Multi-period MILP Research Articles

Case Study of Multi-Period MILP HENS with Heat Pump and Storage Options for the Application in Energy Intensive Industries

The environmental goals of initiatives such as the European Green Deal, which aims to achieve climate neutrality for the EU by 2050, increase the importance of improving and optimizing industrial processes. Mathematical optimization methods like heat exchange network synthesis (HENS) are crucial tools in enabling industry to identify potential energy savings and cost reductions. The lack of publicly available industry data suitable for comprehensive testing of novel optimization procedures is often a major obstacle in development and research. To tackle this problem for extended HENS with potential heat pump and storage integration and show the potential of energy integration in energy-intensive industries (EII), the authors introduce a set of four use-cases based on representative industrial processes from the EII. The application of a previously presented a HENS approach for the integration of heat pumps and storage on these cases resulted in a potential reduction of total annual costs up to 55.43% and total external energy demand up to 87.1%. The presented cases, their solutions, and the open-access mathematical formulation of the optimization procedure make a valuable contribution to the literature and future research in the field of HENS.

Optimal Design and Operation of the green pistachio supply network: A robust possibilistic programming model

As a valuable nut which is rich in minerals and vitamins, the pistachio is now popular with millions of people throughout the world. Since its major producer-exporter countries are limited, paying attention to its supply chain seems quite necessary. The pistachio SC management can play an important role in its more economic development because it involves all the activities related to the product management from supply to the customer delivery. Also, due to the recently changing environmental regulations affecting manufacturing operations, increasing attention is given to developing environmental commitments for the supply chain. The present study has designed a supply chain for the pistachio nut, its by-products, and carbon production. The proposed mathematical model considering a robust possibilistic programming approach to face the uncertainties inherent in this supply chain as regards the supply, products’ price, and demand of the type multi-period MILP. The results of data realizations show that the proposed model is less sensitive to the changes in the uncertain parameters than the exact model. The proposed model’s performance has been verified with a real case study in Iran through which a managerial and practical insight is achieved. The research finally compares the proposed RPP with an exact programming model and shows its advantages; in the standard deviation, its performance has been better by about 36.67%.

Optimal Design of Eco-Industrial Parks with coupled energy networks addressing Complexity bottleneck through an Interdependence analysis

By gathering in Eco-Industrial Parks (EIPs), companies obtain benefits from synergistic cooperation but it also creates a risk by increasing interdependencies. The aim of this paper is to provide a method for optimally design exchanges that takes into consideration real stakes of companies. This resolution method is assessed on a multi-period MILP model of coupled energy networks integrating a utility system producing steam at different pressure levels and a mutualized on-grid Hybrid Power System (HPS) providing electricity using Renewable Energy (RE) sources. Design concerns interconnections between companies such as boilers, turbines and power of RE sources. A multi-stage approach is developped to minimize network complexity and Net Present Value (NPV) of the overall network. Lastly, an interdependency analysis is proposed to choose the optimal solution. Tested on a case study involving 15 companies, the optimal exchanges have been raised to satisfy demands over four time periods.

Optimal design of the second and third generation biofuel supply network by a multi-objective model

The depletion of fossil fuels and their serious environmental concerns have made renewable energy sources much more attractive. One of the more promising renewable energy alternatives is the use of second/third-generation biomass that does not endanger food security, to produce bioenergy. The biomass-to-bioenergy supply chain design is a challenging issue that has attracted the attention of academic and industrial research. In this direction, a multi-objective multi-period MILP model is developed to design the second/third-generation biofuel supply chain using anaerobic digestion and transesterification processes. Three types of biomass (i.e. agricultural residues and livestock manure, microalgae and Jatropha) simultaneously are studied as feedstock to produce clean energy in all climatic and geographic conditions, and even in remote areas. Selection of raw material resources, location of production facilities, location of warehouses, and optimal material flows are the main decisions made by the proposed model to minimize the total cost and maximize the produced energy. The performance of this model is evaluated and validated through conducting a real case study. The results show that considering the amount of produced bioenergy regardless to its type, energy production from microalgae and Jatropha is more viable than bio-wastes. The results also show that production cost (especially biodiesel production cost from Jatropha) and investment cost (especially construction costs of microalgae and Jatropha to biodiesel production sites) have the most effect on the total cost of the supply chain network, respectively.

A multi-period MILP model for the investment and design planning of a national-level complex renewable energy supply system

This study presents a comprehensive approach to plan and analyze strategic investment for the design of an integrated renewable energy source-based energy supply system. Initially, the renewable energy source-based energy supply system superstructure was generated, which included 1) different energy sources (wind, solar, and biomass), 2) various energy facilities (for production, storage, and transportation), and 3) three types of final energy demand (electricity, hydrogen, and liquid fuel). A network optimization model was then developed using a mixed integer linear programming. The optimization model was used to determine the investment timing and allocation to the underlying energy supply system, which includes the type and quantity of utilized renewable sources, in addition to the timing of installation, number and location and of energy facilities installed. The capability of the proposed approach is validated through a case study of future Korea. As a result, we identified the optimal configuration and the investment timing of a complex renewable energy supply system, which was determined by regional resource potentials and cost-effectiveness of the involved technologies. The case study results can be used as a guideline to support decision-making of energy industry stakeholders and government policymakers in the strategic planning of a sustainable energy system.

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.

Multiscale strategic planning model for the design of integrated ethanol and gasoline supply chain

The design and planning of an integrated ethanol and gasoline supply chain is addressed, and is composed of harvesting and production sites for ethanol, petroleum refineries, distribution centers where blending takes place, and the retail gas stations where blends of gasoline and ethanol are sold. We postulate a superstructure that combines all the components of the supply chain and different means of transportation, and model this multiscale design problem as a multiperiod MILP model. In order to identify regions where investments are needed and the optimal configuration of the network, a strategic planning model is considered in which gasoline stations are aggregated in different regions. A detailed formulation is considered where regions are disaggregated into gas stations to determine the retrofit projects for the selection of blending pumps over their expected life. Also, the application of these MILP models with two large‐scale problems are illustrated. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4655–4672, 2013

Composite planning and scheduling algorithm addressing intra-period infeasibilities of gasoline blend planning models

Multi-period planning models result in solutions which are feasible at the boundaries of the periods but may be infeasible within the periods. The composite algorithm presented here (i) solves coarse multi-period MILP model structure for production planning; (ii) sequences operations via a genetic algorithm to minimise switching; (iii) verifies schedule feasibility via agent-based simulation and local logical decision making; and (iv) if infeasible, re-partitions the time horizon into multi-periods and resolves from (i) until feasible. Application of the algorithm to gasoline blending illustrates its effectiveness in computing feasible plans and schedules for such systems. © 2012 Canadian Society for Chemical Engineering

Design and operation of a stochastic hydrogen supply chain network under demand uncertainty

The design of a future hydrogen supply chain (HSC) network is challenging due to the: (1) involvement of many echelons in the supply chain network, (2) high level of interactions between the supply chain components and sub-systems, and (3) uncertainty in hydrogen demand. Most of the early attempts to design the future HSC failed to incorporate all these challenges in a single generic optimization framework using mathematical modeling approach. Building on our previous multiperiod MILP model, the model presented in this paper is expanded to take into account uncertainty arising from long-term variation in hydrogen demand using a scenario-based approach. The model also adds another echelon: fueling stations and local distribution of hydrogen. Our results show that the future HSC network is somewhat similar to the existing petroleum infrastructure in terms of production, distribution, and storage. In both situations, the most feasible solution is centralized production plants with truck and rail delivery and small-to-large storage facilities. The main difference is that the future hydrogen supply has the benefits of using distributed forecourt production of hydrogen at local fueling stations via several production technologies. Finally, the performance of the studied models was evaluated using sensitivity and risk analyses.

Availability and reliability considerations in the design and optimisation of flexible utility systems

Industrial utility plants are usually comprised of many interconnected units that must constitute a flexible and reliable system capable of meeting process energy requirements under different circumstances (e.g. varying prices, demands, or equipment shutdowns). Also, in order to avoid large economic penalties, the design and operation of a utility plant should consider that the equipment is not fully reliable and that each item needs to receive preventive and corrective maintenance. Conventionally, these issues are handled by installing additional units according to rules of thumb or heuristics, which usually imply excessive capital costs and might even result in designs that cannot satisfy the specified demands for certain situations. In contrast, during the present work a systematic methodology has been developed to address the design and operation of flexible utility plants incorporating reliability and availability considerations. The suggested method is based on a novel modelling and optimisation framework that can address grassroots design, retrofit, or (pure) operation problems in which design and operational parameters are optimised simultaneously throughout several scenarios. Thereafter, it is possible to define maintenance and failure situations in different operating periods to ensure that the plant will be able to cope with them, while meeting process requirements at minimum cost. Hence, for design cases, the most cost-effective elements of redundancy can be determined without pre-specifying any structural options in the final configuration (e.g. equipment sizes, types, and number of units). Furthermore, the proposed (multiperiod) MILP formulation is robust enough to tackle problems of the size and complexity commonly found in industry, and has the potential of yielding significant economic savings.

Design and Optimization of Flexible Utility Systems Subject to Variable Conditions: Part 1: Modelling Framework

Industrial utility systems offer many degrees of freedom to improve their design and operation to achieve substantial savings in capital and/or operating costs. However, minimizing such expenditure also represents a challenging task due to the complex and highly-combinatorial nature of the optimization problem. While conventional approaches have simplified the problem by addressing operational and design (synthesis) issues in a separate or iterative way, the present work proposes a novel computational tool for both the design and operation of industrial utility systems in which their inherent flexibility is fully exploited through different operating scenarios. In order to consider the design and operational parameters of these systems as (continuous) mathematical variables to be optimised simultaneously, a new generic modelling framework for energy equipment has been developed and validated in which performance depends on both unit size and operational load. The first part of this paper describes the linear models developed to solve this problem for multi-fuel boilers, steam and gas turbines and heat recovery steam generators. These are employed to build a robust (multiperiod) MILP formulation to tackle grassroots design, retrofit or operational problems of the size and complexity commonly found in large industrial systems.

Synergy analysis of collaborative supply chain management in energy systems using multi-period MILP

Energy, a fundamental entity of modern life, is usually produced using fossil fuels as the primary raw material. A consequence of burning fossil fuels is the emission of environmentally harmful substances. Energy production systems generate steam and electricity that are served to different customers to satisfy their energy requirement. The improvement of economical and environmental performance of energy production systems is a major issue due to central role of energy in every industrial activity. A systematic approach to identify the synergy among different energy systems is addressed in this paper. The multi-period and discrete-continuous nature of the energy production systems including investment costs are modeled using MILP. The proposed approach is applied on two examples that are simplified versions of an industrial problem. It is shown that the approach presented in this paper is very effective in identifying the synergy among different companies to improve their economical and environmental performance significantly.

A systematic approach to the synthesis and design of flexible site utility systems

The paper presents a systematic approach for the synthesis of flexible utility systems satisfying varying energy demands. The approach combines benefits of total site analysis, thermodynamic analysis and mathematical optimisation. A thermodynamic efficiency curve (TEC) is developed, which gives an overview of the maximum thermodynamic efficiencies of all possible design alternatives. TEC and hardware composites guide the selection of candidate structures in the superstructure, excluding uneconomic options from the synthesis model. The integration of thermodynamics yields significant reduction in the synthesis model, addresses the impact of variable loads on the unit efficiencies, and enables a compact formulation of the design problem over long horizons of operation. The optimisation is formulated as a multi-period MILP problem that relies on new target models to describe the performance of steam turbines, condensing turbines, gas turbines and boilers. Target models account for the variation of efficiency with unit size, load and operating conditions in a simple, yet accurate way. As a result, these models are capable of accounting for the efficiency trends of realistic units.

A Bilevel Decomposition Algorithm for Long-Range Planning of Process Networks

The solution of the multiperiod MILP model for long-range planning of process networks by Sahinidis et al. (Comput. Chem. Eng. 1989, 13, 1049) is addressed in this paper. The model determines the optimal selection and expansion of processes over a long-range planning horizon, incorporating multiple scenarios for varying forecasts for demands and prices of chemicals. A rigorous bilevel decomposition algorithm is proposed to reduce the computational cost in the multiperiod MILP model. The decomposition algorithm solves a master problem in the reduced space of binary variables to determine a selection of processes and an upper bound to the net present value. A planning model is then solved for the selected processes to determine the expansion policy and a lower bound to the objective function. Numerical examples are presented to illustrate the performance of the algorithm and to compare it with a full-space branch and bound method.

Reformulation of multiperiod MILP models for planning and scheduling of chemical processes

A large number of planning and scheduling problems can be formulated as multiperiod MILP models which often require substantial computational expense f

Optimization model for long range planning in the chemical industry

In this paper a multiperiod MILP model is presented for the optimal selection and expansion of processes given time varying forecasts for the demands and prices of chemicals over a long range horizon. To reduce the computational expense of solving this long range planning problem, several strategies are investigated, including branch and bound, the use of integer cuts, strong cutting planes, Benders decomposition and heuristics. These procedures, which have been implemented in the program MULPLAN, are illustrated with several example problems. As is shown, the proposed model is especially useful for the study of a variety of different scenarios.