Multi-period Optimization Model Research Articles

A multi-period optimization model for the deployment of public electric vehicle charging stations on network

A multi-period multipath refueling location model is developed to expand public electric vehicle (EV) charging network to dynamically satisfy origin–destination (O–D) trips with the growth of EV market. The model captures the dynamics in the topological structure of network and determines the cost-effective station rollout scheme on both spatial and temporal dimensions. The multi-period location problem is formulated as a mixed integer linear program and solved by a heuristic based on genetic algorithm. The model and heuristic are justified using the benchmark Sioux Falls road network and implemented in a case study of South Carolina. The results indicate that the charging station rollout scheme is subject to a number of major factors, including geographic distributions of cities, vehicle range, and deviation choice, and is sensitive to the types of charging station sites.

Optimal Cellulosic Biomass Contracting with Multiple Feedstocks and Locations, and Multi-Modal Transport

Biorefineries are keen to design optimal biomass supply chains to minimize production, harvest, transport, and other costs. Such a design problem is challenging with the availability of multiple feedstocks (agricultural residues, perennials such as energy crops, short rotation woody crops), sourced from multiple harvest sheds, and transported across multiple modes (trucks, rails, and barges). This paper presents a multi-period optimization model to analyze the feasibility of collection from multiple harvest sheds. The results are demonstrated for a case study location in Alpena, MI served by truck and water transport. The model results suggest that: i) perennial biomass with higher yields would be preferred due to higher biomass production per unit area; ii) transport from farther locations are warranted only if the biomass production costs in the farther harvest sheds are cheaper by 20% - 30% compared to the adjacent harvest shed; and iii) the local situations of a biorefinery—characterized by the parametric inputs in the model—play a key role in determining the optimal feedstock composition across multiple harvest sheds. The results also support long term contracts associated with high yielding perennial feedstocks such as energy crops and short rotation woody crops.

A global optimization for sustainable multi-domain global manufacturing

A multi-period and domain nonlinear optimization model is developed in this article. The model incorporates the design of forward–reverse manufacturing networks topology, product platform and operation capacity planning. The model takes into account the lead times and costs for each period of planning and is formulated as mixed integer nonlinear programming (MINLP). A two stages branch and bound (B–B) with cutting planes and under-estimators is proposed, which exploits the problem structure by solving problem relaxation at the first stage upper bound (UB) and generates cutting planes and under-estimators at the second stage lower bound (LB). The application in a three-echelon forward–reverse global manufacturing network shows that the proposed algorithm is capable of efficiently handling large scale and non-convex problem formulation in order to achieve a global optimum. Some important results from the model are presented in terms of their impacts on the sustainability of global manufacturing.

An improved plant-wide multiperiod optimization model of a byproduct gas supply system in the iron and steel-making process

In an integrated steel mill, the byproduct gases of steel production processes can be recovered as fuel for the plant itself and can be used to generate electricity and steam in power plants. This work addresses the development of a mixed integer linear programming (MILP) model to solve the problem of byproduct fuel distribution, with the goal of maximizing energy utilization. Improvements are made in the formulation of the model and a heuristic procedure is proposed to assign appropriate weights to the objective function penalties, resulting in an increase in the operational performance of the fuel distribution system. Through case studies, a comparison is performed among a previous MILP-based optimization model found in the literature, the improved one proposed in this work and the real-world behavior of a fuel distribution system run by the operators without the aid of a computational tool.

A multi-period shelter location-allocation model with evacuation orders for flood disasters

Floods are a significant threat for several countries, endangering the safety and the well-being of populations. Civil protection authorities are in charge of flood emergency evacuation, providing means to help the evacuation and ensuring that people have comfortable and safe places to stay. This work presents a multi-period location-allocation approach that identifies where and when to open a predefined number of shelters, when to send evacuation orders, and how to assign evacuees to shelters over time. The objective is to minimize the overall network distances that evacuees have to travel to reach the shelters. The multi-period optimization model takes into account that the travel times vary over time depending on the road conditions. People’s reaction to the flood evolution is also considered to be dynamic. We also assume that shelters become available in different time periods and have a limited capacity. We present a mathematical formulation for this model which can be solved using an off-the-shelf commercial optimization solver, but only for small instances. For real size problems, given the dynamic characteristics of the problem, obtaining an optimal solution can take several hours of computing time. Thus, a simulated annealing heuristic is proposed. The efficiency of the heuristic is demonstrated with a comparison between the heuristic and the solver solutions for a set of random problems. The applicability of the multi-period model and of the heuristic is illustrated using a case study which highlights the importance and the benefits of adopting a dynamic approach for optimizing emergency response operations.

Credibilistic multi-period portfolio optimization model with bankruptcy control and affine recourse

Avoiding the possibility of bankruptcy during the investment horizon is very important to multi-period portfolio management. This paper considers a multi-period fuzzy portfolio selection problem with bankruptcy control. A multi-period portfolio optimization model imposed by a bankruptcy control constraint in fuzzy environment is proposed on the basis of credibility theory. In the proposed model, a linearly recourse policy is used to reflect the influence of historical predication basis on current portfolio decision. Three optimization objectives, viz., maximizing the terminal wealth and minimizing the cumulative risk and the cumulative uncertainty of the returns of portfolios over the whole investment horizon, are taken into consideration. For solving the proposed model, a fuzzy programming approach is applied to transform it into a single objective programming model. Then, a hybrid particle swarm optimization algorithm is designed for solution. Finally, an empirical example is presented to illustrate the application of the proposed model and solution comparisons are also given to demonstrate the effectiveness of the designed algorithm.

Multi-period Optimization Model for the UAE Power Sector

A multi-period power optimization model for the UAE's electricity sector is presented. The model aims to minimize the cumulative costs and CO2 emission of the UAE's power sector during the planning horizon. The optimization problem was formulated as a multi-period MILP model in the GAMS modelling system. Previous studies have analyzed the UAE power infrastructure using standard simulation software such as MARKAL and MESSAGE. The present work's novelty consists of determining the optimal evolution of the power generation infrastructure during different time periods under operational and environmental constraints. The optimization model was used to study the UAE's power system for the time periods comprised between the years 2015 and 2040. The simulation results show that the mathematical model is a valuable tool for planning the optimal evolution of the power plants’ fleet in the country, reduce levelized electricity costs and emissions, meet energy targets, and evaluate new power technologies.

Synthesis and optimisation of biomass-based tri-generation systems with reliability aspects

Tri-generation systems are utility systems which produce heat, power and cooling simultaneously. Use of tri-generation systems in industrial sites reduces the importation of power and improves local power reliability; at the same time, their inherently higher efficiency also reduces environmental impacts. However, interdependencies among process units in tri-generation plants can lead to vulnerability to cascading failures. Process units may become non-functional during the course of operations as a result of planned or unplanned stoppages. This issue is normally handled by installing additional capacity to the process units based on heuristics. However, such heuristics may not be able to address complex decisions pertaining to the installation of multiple units to provide redundancy, and may result in excessive capital and/or maintenance costs. In this work, a systematic approach for the grassroots design of a reliable BTS (biomass-based tri-generation system) considering equipment redundancy is presented. Chance-constrained programming and k-out-of-m system modelling are used to develop a multi-period optimisation model for a generic BTS. Two case studies are then solved to illustrate this modelling approach.

A Multi-Period Optimization Model for Service Providers Using Online Reservation Systems: An Application to Hotels.

This paper presents a multi-period optimization model for high margin and zero salvage products in online distribution channels with classifying customers based on number of products required. Taking hotel customers as an example, one is regular customers who reserve rooms for one day, and the other is long term stay (LTS) customers who reserve rooms for a number of days. LTS may guarantee a specific amount of demand and generate opportunity income for a certain number of periods, meanwhile with risk of punishment incurred by overselling. By developing an operational optimization model and exploring the effects of parameters on optimal decisions, we suggest that service providers should make decisions based on the types of customers, number of products required, and duration of multi-period to reduce the loss of reputation and obtain more profit; at the same time, multi-period buying customers should buy products early. Finally, the paper conducts a numerical experiment, and the results are consistent with prevailing situations.

Design multiperiod optimization model for the electricity sector under uncertainty – A case study of the Emirate of Abu Dhabi

In this study, a multiperiod model that considers uncertainty in the gas feedstock fuel price is developed for the optimal design of electric power systems. The optimization problem was formulated as a multiperiod stochastic programming model using the GAMS® modeling system. Previous studies have analyzed the United Arab Emirates’ (UAE) power infrastructure either using a deterministic point of view or simulation tools (e.g., MESSAGE and MARKAL). These previous research has demonstrated that natural gas will remain playing a significant role as key feedstock fuel in the UAE’s power sector. However, the present work is designed to be the first to consider different supply options for the natural gas feedstock (i.e., domestic, pipeline imports, and LNG imports) and electricity imports in the UAE power sector. Moreover, the natural gas supply and electricity import options are considered to be decision variables in the problem’s formulation. Additionally, the considered case studies assumed a realistically existing power infrastructure for the UAE, whereas previous works considered the planning of the UAE power infrastructure as a Greenfield project. Also, to the authors’ knowledge this is the first work to consider a robust optimization model for planning the UAE power infrastructure under uncertainty in the long term horizon. The model was used to study the planning of the power plant infrastructure in the UAE between 2015 and 2040 under uncertainty in the natural gas price. The optimization results show that the model is a valuable tool for planning the optimal power plant infrastructure of the country, reducing levelized electricity costs, and mitigating social and environmental damages.

Multi-Period Optimization Model for Electricity Generation Planning Considering Plug-in Hybrid Electric Vehicle Penetration

One of the main challenges for widespread penetration of plug-in hybrid electric vehicles (PHEVs) is their impact on the electricity grid. The energy sector must anticipate and prepare for this extra demand and implement long-term planning for electricity production. In this paper, the additional electricity demand on the Ontario electricity grid from charging PHEVs is incorporated into an electricity production planning model. A case study pertaining to Ontario energy planning is considered to optimize the value of the cost of the electricity over sixteen years (2014–2030). The objective function consists of the fuel costs, fixed and variable operating and maintenance costs, capital costs for new power plants, and the retrofit costs of existing power plants. Five different case studies are performed with different PHEVs penetration rates, types of new power plants, and CO2 emission constraints. Among all the cases studied, the one requiring the most new capacity, (~8748 MW), is assuming the base case with 6% reduction in CO2 in year 2018 and high PHEV penetration. The next highest one is the base case, plus considering doubled NG prices, PHEV medium penetration rate and no CO2 emissions reduction target with an increase of 34.78% in the total installed capacity in 2030. Furthermore, optimization results indicate that by not utilizing coal power stations the CO2 emissions are the lowest: ~500 tonnes compared to ~900 tonnes when coal is permitted.

Optimizing Spinning Reserve Requirement of Power System With Carbon Capture Plants

Spinning reserve (SR) is one of the most important resources used by system operators to respond to unforeseen events. In a low-carbon economy mode, carbon capture plant is an important CO <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$_{2}$</tex></formula> abatement option and might constitute a significant proportion of the generation mix. Due to their potential flexibility, such plants might affect the requirement for SR. This paper describes a multi-period optimization model for coordinating the generation, carbon capture and SR provision. In turn, this model is used to optimize the SR requirements, with the objective of minimizing the overall cost. Since this objective function combines the generation production cost, the expected energy not supplied (EENS) cost, SR provision cost and the carbon emission cost, it is better suited to evaluate the SR requirements of power system with carbon capture plants. Numerical results based on a 26-unit test system show that the proposed model is effective and practical.

Port Multi-Period Investment Optimization Model Based on Supply-Demand Matching

AbstractWith China’s economic slowdown and port low-level repeated construction, China ports are facing the problem of overheated investment. In this paper, using the port supply-demand balance and comprehensive cost as the two main optimization goals, the ecological carrying capacity and the port profit-loss as the constraints, the port multi-period investment decision optimization model is built up by means of dynamic programming. Sustainable development ability about port supply-demand matching and ecological carrying capacity are considered into the decision-making model, which is used to solve the existing literature disadvantage of port investment planning decision based on operation efficiency and benefit. It helps to prevent the port resources waste and ecological environment destruction, and has the reality instruction significance.

Modal split in offshore supply network under the objective of emissions minimization

We study modal split under the objective of emissions minimization in the transportation of cargo from centralized vendors in the oil and gas industry to decentralized supply bases on the Norwegian coast. The supply network includes direct road transport and a sea route along the coast. To gain insight into modal split decisions between road and sea transport from the shipper’s perspective multi-period mixed integer optimization models are formulated. Particularly the models give possibilities to examine how weekly demand patterns at supply bases, cargo commitments to sea transport, storage possibilities at supply bases, and shipper’s responsibility for a certain share of vessel capacity may effect the emissions and the modal split. Experiments on real data from an oil and gas company operating offshore show that the size of the share of vessel capacity and the possibility for storage at supply bases are the major determinants for a larger shift to environmentally friendly sea transport. The models can be used as means for making decisions regarding how a shipper can commit to sea transport to achieve less emissions.

Nash Equilibrium for a Special Class of Interval Functions. Applications to Economy

Abstract In this paper we want to apply a special type of Nash Equlibrium conditions obtained by the above author for interval functions to a particular class of interval functions that are applied in economy. We also give some generalizations for some particular problems from multi-period portfolio selection optimization models by using interval analysis.

A multi-period fuzzy portfolio optimization model with minimum transaction lots

Abstract In this paper, we consider a multi-period fuzzy portfolio optimization problem with minimum transaction lots. Based on possibility theory, we formulate a mean-semivariance portfolio selection model with the objectives of maximizing the terminal wealth and minimizing the cumulative risk over the whole investment horizon. In the proposed model, we take the return, risk, transaction costs, diversification degree, cardinality constraint and minimum transaction lots into consideration. To reflect investor’s aspiration levels for the two objectives, a fuzzy decision technique is employed to transform the proposed model into a single objective mixed-integer nonlinear programming problem. Then, we design a genetic algorithm for solution. Finally, we give an empirical application in Chinese stock markets to demonstrate the idea of our model and the effectiveness of the designed algorithm.

Volatility vs. Downside Risk: Optimally Protecting Against Drawdowns and Maintaining Portfolio Performance

As a consequence of recent market conditions an increasing number of investors are realizing the importance of controlling tail risk to reduce drawdowns thus increasing possibilities of achieving long-term objectives. Recently, so called volatility control strategies and volatility target approaches to investment have gained a lot of interest as strategies able to mitigate tail risk and produce better risk-adjusted returns. Essentially these are rule-based backward looking strategies in which no optimization is considered. In this contribution we focus on the role of volatility in downside risk reduction and, in particular, in tail risk reduction. The first contribution of our paper is to provide a viable way to integrate a target volatility approach, into a multiperiod portfolio optimization model, through the introduction of a local volatility control approach. Our optimized volatility control is contrasted with existing rule-based target volatility strategies, in an out-of sample simulation on real data, to assess the improvement that can be obtained from the optimization process. A second contribution of this work is to study the interaction between volatility control and downside risk control. We show that combining the two tools we can enhance the possibility of achieving the desired performance objectives and, simultaneously, we reduce the cost of hedging. The multiperiod portfolio optimization problem is formulated in a stochastic programming framework that provides the necessary flexibility for dealing with different constraints and multiple sources of risk.

Improving Geographic Equity in Kidney Transplantation Using Alternative Kidney Sharing and Optimization Modeling.

The national demand for kidney transplantation far outweighs the supply of kidney organs. Currently, a patient's ability to receive a kidney transplant varies depending on where he or she seeks transplantation. This reality is in direct conflict with a federal mandate from the Department of Health and Human Services. We analyze current kidney allocation and develop an alternative kidney sharing strategy using a multiperiod linear optimization model, KSHARE. KSHARE aims to improve geographic equity in kidney transplantation while also respecting transplant system constraints and priorities. KSHARE is tested against actual 2000-2009 kidney allocation using Organ Procurement and Transplant Network data. Geographic equity is represented by minimizing the range in kidney transplant rates around local areas of the country. In 2009, less than 25% of standard criteria donor kidneys were allocated beyond the local area of procurement, and Donor Service Area kidney transplantation rates varied from 3.0% to 30.0%, for an overall range of 27.0%. Given optimal sharing of kidneys within 600 miles of procurement for 2000-2009, kidney transplant rates vary from 5.0% to 12.5% around the country for an overall kidney transplant range of 7.5%. Nationally sharing kidneys optimally between local areas only further decreases the transplant rate range by 1.7%. Enhancing the practice of sharing kidneys by the KSHARE model may increase geographic equity in kidney transplantation.

Multi-period planning for electric car charging station locations: A case of Korean Expressways

Abstract One of the most critical barriers to widespread adoption of electric cars is the lack of charging station infrastructure. Although it is expected that a sufficient number of charging stations will be constructed eventually, due to various practical reasons they may have to be introduced gradually over time. In this paper, we formulate a multi-period optimization model based on a flow-refueling location model for strategic charging station location planning. We also propose two myopic methods and develop a case study based on the real traffic flow data of the Korean Expressway network in 2011. We discuss the performance of the three proposed methods.

Investment planning in energy considering economic and environmental objectives

This work proposes a linear disjunctive multiperiod optimization model for planning investments in energy sources considering two objectives, one economical (maximization of the net present value), and the other environmental (minimization of greenhouse gas emissions – GHG). The general goal of this approach is to provide an analysis tool for energy decision makers in planning investment considering different scenarios in GHG emanation. The decision variables of the model are the investment needs in money, capacity and time in order to satisfy 100% of the energy market for Argentina in the period 2010–2030. Two models are proposed, the first one considers the total amount of GHG released in the horizon time; and the other contemplates the amount of GHG year by year. Twenty scenarios are evaluated with both models. The results obtained are presented, which show the trade-offs between both objectives.