Scenario-based Stochastic Programming Research Articles

Global supply chain network design for shelf-life products under uncertainty: a case study of pistachios

PurposeSupply chain management has become critical in today’s globalized environment, with growingly intense competition on the international level. The particular characteristics of modern trade have led companies to globalize and devise increasingly sophisticated supply chains to meet customer demand worldwide. Motivated by the need to address these challenges, we have developed a new model for a global supply chain that incorporates uncertainties in exchange rates, demand fluctuations, and the quantity of produce.Design/methodology/approachThe objective of the proposed model is to maximize supply chain profitability. Our model optimizes several critical decisions in the proposed global supply chain, including the location of domestic and foreign distribution centers, allocating the centers to customers, transportation mode selection, storage temperature, optimal farm purchase quantities, product flows across the network, and the shelf-life of products. Scenario-based stochastic programming approach is employed to account for the inherent uncertainties within the model. A pistachio supply chain is examined as a case study in this article, and the efficiency of the proposed model is demonstrated through computational results.FindingsThe model was solved using the CPLEX solver in GAMS and the results, the Sirjan DDC and Turkey FDC have been selected. In general, 40% of demand for customers from FDC (turkey) and 60% of demand from DDC (sirjan) is provided. Changes in the demand of foreign customers make the net profit more effective than changes in the demand for domestic customers. The decrease in exchange rate decreases the network profit with a higher slope and the increase in exchange rate will increase network profit with a relatively stable slope.Originality/valueWhile research on GSCs for perishable products has been ongoing for several years, the importance of the subject necessitates continued investigation in this area. This paper aimed to address this gap by presenting an optimization model for designing GSCs for perishable products under uncertainty and with various transportation modes. The proposed model was designed with the aim of improving supply chain performance and real-world applicability.

Economic and risk based optimal energy management of a multi-carrier energy system with water electrolyzing and steam methane reform technologies for hydrogen production

This paper proposes stochastic programming to optimal economic scheduling problems of a sustainable integrated energy system with renewable resources including power, natural gas, and hydrogen carriers. Hydrogen is considered a byproduct of electrical power and natural gas carriers using water electrolysis and steam methane reform process technologies. The main objective is to minimize the operation and emission costs while addressing uncertainties of electric/heating/cooling demands, electricity price, and renewable generation using scenario-based stochastic programming. To achieve a risk-hedging strategy, downside risk constraints are involved to minimize the risky scenarios portfolio. The whole problem is modeled as mixed-integer linear programming in GAMS optimization software. The analysis revealed that the expected operation cost without DRC is $ 577.52 and the expected risk-in-cost value for risky scenarios is $ 470.7. However, a conservative decision for reaching zero risk is costly and increases the expected cost up to $ 2901.1, which is not economically viable. A modest decision-making strategy compromises the cost and risk values where for decreasing the risk-in-cost to $ 288.7 (36.8%), the expected cost increased by to $1010.39 (75.95%). Moreover, the risk-averse decision-maker lowers the power sold to the grid, increases the use of water electrolyzing instead of the SMR process to reduce the environmental charges, and tries to increase flexibility with the help of hydrogen and battery storage.

Transactive energy framework in fuel cell based multi-carrier energy hubs based on conditional value-at-risk

The prevalence of peer-to-peer operation among industrial energy hubs is considered a promoting method to enhance local energy autonomy, efficiency, and flexibility. By conducting stochastic programming, this paper aims to minimize the operating cost of multiple industrial energy hubs that trade power and heat energies with each other and utility. Concerning the important role of hydrogen systems, fuel cell-based combined heat and power (CHP) generators are employed within the hubs to increase sustainability. The presence of electric vehicles (EVs) and shiftable loads enhances the flexibility during peer-to-peer operating mode. The trading price for power and heat energies are derived at first by solving a deterministic problem and considering average values for demands and generation. However, to address the uncertainties in renewable generation, electric and heat demands, and electricity prices under operation, scenario-based stochastic programming tries to optimize the expected objective function. Furthermore, the Conditional Value-at-Risk (CVaR) approach is proposed to provide various risk-averse scheduling tactics and measure the risk of each scenario. The results show that the proposed risk-constrained approach reduces the risk and makes cautious decisions about energy resources and trades. In this regard, the expected profit has been reduced by 75%, i.e., from 1636.78 NOK under a risk-neutral case to 414.97 NOK under a risk-averse case to reduce the expected risk in operating cost.

Multi-objective placement and sizing of energy hubs in energy networks considering generation and consumption uncertainties

This paper presents the placement and sizing of energy hubs (EHs) in electricity, gas, and heating networks. EH is a coordinator framework for various power sources, storage devices, and responsive loads. For simultaneous modeling of economic, operation, reliability, and flexibility indices, the proposed scheme is expressed as a three-objective optimization in the form of Pareto optimization based on the sum of weighted functions. The objective functions of this problem respectively minimize the planning cost of EHs (equal to the total cost of construction of hubs and their expected operating cost), the expected energy loss of the mentioned networks, and the expected energy not-supplied (EENS) of these networks in the case of an N − 1 event. The problem is constrained by power flow equations and operation and reliability constraints of these network together with the EH planning and operation model, and flexibility constraints of the EHs. Then, to achieve unique optimal solution in the shortest possible time, a linear approximation model is extracted for the proposed scheme. Moreover, scenario-based stochastic programming (SBSP) is employed to model uncertainties of load, energy cost, renewable power, and accessibility of the mentioned network equipment. Finally, the obtained numerical results indicate the capability of the proposed scheme in enhancing the economic and flexibility situation of EHs and improving the reliability and operation status of energy networks along with achieving optimal planning and operation for EHs.

A stochastic optimization model for patient evacuation from health care facilities during hurricanes

We propose a rigorous modeling and methodological effort that integrates statistical implementation of hydrology models in predicting inland and coastal flood scenarios due to hurricanes and a scenario-based stochastic integer programming model which suggests resource and staging area decisions in the first stage and the evacuation decisions in the second stage. This novel study combines physics-based flood prediction models and stochastic optimization for large-scale multi-facility coordination of hospital and nursing home evacuations before impending hurricanes. The optimization model considers scenario-dependent evacuation demand, transport vehicles with varying capacities, and both critical and non-critical patients. Utilizing Hurricane Harvey of 2017 as a case study and actual healthcare facility locations in southeast Texas, we explore various evacuation policies, demonstrating the impact of routing strategies, staging area decisions, flood thresholds, and receiving facility capacities on evacuation outcomes. One of the findings is that choosing staging area(s) and deploying evacuation vehicles optimally considering the uncertainty of the hurricane’s path at the time of decision making could have significant effect on the total cost of the operation and evacuation time experienced by the evacuees. We also show the non-negligible value of the scenario-based staging and routing solution conservatively calculated in relation to a single scenario solution using the concept of value of stochastic solution.

Wind Power Bidding Based on an Ensemble Differential Evolution Algorithm with a Problem-Specific Constraint-Handling Technique

The intermittent nature of wind power generation induces great challenges for power bidding in the electricity market. The deployment of battery energy storage can improve flexibility for power bidding. This paper investigates an optimal power bidding strategy for a wind–storage hybrid power plant in the day-ahead electricity market. To handle the challenges of the uncertainties of wind power generation and electricity prices, the optimal bidding problem is formulated as a risk-aware scenario-based stochastic programming, in which a number of scenarios are generated using a copula-based approach to represent the uncertainties. These scenarios consider the temporal correlation of wind power generation and electricity prices between consecutive time intervals. In the stochastic programming, a more practical but nonlinear battery operation cost function is considered, which leads to a nonlinear constrained optimization problem. To solve the nonlinear constrained optimization problem, an ensemble differential evolution (EDE) algorithm is proposed, which makes use of the merits of an ensemble of mutant operators to generate mutant vectors. Moreover, a problem-specific constraint-handling technique is developed. To validate the effectiveness of the proposed EDE algorithm, it is compared with state-of-the-art DE-based algorithms for constrained optimization problems, including a constrained composite DE (C2oDE) algorithm and a novel DE (NDE) algorithm. The experimental results demonstrate that the EDE algorithm is much more reliable and much faster in finding a better bidding strategy against benchmarking algorithms. More precisely, the average values of the success rate are 0.893, 0.667, and 0.96 for C2oDE, NDE, and EDE, respectively. Compared to C2oDE and NDE, the average value of the mean number of function evaluations to succeed with EDE is reduced by 76% and 59%, respectively.

Multi-stage scenario-based stochastic programming for managing lot sizing and workforce scheduling at Vestel

Multi-stage scenario-based stochastic programming for managing lot sizing and workforce scheduling at Vestel

Sustainable project selection and scheduling using scenario-based stochastic programming: a case study of industrial projects

Sustainable project selection and scheduling using scenario-based stochastic programming: a case study of industrial projects

Optimal Probabilistic Allocation of Photovoltaic Distributed Generation: Proposing a Scenario-Based Stochastic Programming Model

The recent developments in the design, planning, and operation of distribution systems indicate the need for a modern integrated infrastructure in which participants are managed through the perceptions of a utility company in an economic network (e.g., energy loss reduction, restoration, etc.). The penetration of distributed generation units in power systems are growing due to their significant influence on the key attributes of power systems. As a result, the placement, type, and size of distributed generations have an essential role in reducing power loss and lowering costs. Power loss minimization, investment and cost reduction, and voltage profile improvement combine to form a conceivable goal function for distributed generation allocation in a constrained optimization problem, and they require a complex procedure to control them in the most appropriate way while satisfying network constraints. Such a complex decision-making procedure can be solved by adjusting the dynamic optimal power flow problem to the associated network. The purpose of the present work is to handle the distributed generation allocation problem for photovoltaic units, attempting to reduce energy and investment costs while accounting for generation unpredictability as well as load fluctuation. The problem is analyzed under various scenarios of solar radiation through a stochastic programming technique because of the intense uncertainty of solar energy resources. The formulation of photovoltaic distributed generation allocation is represented as a mixed-integer second-order conic programming problem. The IEEE 33-bus and real-world 136-bus distribution systems are tested. The findings illustrate the efficacy of the proposed mathematical model and the role of appropriate distributed generation allocation.

Optimal risk-driven operation of renewable-penetrated distribution network during natural-disasters: A resiliency-oriented analysis

The increasing penetration of renewable energy sources in distribution networks has brought new challenges in ensuring reliable and resilient operation during natural disasters. The proposed approach considers the uncertainties associated with renewable energy sources, natural disasters, and demand using scenario-based stochastic programming to minimize the expected operational cost of the distribution network. Due to the huge uncertainties related to renewable resources, an efficient risk analysis is applied to obtain a sense of the worst realizations of uncertainties using the downside risk constraints method. Besides, two types of demand response schemes (DRSs) are considered to prevent widespread blackouts in the distribution network. This study provides insights into the integration of renewable energy sources in distribution networks and highlights the importance of considering resiliency optimization of this networks. The effectiveness of the proposed approach is demonstrated through simulations on a 33-bus test distribution system, and the results show successful ride-through of the islanding hours with 100% risk reduction by only 2.91% increase in operation cost over the considered scenarios, while risks may still be present in other set of scenarios. Overall, this research contributes to the investigate the uncertainty-driven operational risks of renewable energy integration of resilient distribution network.

A multi-objective closed-loop supply chain under uncertainty: An efficient Lagrangian relaxation reformulation using a neighborhood-based algorithm

Population growth and unprecedented industrialization have contributed to a significant surge in global waste generation, underscoring the need for efficient waste management practices such as recycling, disassembling, restoration, and disposal. Closed-loop supply chain (CLSC) networks offer a solution for effective waste management by enabling the recycling, reassembly, and reuse of waste products. However, designing an optimal CLSC network presents challenges due to uncertainties associated with various parameters, including customer demand, sustainable development goals, and the complexity of network design optimization. This paper addresses these challenges by proposing a comprehensive CLSC network that optimizes environmental, economic, and social footprints through a multi-objective optimization approach. To account for parameter uncertainties, we employ scenario generation using a scenario-based stochastic programming procedure. To solve the proposed model, we transform the multi-objective formulation into a single-objective model using a weighted sum method considering a set of problem-specific heuristics. Furthermore, we leverage Lagrangian relaxation theory to formulate various problem reformulations, aimed at attaining an optimal lower bound for the CLSC problem. We complement this with a neighborhood-based algorithm that helps identify a feasible upper bound. By utilizing a sub-gradient framework, we iteratively reoptimize both the selected reformulation and the neighborhood-based algorithm, culminating in the achievement of an optimal solution. To exemplify the practical applicability of our research, we present a case study focusing on the light engineering industry in Bangladesh. Through rigorous analyses, we showcase that our proposed algorithm can deliver an optimal solution with an optimality gap of 0.06. By offering insights into the successful implementation of our CLSC network in a real-world context, we aim to provide valuable guidance for practitioners seeking to establish efficient and sustainable waste management systems.

Day-ahead bidding strategy of regional integrated energy systems considering multiple uncertainties in electricity markets

The regional integrated energy system (IES) is considered a promising paradigm for economic multi-energy provision while promoting the accommodation of renewable distributed energy resources (RDER). However, various uncertainties faced by the IES pose challenges to fulfilling its functionalities and economic promises. This paper proposes a day-ahead optimal bidding strategy of IES in electricity markets with multiple time scales of electricity settlement and energy dispatch for minimizing its expected operational cost based on the hybrid scenario-based stochastic and chance-constrained programming. It enables the IES to determine the optimal bidding electricity quantities in the day-ahead market in a multi-energy complementary manner by incorporating the potential real-time clearing price scenarios, with the uncertainties introduced by RDER generation and multi-energy loads efficiently addressed using chance constraints. Herein, a gradient boosted regression tree (GBRT) based quantile forecasting method is developed to equivalently reformulate the chance constraints to tractable deterministic constraints without any prior knowledge or probability distribution assumptions. The proposed day-ahead bidding strategy is extensively assessed through simulation experiments in the PJM and Guangdong electricity markets and the numerical results confirm the effectiveness of the proposed solution.

Flexibility Pricing of Grid-Connected Energy Hubs in the Presence of Uncertain Energy Resources

The paper expresses the problem of flexibility pricing in energy hubs (EHs) that are in connection with electricity, heat, and gas networks considering of uncertain energy generation sources. Scheme includes a bilevel formulation. Its upper-level states for modeling of the flexibility services are provided by various resources within the EH. The problem considers maximization of the expected profit of these resources in the flexibility market. The problem constraints include the flexibility model of flexible resources such as storage devices, responsive loads, and controllable distributed generations (DGs). The flexibility model of resources relies on their active and heat power. The lower-level problem calculates energy and flexibility prices and formulates the flexible operation of energy resources considering EHs. Here, constraints include optimal power flow equations in the energy networks; operation model of EHs with power sources, storage devices, and different responsive loads; and flexibility limits of EHs. Also, a linear approximation model is adopted in the suggested design using conventional linearization techniques. Next, the Karush–Kuhn–Tucker (KKT) method is used to derive a single-level model for the problem. The scheme adopts scenario-based stochastic programming (SBSP) so that uncertainties of renewable power, energy price, load, and energy consumption of mobile storage devices are properly modeled. Finally, the results validate the suggested design’s potential in modifying and enhancing the operation, flexibility, and economic situation of energy networks and EHs.

Resilience strategies in coping to disruptions of wheat supply chain caused by the Russia–Ukraine war crisis: case study from an emerging economy

PurposeThe Russia–Ukraine war has disrupted the wheat supply worldwide. Given that wheat is one of the most important agri-food products in the world, it is necessary to pay attention to the wheat supply chain during the global crises. The use of resilience strategies is one of the solutions to face the supply chain disruptions. In addition, there is a possibility of multiple crises occurring in global societies simultaneously.Design/methodology/approachIn this research, the resilience strategies of backup suppliers (BS) and inventory pre-prepositioning (IP) were discussed in order to cope with the wheat supply chain disruptions. Furthermore, the p-Robust Scenario-based Stochastic Programming (PRSSP) approach was used to optimize the wheat supply chain under conditions of disruptions from two perspectives, feasibility and optimality.FindingsAfter implementing the problem of a real case in Iran, the results showed that the use of resilience strategy reduced costs by 9.33%. It was also found that if resilience strategies were used, system's flexibility and decision-making power increased. Besides, the results indicated that if resilience strategies were used and another crisis like the COVID-19 pandemic occurred, supply chain costs would increase less than when resilience strategies were not used.Originality/valueIn this study, the design of the wheat supply chain was discussed according to the wheat supply disruptions due to the Russia–Ukraine war and its implementation on a real case. In the following, various resilience strategies were used to cope with the wheat supply chain disruptions. Finally, the effect of the COVID-19 pandemic on the wheat supply chain in the conditions of disruptions caused by the Russia–Ukraine war was investigated.

Energy-sharing operation strategy of multi-district integrated energy systems considering carbon and renewable energy certificate trading

District integrated energy systems (IESs) have proceeded to the practice stage. A day-ahead (DA) coordinated operation strategy of multi-district IESs is proposed when the entities participate in the energy market (EM), the spinning reserve market (SRM), the natural gas market, the carbon market, and the renewable energy certificate (REC) market simultaneously. We adopt the scenario-based stochastic programming method and the two-settlement mechanism to measure the uncertainties brought by electricity prices, photovoltaic (PV) outputs, and loads. Considering the topologies of electricity, heating, and cooling networks, the energy-sharing mechanism and the integrated demand response (IDR) mechanism are both implemented. We study the overlapped benefits of renewable energy generation (REG) from carbon and REC markets and propose a concept of the green index (GI). Case studies demonstrate that the proposed strategy model and the evaluation indicator can not only contribute to the economical and eco-friendly operation of the multi-district league (MDL), but also stimulate the coupling and complementarity of multiple energies.

Resilient relief supply planning using an integrated procurement-warehousing model under supply disruption

In order to mitigate the damage caused by natural disasters, appropriate relief supply planning is essential for humanitarian relief chains. This paper develops a resilient relief supply plan by formulating a novel integrated procurement-warehousing model under supply disruption via utilizing a portfolio of long-term contracts between a relief organization, multiple main and backup suppliers, and a third party who provides warehousing service. By using a portfolio of supply sources, a tailored two-stage scenario-based stochastic programming model is presented for determining an integrated relief procurement-warehousing plan. The plan includes (1) a number of multi-period quantity flexibility contracts with the main suppliers at pre-disaster, for prepositioning of relief supplies while ensuring to receive extra required amounts at post-disaster, (2) a number of dynamic option contracts with backup suppliers for decreasing the impacts of risks pertaining to the demand uncertainty and supply disruption at the main suppliers, and (3) a multi-period warehousing contract with a third party which allows the relief organization to adjust the required storage space in different periods to avoid extra cost pertaining to the storage space surplus/shortage. An effective differential evolution (DE) solution algorithm is also devised to solve the real scale instances efficiently. Applicability of the proposed model is illustrated by a real case study and useful managerial insights are extracted through conducting several sensitivity analyses.

Coordinated operation for multi-EHs with different risk preferences: A hybrid approach with stochastic programming and cooperative game

The energy hub (EH) integrates various types of energy supply equipment and loads, improving operational efficiency but bringing uncertainty. For dealing with the uncertainty factors that EH faces, the multi-EHs operation mode has more advantages than the single-EH operation mode. Therefore, a cooperative game-based coordinated model for multiple EHs with different risk preferences is built. The expected cost of all EHs is served as the objective function. Also, all EH’s conditional value at risk (CVaR) does not exceed its acceptable upper limit. The upper limit of CVaR can be obtained by solving a bi-objective optimization model for the independent operation of EH. Especially each EH has a different risk preference in the independent operation model, i.e., the weighting factor between costs and risks. Furthermore, by using scenario-based stochastic programming, the above models are transformed into linear models. Then, a novel two-factor cost allocation method for multi-EH with different risk preferences is proposed. The fixed and proportional allocation coefficient of each EH is obtained by solving a set of allocation equations based on the Shapley value. Finally, numerical studies with three EHs demonstrate the effectiveness of the proposed method. In the case study, the overall expected cost and CVaR of multiple EHs decreased by 4.99 % and 15.88 %, respectively.

Reshore or not Reshore: A Stochastic Programming Approach to Supply Chain Optimization

This paper presents a scenario-based stochastic mixed integer programming model for risk-neutral or risk-averse optimization of supply chain reshoring to domestic region, under the ripple effect propagated from a foreign disruption source region. The reshoring decisions with respect to tier-one suppliers of parts and tier-zero OEM (Original Equipment Manufacturer) assembly plants are considered under disruptions in supply, manufacturing, logistics and demand rippling across the entire supply chain. The proposed innovative approach integrates strategic supply chain reshoring and operational supply chain scheduling, which allows the decision maker to evaluate the operational impact of the strategic decision. Results of computational experiments, partially modeled after a supply chain reshoring problem in the smartphone industry, are provided. The findings indicate that reshoring decisions are strongly dependent on the level of government subsidy for capital expenditure and for risk-neutral reshoring, a portfolio of supply chain nodes with positive expected net savings can be considered only. In general, the reshored supply chain can better meet domestic market demand. Moreover, full reshoring of a supply chain improves its business as usual performance and even partial reshoring mitigates the impact of the ripple effect. However, for risk-averse decision-making, if reshoring is incapable of reducing worst-case cost, in particular, worst-case lost sales, no reshoring is selected.

Integrated stochastic transmission network and wind farm investment considering maximum allowable capacity

• A stochastic model is presented for transmission and wind power investment. • The model considers demand and wind generation uncertainty. • The model considers maximum allowable capacity. • The model is formulated as a stochastic bilevel optimization problem. • Multi-parametric programming is used to solve the problem. This research presents a novel mathematical methodology for integrated transmission network and wind farm investment (ITWI) considering maximum allowable capacity (MAC). The joint problem of transmission and wind farm investment planning is carried out under a central planner perspective, where load and wind power uncertainties are managed using scenario-based stochastic programming. Distinct from the existing models in which the installation capacity of wind farms is restricted only by the available investment budget, the wind power capacity is limited by MAC considering strength measures. In this regard, the investment problem is addressed as a bi-level programming model where the upper level seeks to minimize the investment cost associated with transmission lines and wind farms plus the operation cost while the lower level determines the MAC of wind farms. The existence of integer decision variables in the lower level renders Karush-Kuhn-Tucker (KKT) conditions invalid. Thus, the multi-parametric programming (MPP) method is utilized to solve the mixed-integer bi-level linear programming (MIBLP). Numerical tests on two different power systems corroborate the efficiency of the proposed model. The comparable results demonstrate that ignoring the MAC of wind farms leads to inefficient solutions due to additional unnecessary investment in the wind energy sector.

A decentralized stochastic bidding strategy for aggregators of prosumers in electricity reserve markets

Recent years have seen an increasing interest in demand response as a means to provide flexibility and support the penetration of renewable resources in the power system. Aggregators play a key role, in this regard, by enabling the participation of small-scale distributed energy resources and loads connected at the distribution network into local and central markets.This paper proposes an optimal strategy to support aggregators of a large number of small prosumers to participate in the tertiary reserve procurement market. In particular, a two-stage decentralized approach is proposed in which, first, prosumers individually optimize their flexible appliances schedule according to their own requirements and preferences, without sharing any information with the aggregator. At the aggregator level, a trading strategy is proposed for participation in the reserve market aiming at maximizing the aggregator’s profit under the pay-as-bid pricing scheme, while only requiring a linear programming formulation ensuring the efficiency of the trading problem. In the developed approach, a scenario-based stochastic programming method is introduced to capture the uncertainties of market prices, weather conditions, loads, and user behavior.To demonstrate the applicability of the proposed method, using real data, simulations on 2500 small prosumers in a realistic setting are carried out. The proposed linear and decentralized method can be executed within a few minutes, enabling its applicability for aggregators with a large number of customers.