the uncertainty of consumer behavior make the demand for E-waste recycling difficult to predict, presenting challenges for the design and management of recycling networks. This paper investigates the reverse logistics network design problem for E-waste under uncertain recycling demand from the perspective of 4PL innovation. Multiple 3PLs and temporary outsourcing service models are incorporated to address the uncertainty of recycling demand. A two-stage stochastic optimization model is introduced to reduce overall expenses. To improve solving efficiency, a new LHS-SAA algorithm is proposed. The model and method's effectiveness is shown through a real case study of a household appliance recycling company in northern Turkey. The comparative analysis shows that the LHS-SAA algorithm outperforms CPLEX. For the company, the 4PL operational model is more suitable for constructing the corresponding recycling network. Compared to the traditional supply chain network, the 4PL network can reduce overall costs through the collaborative cooperation of 3PLs. In addition, the results of the parameter sensitivity analysis show that the unit penalty cost, unit outsourcing cost, and minimum recycling ratio have a complex interdependent relationship in their effects on the results. The magnitude of the unit penalty cost for uncollected items has a decisive impact on the decision outcomes. When the penalty cost is low, the company can determine the scale of the 4PL network based on the minimum recycling ratio. As the minimum recycling ratio and unit outsourcing cost increase, the company should prepare more funds to build the 4PL recycling network. As the unit penalty cost increases, the scale of the 4PL network is solely dependent on the unit outsourcing cost, regardless of the value of the minimum recycling ratio.

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

ERCOT is transitioning from a current zonal market to a newly redesigned nodal market. In the new ERCOT nodal wholesale market, a Reliability Unit Commitment (RUC) process is designed and implemented to ensure transmission system reliability and security. The main objective of RUC is to ensure that enough resource capacity, in addition to ancillary service capacity, is committed in the right locations to reliably serve the forecasted load in the ERCOT system. The RUC is implemented in a Security Constrained Unit Commitment (SCUC) framework that minimizes the total operation costs based on generator three-part supply offers subject to various system and resource security constraints. Some enhanced features have been implemented in the RUC SCUC engine to handle special resource scheduling such as combined cycle resources, split generation resources and self-committed resources. The RUC settlement uses a ldquomake-wholerdquo payment to ensure all generating resources committed by RUC are adequately compensated for their operation costs.

Level of blood and blood products in human body is very important. Therefor, managing supply of blood is critical issue in healthcare system specially when the system faced with high demand for the product. In natural disasters, demand for blood units increase sharply because of injuries. Hence, efficiency in blood supply chain management play a significant role in this situation in supplying blood for transfusion centers, it is vital to supply in right time to prevent from casualties. Present paper proposes an optimization model for designing blood supply chain network in case of an earthquake disaster. The proposed two-stage stochastic model is Programmed based on scenarios for earthquake in a populated mega-city. The designed network has three layers; first layer is donation areas, the second layer consists distribution centers and facilities and the last layer is transfusion centers. In proposed two-stage stochastic optimization model, decisions of locating permanent collection facilities and amount of each blood type pre-inventory are made in first stage and operation decisions that have dependent on possible scenarios are made in second stage. The model also considers the possibility of blood transfusion between different blood types and its convertibility to blood derivatives regarding medical requirements. In order to solve the proposed two-stage stochastic model, L-shaped algorithm, an efficient algorithm to solve scenario based stochastic models, has been used. In addition, application of the model and the algorithm tests with real data of likely earthquake in Tehran mega city (Densest city of Iran).