Multi-period Planning Model Research Articles

Multi-period optimal capacity expansion planning scheme of regional integrated energy systems considering multi-time scale uncertainty and generation low-carbon retrofit

With increasingly challenging climate crisis, carbon neutrality has become a necessary path for the whole world. However, there still lacks a comprehensive investigation on the optimal capacity expansion planning for a low-carbon transformation while considering multiple uncertainties. In this paper, a multi-period optimal capacity expansion planning scheme for regional integrated energy systems considering multi-time scale uncertainties and generation low-carbon retrofit is proposed. First, to better describe the short-time scale uncertainty caused by renewable energy and load fluctuations, a multi-dimensional tempo-spatial correlated scenario generation method is proposed to more accurately capture stochastic features with the least amounts of representative scenarios. Second, a multi-period optimal planning model considering generation low-carbon retrofit and short-/long-time scale uncertainties is developed. The proposed model combines information gap decision theory and chance constraints to stress both uncertainties simultaneously, which is further linearized to facilitate the computation. Third, an improved bilinear Benders decomposition (IBBD) method is utilized to efficiently solve the proposed large-scale optimal planning problem. Finally, numerical experiments of a real world test system of WF city show: 1) the maximum errors of PDF and CDF between generated scenarios and historical data are 0.108 and 0.016, validating the effectiveness of the proposed scenario generation method; 2) the low-carbon retrofit reduces system carbon emissions by 14.12 × 107 kg, while the total system cost is $956,411,387 with additional energy coupling units and renewables installed, indicating the reliability of the multi-period planning model; 3) the IBBD algorithm demonstrates applicability and efficiency in solving the proposed multi-period optimal expansion planning problem, reducing computation time by over 80.39 % compared to commercial solvers, such as GUROBI.

Mapping the path to a net‐zero chemicals industry by long‐term planning with changes in technologies and climate

AbstractThe chemical industry, along with many other industries, has pledged to reach net‐zero emissions within the next few decades for greenhouse gases, plastics, etc. This requires systematic methods to guide investment in technologies and value‐chain alternatives, and develop roadmaps. The proposed framework is a multiperiod planning model to guide optimal reforms in cradle‐to‐cradle life‐cycle networks across the pledged time horizon. It aims to meet environmental targets while minimizing the total annualized cost of natural resources and the investment cost associated with adoption of novel technologies. This considers the evolution of technology readiness levels as S‐curves or continuous time Markov‐chains. Integrated Assessment models account for climate change, decarbonization due to energy mix changes, and carbon taxes. Multiple climate change scenarios and shared socioeconomic pathways are used to model future scenarios. In addition to providing roadmaps, the outputs can also be used to identify technologies that will be robust to future scenarios.

Organic waste derived biodiesel supply chain network: Deterministic multi-period planning model

In this study, a multi-period model of an organic waste-to-biodiesel phased supply chain network is developed to strategically consider variations in the biodiesel demand and the organic waste usage over a long-term planning interval. The proposed model can facilitate planning to determine the biorefinery location and the amount of biodiesel to produce, transport, or utilize to reduce the total cost of the organic waste-to-biodiesel supply chain network design while meeting the biodiesel demand during each period of the planning interval. The features and capabilities of the model are validated by application of a future organic waste-to-biodiesel supply chain network design in South Korea. The optimization results illustrate that the average total annual cost of the organic waste of biodiesel based on the multi-period model will be $US 4.2 billion per year during the period 2020–2030. The minimum selling prices for the optimal network design were determined ranged from $US 3.154–3.156/gallon of biodiesel containing 3% butanol derived from organic waste combined with diesel. A small portion (4.9–6.6%) of the total biodiesel demand was produced from organic waste because of low organic waste availability in the existing anaerobic digestion facilities, leading to increasing the outsourcing costs of butanol. The proposed approach will facilitate the strategic development of a sustainable supply chain network for organic waste recycling for material and energy valorization.

An Integrated Planning Framework for Sustainable Water and Energy Supply

This study aims to reveal the economic, technical, and environmental impacts of different system configurations (centralized or decentralized, components, and technologies) on transition plans to achieve a higher share of renewable energy and desalination supplies for regions facing water scarcity. The main contribution of this research is the comparative evaluation of on-grid decentralized or distributed renewable-powered desalination systems for sustainable water and energy supply planning. Applying a novel nexus approach, an interactive multi-period planning model is developed to highlight synergies and to identify conflicts of planning both energy and water sectors at the same time as endogenous subsystems of one overall system. For studying these synergies in this study, the pace of technology deployment and the path of decline in overall costs are assumed to be a function of experience and knowledge as two-factor learning curves. Using data from 81 projects, the levelized cost and capacity factor of utility-scale photovoltaic and wind supplies in the Middle East were calculated. The results indicate that a scenario with a decentralized water sector and renewable-powered multiple-effect distillation technology has the best overall performance among the proposed scenarios.

Multi-period planning of multi-energy microgrid with multi-type uncertainties using chance constrained information gap decision method

In this paper, we study the multi-period planning problem of multi-energy microgrids considering the long-term uncertainty (i.e., the declining trend of battery storage investment cost) and the short-term uncertainty (i.e., renewable energy generation and electrical/heat load). We first present the joint deterministic multi-period planning approach for multi-energy microgrid coupling electricity and heat carriers. Then, an information gap decision (IGD)-based multi-energy microgrid multi-period planning model dealing with the long-term uncertainty is proposed, and the proposed model is further converted into a mixed integer linear planning (MILP) IGD-based planning model. Next, to coordinate the long-term uncertainty and the short-term uncertainty in multi-energy microgrid planning problems, we develop a chance constrained (CC) IGD-based multi-period planning model and then convert such model into a MILP CC-IGD equivalence. Finally, the strengthened bilinear Benders decomposition (SBBD) algorithm is adopted to efficiently solve our proposed MILP CC-IGD model for large-scale multi-energy microgrid planning problems. Our numerical results demonstrate the advantage of the joint planning of electricity and heat supply systems in multi-energy microgrids. Case studies verify the effectiveness of considering multi-type uncertainties in multi-energy microgrid planning, especially the declining trend uncertainty of battery storage investment cost. Experimental results also show that the SBBD algorithm is more efficient on computing our proposed MILP CC-IGD model compared to commercial solvers, such as CPLEX.

An interactive planning model for sustainable urban water and energy supply

An interactive multi-period planning model is presented for sustainable urban water and energy supply, taking into account surplus output from grid-connected residential photovoltaics as a part of the water-related energy mix. The two-level mixed integer linear model finds the optimal strategic and operational decisions for a desalination-based water supply system driven by hybrid energy sources and determines the evolution of the potential capacity of a renewable energy technology over the planning horizon. It considers demands, supply systems configuration, resources capacities and electricity tariffs as well as economic, subjectivity and technical criteria for uptaking rooftop photovoltaic systems. The model was then applied to Perth (Australia) and solved for alternative scenarios. The results show operational flexibility and decentralised planning of the integrated system lead to $251,515,132 less discounted total cost over centralised water supply system operated in fixed mode. They also indicate that decentralised scenario results in 42,765.1 kW higher potential photovoltaics uptake capacity on average in each year over the planning horizon in the case study area compared to centralised scenarios. However, based on the results of the sensitivity analysis, the selection of this scenario as the best alternative highly depends on the parameters values associated with subjectivity criterion and operational and maintenance cost of flexible mode of operation.

A subway planning bi-objective multi-period optimization model integrating timetabling and vehicle scheduling: a case study of Tehran

Due to the interaction among different planning levels and various travel demands during a day, the transit network planning is of great importance. In this paper, a bi-objective multi-period planning model is proposed for the synchronization of timetabling and vehicle scheduling. The main aim of the problem is to minimize the weighted transfer waiting time in the interchange stations along with the operational costs of vehicles. In order to demonstrate the effectiveness of the proposed integrated model, a real case study of Tehran subway is considered. The proposed model is solved by the e-constraint method and some outstanding results are achieved.

Survivable Network Capacity Allocation and Topology Design Using Multi-period Network Augmentation

This paper examines the effect of incorporating multi-period network augmentation into the survivable network design process. The framework presented can handle variable restorability requirements, potential economies of scale, and technology shifts. By utilizing a multi-period planning model, shifts and uncertainties in demand and policy can be accounted for. This study examined the design of survivable networks using both demand-wise shared protection and shared backup path protection (representing opposite ends of the mesh network efficiency spectrum) with topology augmentation over multiple time horizons.

Optimal operation of a distributed energy generation system for a sustainable palm oil-based eco-community

The palm oil industry potentially can be environmentally sustainable through utilizing the vast availability of biomass residues from palm oil mills as renewable energy sources. This work addresses the optimal operation of a combined bioenergy and solar PV distributed energy generation system to meet the electricity and heat demands of an eco-community comprising a palm oil mill and its surrounding residential community. A multiperiod mixed-integer linear programming planning and scheduling model is formulated on an hourly basis that optimally selects the power generation mix from among available biomass, biogas, and solar energy resources with consideration for energy storage and load shifting. A multiscenario approach is employed that considers scenarios in the form of many possible weather conditions and various energy profiles under varying mill operation modes and residential electricity consumption. The proposed approach is demonstrated on a realistic case study for a palm oil mill in the Iskandar Malaysia economic development region. The computational results indicate that biomass-based resource is the preferred renewable energy to be implemented due to the high cost associated with solar PV. As well, load shifting and energy storage can be feasibly deployed for demand peak shaving particularly for solar PV systems.

Multiperiod Planning Model for Integrated Optimization of a Refinery Production and Utility System

In this work, a novel integrated optimization approach that couples the production system and the utility system of a refinery is proposed to explore the potential for increasing the overall refinery margin and reducing the economic losses due to energy waste compared with the traditional approach in which the two systems are optimized sequentially. A multiperiod refinery-wide mixed-integer nonlinear programming (MINLP) model is formulated to optimize the production planning of the processing unit and the operational planning of the utility equipment simultaneously. The energy consumption and generation model of the processing unit is introduced to correlate the two systems in terms of energy by linking the amounts of energy consumed and generated with the unit throughput, product properties, and operation mode. A material balance of fuel oil and fuel gas is considered to integrate the two systems in terms of materials to improve energy utilization in a multiperiod planning site. A real industrial example...

Fuzzy Multi-Objective Programming Model for Facility Location in an Integrated Supply Chain Network

Traditional supply chain network design problems are often taken as a single objective. However, supply chains are complex networks formed by organizations having conflicting objectives with each other in real life. In this study, a multi-product, multi-stage and multi-period planning model is proposed to achieve multiple incommensurable goals in an integrated supply chain network with uncertain market demands. The supply chain planning model is constructed as a mixed-integer nonlinear programming problem to satisfy several conflicting objectives with each other. The proposed model consists of two objective functions. The first one is minimizing the fixed opening and operating costs with transportation costs determined depending on distances. Second one is minimizing the purchasing, ordering, inventory and backlogging costs according to Economic Production Quantity (EPQ) model. Fuzzy goal programming approach is used in order to include decision maker's imprecise goal values in proposed model. The model is solved using GAMS optimization program. The application results presented in this study, demonstrates that fuzzy modeling and solution approaches could be used in the creation of more realistic models of the supply chain.

Stochastic Programming Approach to Optimal Design and Operations of Integrated Hydrocarbon Biofuel and Petroleum Supply Chains

This paper addresses the optimal design and strategic planning of the integrated biofuel and petroleum supply chain system in the presence of pricing and quantity uncertainties. The drop-in properties of advanced hydrocarbon biofuels pose considerable potential for biofuel supply chains to leverage the existing production and distribution infrastructures of petroleum supply chains, which may lead to significant capital savings. To achieve a higher modeling resolution and improve the overall economic performance, we explicitly model equipment units and material streams in the retrofitted petroleum processes and propose a multi-period planning model to coordinate the various activities in the petroleum refineries. Furthermore, in order to develop an integrated supply chain that is reliable in the dynamic marketplace, we employ a stochastic programming approach to optimize the expectation under a number of scenarios associated with biomass availability, fuel demand, crude oil prices, and technology evolution. The integrated model is formulated as a stochastic mixed-integer linear program, which is illustrated by a case study involving 21 harvesting sites, 7 potential preconversion facilities, 6 potential integrated biorefineries, 2 petroleum refineries, and 39 demand zones. Results show the market share of biofuels increases gradually due to the increasing crude oil price and biomass availability.

A multiperiod planning model for gas production system

A gas production system is described from the process engineering point of view and formulated as a generalized disjunctive program for the multiperiod planning problem of this system. The model is applicable to a fixed topology of wells that may have been drilled in different reservoirs and are interconnected with manifolds at the surface. Constraints in the model include not only geological aspects in the reservoir but also other physical constraints from the existing facilities in the production system. The results are concerned with decisions on closing wells or keeping them under a constant calculated production flow during time periods of uniform length. The model was reformulated as a mixed-integer nonlinear programming (MINLP) via the convex-hull methodology and solved for a number of examples with the GAMS modeling system. Several typical scenarios of the production system are presented. Computational performances of three basic formulations are also discussed.

Optimal design of multiperiod batch‐storage network including transportation processes

AbstractAn optimally designed of batch‐storage network that uses a periodic square wave model provides analytical lot‐sizing equations for a complex supply chain network characterized as a multisupplier, multiproduct, multi‐stage, nonserial, multicustomer, cyclic system, with recycling or remanufacturing. The network structure includes multiple currency flows and material flows. The processes involve multiple feedstock and product materials with fixed compositions that are highly suitable for production processes. Transportation processes that carry multiple materials of unknown composition are included in this study, and the time frame is varied from a single infinite period to multiple finite periods to accommodate nonperiodic parameter variations. The objective function in the optimization is chosen to minimize the difference between the opportunity costs of currency/material inventories and stockholder benefits given in the numeraire currency. Expressions for the Kuhn‐Tucker conditions for the optimization problem are reduced to a multiperiod subproblem describing the average flow rates and the analytical lot‐sizing equations. The multiperiod lot‐sizing equations are shown to differ from their single‐period counterparts. The multiperiod subproblem yields a multiperiod planning model that has many advantages over existing planning models. For example, it contains terms that represent operation frequency dependent costs. Realistically sized numerical examples that deal with multinational corporations are formulated and tested. The effects of corporate income taxes, interest rates, and exchange rates are presented. © 2011 American Institute of Chemical Engineers AIChE J, 2011

The effect of uncertainty on the optimal closed-loop supply chain planning under different partnerships structure

In a global economy, the key to success is providing products around the world at the right time in the right quantity and quality, at a low cost. Efficient supply chains have an important role in guaranteeing this success. Optimized planning of such structures is required and uncertainties regarding product demands and prices, amongst other supply chain conditions, should also be considered. In this paper, we look into supply chain planning decisions that account for uncertainty on product portfolios demand and prices. A multi-period planning model is developed where the supply chain operational decisions on supply, production, transportation, and distribution at the actual period consider the uncertainty on products’ demand and prices. Different decision scenarios, involving the evaluation of the supply chain economical performance, are analyzed (e.g. global operating costs/profit realized) for different criteria on the importance of the partners within the global chain (i.e. partners’ structure). A Mixed Integer Linear Programming (MILP) formulation is formulated for each planning scenario and the optimal solution is reached using a standard Branch and Bound (B&B) procedure. The final results provide details on the supply chain partners production, transportation and inventory, at each planning period, while accounting for the importance of each partner in the global chain as well as demand/price uncertainties. The applicability of the developed formulation is illustrated through the solution of a real case-study involving an industrial chain in the pharmaceutical sector.

Design and Operation of an Enterprise-wide Process Network Using Operation Policies. 1. Design

In recent years there has been great industrial and academic interest in the design and operation of enterprise-wide supply chains because of their economic impact under increasingly competitive and narrow profit environments. In this two-paper series, a new modeling framework is presented in order to establish systematic and effective decision support tools for the enterprise-wide supply chains which consist of a large number of industrial production elements such as suppliers, plants, and demands that may be in geographically distinct places. Particularly in part 1, the focus is how to incorporate multiple nodes for the purpose of designing the supply chain. After showing an example to motivate the need of an operating policy in the design of multiple plants, three operating policies, namely, coordination, cooperation, and competition are proposed. Mixed integer linear programming (MILP) models based on these policies are then presented. An illustrative example is presented to demonstrate the potential of the proposed framework. Uncertainty is also one of the most important issues. Therefore in part 2, the effect of uncertainty will be investigated in detail using multiperiod planning models based on the proposed operating policies.

Optimization of Multi-Echelon Supply Chain Networks with Uncertain Sales Prices

A multi-product, multi-stage, and multi-period production and distribution planning model is proposed in this paper to tackle the compromised sales prices and the total profit problem of a multi-echelon supply chain network with uncertain sales prices. This model is constructed as a mixed-integer nonlinear programming problem to achieve a maximum total profit of the whole network and to guarantee the maximum satisfactory levels of sellers’ and buyers’ preference on sales prices. For the purpose that a compensatory solution among all participants of the supply chain can be achieved, a fuzzy decision-making method is proposed and, by means of applying it to a numerical example, proved effective in providing a compromised solution in a multi-echelon supply chain network.

Interactions of Maintenance and Production Planning for Multipurpose Process PlantsA System Effectiveness Approach

Process design and operations are typically concerned with the optimal selection, design, and efficient utilization of assets and resources over a time horizon of interest. The degree of utilization of process plant components critically depends on the availability level of equipment components. These availability levels are mainly associated with equipment reliability, failure characteristics, and maintenance policies. This paper presents a system effectiveness optimization framework for multipurpose plants that involves a novel preventive maintenance model coupled with a multiperiod planning model. This provides the basis for simultaneously identifying production and maintenance policies by exploiting (i) opportunities to perform preventive maintenance during equipment idle time and (ii) flexibility in selecting different production routes to potentially mitigate the adverse effects of equipment failure on the production plan. Extensions to include design decisions are also discussed. All problems are formulated as mixed integer linear programming (MILP) models, and their applicability is demonstrated by a number of illustrative examples.

動的計画法を用いた坑内充填採掘の多期間生産計画に関する研究

A multi-period planning model for underground cut-and-fill operations was constructed for the purpose of maximizing discounted profit under given production constraints. The ore grades were estimated through geostatistics for minimizing the estimation errors, and production costs were calculated on the basis of the practical operation data. A sequential planning algorithm based on dynamic programming (DP) was then developed to specify the most profitable mining sequence, and applied to a Chinese copper-iron mine employing cut-and-fill stoping. Calculation results showed that the proposed DP-based sequential planning strategy can produce larger discounted profits than those obtained by the advance and retreat mining sequences.

A multiperiod planning model for the capacitated minimal spanning tree problem

The Multiperiod Capacitated Minimal Spanning Tree (MCMST) Problem consists of scheduling the installation of links in a network so as to connect a set of terminal nodes S=[2,3,…, N] to a central node (node 1) with minimal present value of expenditures, where link capacities limit the number of terminal nodes sharing a link. Some of the terminal nodes are active at the beginning of the planning horizon while others are activated over time. We formulate this problem as an integer programming problem. A branch exchange heuristic procedure for solving the problem is presented. We also present a Lagrangian relaxation method to find a lower bound for the optimal objective function value. This lower bound may be used to estimate the quality of the solution given by the branch exchange heuristic. Experimental results over a wide range of problem structures show that the branch exchange heuristic method yields verifiably good solutions to this problem.