Multistage Stochastic Mixed-integer Program Research Articles

Scenario-dominance to multi-stage stochastic lot-sizing and knapsack problems

This paper presents strong scenario dominance cuts for effectively solving the multi-stage stochastic mixed-integer programs (M-SMIPs), specifically focusing on the two most well-known M-SMIPs: stochastic capacitated multi-item lot-sizing (S-MCLSP) and the stochastic dynamic multi-dimensional knapsack (S-MKP) problems. Scenario dominance is characterized by a partial ordering of scenarios based on the pairwise comparisons of random variable realizations in a scenario tree of a stochastic program. In this paper, we study the implications of scenario-dominance relations and inferences obtained by solving scenario sub-problems to drive new strong cutting planes to solve S-MCLSP and S-MKP instances faster. Computational experiments demonstrate that our strong scenario dominance cuts can significantly reduce the solution time for such M-SMIP problems with an average of 0.06% deviation from the optimal solution. The results with up to 81 random variables for S-MKP show that strong dominance cuts improve the state-of-the-art solver solution of two hours by 0.13% in five minutes. The proposed framework can also be applied to other scenario-based optimization problems.

Lagrangian Dual Decision Rules for Multistage Stochastic Mixed-Integer Programming

On Decision Rules for Multistage Stochastic Programs with Mixed-Integer Decisions Multistage stochastic programming is a field of stochastic optimization for addressing sequential decision-making problems defined over a stochastic process with a given probability distribution. The solution to such a problem is a decision rule (policy) that maps the history of observations to the decisions. Design of the decision rules in the presence of mixed-integer decisions is quite challenging. In “Lagrangian Dual Decision Rules for Multistage Stochastic Mixed-Integer Programming,” Daryalal, Bodur, and Luedtke introduce Lagrangian dual decision rules, where linear decision rules are applied to dual multipliers associated with Lagrangian duals of a multistage stochastic mixed-integer programming (MSMIP) model. The restricted decisions are then used in the development of new primal- and dual-bounding methods. This yields a new general-purpose approximation approach for MSMIP, free of strong assumptions made in the literature, such as stagewise independence or existence of a tractable-sized scenario-tree representation.

A Multistage Stochastic Program to Optimize Prescribed Burning Locations Using Random Fire Samples

Selecting the optimal locations and timing for prescribed burning is challenging when considering uncertainties in weather, fire behavior, and future fire suppression. In this study, we present a sample average approximation (SAA) based multistage stochastic mixed integer program with recourse to optimize prescribed burning decisions. The recourse component of the SAA model considers post-fuel-treatment suppression decisions to manage fire spreads in multiple future planning periods. Our research aims at studying how an SAA model may benefit from using random fire samples to find good locations for prescribed burning during the first planning period. Two hypothetical test cases are designed to compare the impact of fire sample sizes on solution quality, and to illustrate how to identify high-quality period-one prescribed burning solutions. Results suggest that running SAA models using larger fire sample sizes can lead to better period-one solutions, but this benefit will diminish after the sample size reaches to certain thresholds. We found multiple period-one prescribed burning decisions that may result in similar effects in mitigating future wildfire risks.

Stage-t scenario dominance for risk-averse multi-stage stochastic mixed-integer programs

This paper presents a new and general approach, named “Stage-t Scenario Dominance,” to solve the risk-averse multi-stage stochastic mixed-integer programs (M-SMIPs). Given a monotonic objective function, our method derives a partial ordering of scenarios by pairwise comparing the realization of uncertain parameters at each time stage under each scenario. Specifically, we derive bounds and implications from the “Stage-t Scenario Dominance” by using the partial ordering of scenarios and solving a subset of individual scenario sub-problems up to stage t. Using these inferences, we generate new cutting planes to tackle the computational difficulty of risk-averse M-SMIPs. We also derive results on the minimum number of scenario-dominance relations generated. We demonstrate the use of this methodology on a stochastic version of the mean-conditional value-at-risk (CVaR) dynamic knapsack problem. Our computational experiments address those instances that have uncertainty, which correspond to the objective, left-hand side, and right-hand side parameters. Computational results show that our “scenario dominance"-based method can reduce the solution time for mean-risk, stochastic, multi-stage, and multi-dimensional knapsack problems with both integer and continuous variables, whose structure is similar to the mean-risk M-SMIPs, with varying risk characteristics by one-to-two orders of magnitude for varying numbers of random variables in each stage. Computational results also demonstrate that strong dominance cuts perform well for those instances with ten random variables in each stage, and ninety random variables in total. The proposed scenario dominance framework is general and can be applied to a wide range of risk-averse and risk-neutral M-SMIP problems.

Risk-averse multi-stage stochastic optimization for surveillance and operations planning of a forest insect infestation

We derive a nested risk measure for a maximization problem and implement it in a scenario-based formulation of a multi-stage stochastic mixed-integer programming problem. We apply the risk-averse formulation to the surveillance and control of a non-native forest insect, the emerald ash borer (EAB), a wood-boring beetle native to Asia and recently discovered in North America. Spreading across the eastern United States and Canada, EAB has killed millions of ash trees and cost homeowners and local governments billions of dollars. We present a mean-Conditional Value-at-Risk (CVaR), multi-stage, stochastic mixed-integer programming model to optimize a manager’s decisions about surveillance and control of EAB. The objective is to maximize the benefits of healthy ash trees in forests and urban environments under a fixed budget. Combining the risk-neutral objective with a risk measure allows for a trade-off between the weighted expected benefits from ash trees and the expected risks associated with experiencing extremely damaging scenarios. We define scenario dominance cuts (sdc) for the maximization problem and under the decision-dependent uncertainty. We then solve the model using the sdc cutting plane algorithm for varying risk parameters. Computational results demonstrate that scenario dominance cuts significantly improve the solution performance relative to that of CPLEX. Our CVaR risk-averse approach also raises the objective value of the least-benefit scenarios compared to the risk-neutral model. Results show a shift in the optimal strategy from applying less expensive insecticide treatment to more costly tree removal as the manager becomes more risk-averse. We also find that risk-averse managers survey more often to reduce the risk of experiencing adverse outcomes.

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 tradeoff 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.

A distributed computing framework for multi-stage stochastic planning of renewable power systems with energy storage as flexibility option

An integrated generation, transmission, and energy storage planning model accounting for short-term constraints and long-term uncertainty is proposed. The model allows to accurately quantify the value of flexibility options in renewable power systems by representing short-term operation through the unit commitment constraints. Long-term uncertainty is represented through a scenario tree. The resulting model is a large-scale multi-stage stochastic mixed-integer programming problem. To overcome the computational burden, a distributed computing framework based on the novel Column Generation and Sharing algorithm is proposed. The performance improvement of the proposed approach is demonstrated through study cases applied to the NREL 118-bus power system. The results confirm the added value of modeling short-term constraints and long-term uncertainty simultaneously. The computational case studies show that the proposed solution approach clearly outperforms the state of the art in terms of computational performance and accuracy. The proposed planning framework is used to assess the value of energy storage systems in the transition to a low-carbon power system.

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.

A progressive hedging approach for large-scale pavement maintenance scheduling under uncertainty

ABSTRACT This study approaches a multi-stage stochastic mixed-integer programming model for the high-level complexity of large-scale pavement maintenance scheduling problems. The substance of some parameters in the mentioned problems is uncertain. Ignoring the uncertainty of these parameters in the pavement maintenance scheduling problems may lead to suboptimal solutions and unstable pavement conditions. In this study, annual budget and pavement deterioration rate are considered uncertain parameters. On the other hand, pavement agencies generally face large-scale pavement networks. The complexity of the proposed stochastic model increases exponentially with the number of network sections and scenarios. The problem is solved using the Progressive Hedging Algorithm (PHA), which is suitable for large-scale stochastic programming problems, by achieving an effective decomposition over scenarios. A modified adaptive strategy for choosing the penalty parameter value is applied that aims to improve the solution process. A pavement network including 251 sections is considered the case study for this investigation, and the current study seeks optimal maintenance scheduling over a finite analysis period. The performance of the stochastic model is compared with that of the deterministic model. The results indicate that the introduced approach is competent to address uncertainty in maintenance and rehabilitation problems.

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.

Multistage stochastic programming approach for joint optimization of job scheduling and material ordering under endogenous uncertainties

Job scheduling incorporated with material ordering can better meet practical needs and lead to overall cost reduction. In this paper, we present a stochastic approach for this joint optimization problem, considering uncertainties in job processing times and resource consumptions. We formulate this integrated problem as a multistage stochastic mixed-integer program involving endogenous uncertainties. Several theoretical properties that can reduce the model size are studied. Based on this, a branch-and-bound exact algorithm and a sampling-based approximate method are designed as solution algorithms. The effectiveness of the integrated scheduling approaches and the efficiency of the proposed solution algorithms are evaluated via numerical experiments. It is shown that our approach can greatly reduce the overall cost compared with the traditional separate production planning approach, especially when production resources are not very restricted.

Using stochastic programming to solve an outpatient appointment scheduling problem with random service and arrival times

AbstractWe study a stochastic outpatient appointment scheduling problem (SOASP) in which we need to design a schedule and an adaptive rescheduling (i.e., resequencing or declining) policy for a set of patients. Each patient has a known type and associated probability distributions of random service duration and random arrival time. Finding a provably optimal solution to this problem requires solving a multistage stochastic mixed‐integer program (MSMIP) with a schedule optimization problem solved at each stage, determining the optimal rescheduling policy over the various random service durations and arrival times. In recognition that this MSMIP is intractable, we first consider a two‐stage model (TSM) that relaxes the nonanticipativity constraints of MSMIP and so yields a lower bound. Second, we derive a set of valid inequalities to strengthen and improve the solvability of the TSM formulation. Third, we obtain an upper bound for the MSMIP by solving the TSM under the feasible (and easily implementable) appointment order (AO) policy, which requires that patients are served in the order of their scheduled appointments, independent of their actual arrival times. Fourth, we propose a Monte Carlo approach to evaluate the relative gap between the MSMIP upper and lower bounds. Finally, in a series of numerical experiments, we show that these two bounds are very close in a wide range of SOASP instances, demonstrating the near‐optimality of the AO policy. We also identify parameter settings that result in a large gap in between these two bounds. Accordingly, we propose an alternative policy based on neighbor‐swapping. We demonstrate that this alternative policy leads to a much tighter upper bound and significantly shrinks the gap.

A multistage stochastic programming approach for preventive maintenance scheduling of GENCOs with natural gas contract

A preventive maintenance scheduling problem is studied on behalf of generation companies (GENCOs) with natural gas power plants, while taking into account their signed natural gas contracts and the opportunities of purchasing and selling natural gas in the spot market. This paper considers the uncertain prices of both natural gas and electricity in the spot market, and proposes a multistage stochastic mixed integer programming (MSMIP) model seeking the optimal operations regarding maintenance outage scheduling and natural gas trading. Large-scale MSMIP problems suffer not only the curse of dimensionality, but also computational difficulties with both discrete and continuous variables at each stage. To this respect, this paper leverages the progressive hedging algorithm based on scenario-based decomposition to solve large MSMIP problems. The solutions obtained from the algorithm exhibit promising quality under our numerical studies. Due to the independence among all the subproblems after the decomposition, the algorithm is amenable to parallel computing, which leads to faster convergence as demonstrated in the numerical results. Computational experiments also show that it is beneficial to use MSMIP while considering both maintenance planning and natural gas contracting. In addition, the results also indicate the GENCOs with a larger number of small generators perform better than those with a smaller number of big generators.

Pavement maintenance and rehabilitation planning optimisation under budget and pavement deterioration uncertainty

ABSTRACT One of the key parts of a pavement management system is the maintenance and rehabilitation planning. The planning is usually developed under the assumption that all parameters are known with certainty. In practice, there are various parameters afflicted with large uncertainty. Ignoring the uncertainty may lead to a suboptimal plan adversely affecting the network conditions. The objective of this study is to develop an optimisation framework for network-level pavement maintenance and rehabilitation planning considering the uncertain nature of pavement deterioration and the budget with an applicable approach. A multistage stochastic mixed-integer programming model is proposed to find the optimal plan that is feasible for all possible scenarios of uncertainty and optimise the expectation of objective function. Two case studies of 4 and 21 pavement sections are presented to show the applicability of the proposed method. The value of stochastic solution and the expected value of perfect information which are the indices for evaluating the benefits of using the stochastic model are, respectively, 30% and 85% of the objective function of here and now model for the first case study and 26% and 42% of it regarding the second one. The indices are high indicating the effectiveness of the stochastic solution.

A Multi-Stage Stochastic Programming Approach to the Optimal Surveillance and Control of 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 multi-stage 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 upon 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 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.

Land use optimization for nutrient reduction under stochastic precipitation rates

A nutrient reduction strategy for Iowa identifies land use and conservation alternatives to reduce nutrient loss from agriculture and the resulting Gulf of Mexico hypoxia. From the viewpoint of a policy maker concerned with regional costs and benefits, we develop a land use optimization model to maximize profit while satisfying nutrient reduction constraints. Because uncertain precipitation levels affect both yields and nutrient loss, we formulate two variants of a multistage stochastic mixed-integer program with probabilistic scenarios for annual precipitation generated from a Markov chain model. Numerical sensitivity analyses on the recourse variant reveal complicated interactions among the nutrient reduction and labor availability constraints as well as crop prices. The chance-constrained variant provides needed flexibility in meeting nutrient reduction goals by neglecting low-probability precipitation outcomes. Case study results indicate that, although significant financial incentives might be required for landowners to implement optimal strategies, substantial reductions in nutrient loss can be achieved.

Electric power infrastructure planning under uncertainty: stochastic dual dynamic integer programming (SDDiP) and parallelization scheme

We address the long-term planning of electric power infrastructure under uncertainty. We propose a Multistage Stochastic Mixed-integer Programming formulation that optimizes the generation expansion to meet the projected electricity demand over multiple years while considering detailed operational constraints, intermittency of renewable generation, power flow between regions, storage options, and multiscale representation of uncertainty (strategic and operational). To be able to solve this large-scale model, which grows exponentially with the number of stages in the scenario tree, we decompose the problem using Stochastic Dual Dynamic Integer Programming (SDDiP). The SDDiP algorithm is computationally expensive but we take advantage of parallel processing to solve it more efficiently. The proposed formulation and algorithm are applied to a case study in the region managed by the Electric Reliability Council of Texas for scenario trees considering natural gas price and carbon tax uncertainty for the reference case, and a hypothetical case without nuclear power. We show that the parallelized SDDiP algorithm allows in reasonable amounts of time the solution of multistage stochastic programming models of which the extensive form has quadrillions of variables and constraints.

A Lagrangian relaxation approach for stochastic network capacity expansion with budget constraints

In this paper, we consider capacity expansion for network models subject to uncertainty and budget constraints. We use a scenario tree approach to handle the uncertainty and construct a multi-stage stochastic mixed-integer programming model for the network capacity expansion problem. We assume that permanent capacity and spot market capacity are available, which can be used permanently or temporarily by the decision maker respectively. By relaxing the budget constraints, we propose a heuristic Lagrangian relaxation method to solve the problem. Two algorithms are developed to find tight upper bounds for the Lagrangian relaxation procedure. The experimental results show superior performance of the proposed Lagrangian relaxation method compared with CPLEX.

Scenario analysis of carbon emissions' anti-driving effect on Qingdao's energy structure adjustment with an optimization model, Part II: Energy system planning and management

In this study, an inexact multistage stochastic mixed-integer programming (IMSMP) method was developed for supporting regional-scale energy system planning (EPS) associated with multiple uncertainties presented as discrete intervals, probability distributions and their combinations. An IMSMP-based energy system planning (IMSMP-ESP) model was formulated for Qingdao to demonstrate its applicability. Solutions which can provide optimal patterns of energy resources generation, conversion, transmission, allocation and facility capacity expansion schemes have been obtained. The results can help local decision makers generate cost-effective energy system management schemes and gain a comprehensive tradeoff between economic objectives and environmental requirements. Moreover, taking the CO2 emissions scenarios mentioned in Part I into consideration, the anti-driving effect of carbon emissions on energy structure adjustment was studied based on the developed model and scenario analysis. Several suggestions can be concluded from the results: (a) to ensure the smooth realization of low-carbon and sustainable development, appropriate price control and fiscal subsidy on high-cost energy resources should be considered by the decision-makers; (b) compared with coal, natural gas utilization should be strongly encouraged in order to insure that Qingdao could reach the carbon discharges peak value in 2020; (c) to guarantee Qingdao's power supply security in the future, the construction of new power plants should be emphasised instead of enhancing the transmission capacity of grid infrastructure.