Multiperiod Mixed-integer Nonlinear Programming Research Articles

Production planning optimization of an ethylene plant considering process operation and energy utilization

A novel short-term planning model of the ethylene plant that incorporates the operating variables and energy utilization in both the thermal cracking and the down-stream process is proposed to explore the potential for increasing the production margin and reducing the energy losses. A multi-period mixed-integer nonlinear programming (MINLP) model is formulated to attain the scheduling of parallel furnaces and the energy distribution of the overall plant, along with the determination of the key process operation involving the coil outlet temperature (COT) and coke deposition. The behavior of the product yields and coke formation in terms of varying COT profiles is investigated to enhance the profitability of the whole plant. A real industrial example is investigated to exploit the performance of the proposed model. The results show that the integrated approach attains an improvement in overall profit and achieves significant enhancement in energy savings, compared with the original optimization approach.

Designing a Total Site for an entire lifetime under fluctuating utility prices

This paper describes a synthesis of Total Site in order to obtain additional energy savings by process-to-process heat integration. Enhanced Heat Integration and economically viable designs can be obtained by establishing an appropriate trade-off between the operating cost and the investment. The aim of this work was to improve the modeling of the Total Site by including proper pressure levels selection for intermediate utilities, preheating of intermediate utilities because of incomplete condensate recovery, pipeline layout design, and optimal pipe design with optimal pressure/temperature drops and optimal insulation thickness and heat losses during transportation along the pipes. Additionally, future utility prices are considered when synthesizing the Total Site as they are expected to influence the trade-off between investment and operating cost. A stochastic multi-period mixed-integer nonlinear programming model for the optimal synthesis of Total Site over its entire lifetime has been developed by including all the above-mentioned design aspects.

Optimising entire lifetime economy of heat exchanger networks

This contribution presents an optimisation methodology for a Heat Exchanger Network (HEN) design over its entire lifespan. Consideration of fluctuating energy prices is essential for achieving an optimal HEN design. The objective function presents a trade-off between investment and operating costs. Accounting for higher energy prices supports greater investments compared to solutions obtained with current prices. However, due to the uncertainty of utility prices' forecasts, retrofit with the extension of HEN regarding the lifespan, will usually be the future strategy. As there can be various designs featuring similar initial investments, the objective is to identify one design that will be the most suitable for effective future extensions, preferably with low sensitivity to energy price fluctuations. These observations resulted in development of a stochastic multi-period mixed-integer nonlinear programming (MINLP) model for the synthesis of HEN designs, with extensions accounting for future energy prices. The objective of this work was to maximise both the Expected Net Present Value with no risk assessment performed, and the Certainty Equivalent with risk assessment regarding future utility prices and investment. The results obtained indicate that when applying the proposed approach, a design with improved economic performance could be obtained, especially when compared with Total Annual Cost.

A disjunctive programming model and a rolling horizon algorithm for optimal multiperiod capacity expansion in a multiproduct batch plant

This paper addresses a multiperiod mixed integer nonlinear programming problem for the capacity expansion of multiproduct batch plants. Given a certain batch plant with its current configuration, product recipes, and growing production targets, modular expansions are wanted so that new demand can be met. Unlike most work for the batch retrofit problem, a multiperiod disjunctive model is presented, such that long term investments and expansions can be planned out in advance. To solve the model we propose a rolling horizon algorithm that further exploits the advantages of a disjunctive programming model. Empirical work shows that the rolling horizon algorithm is very effective on finding near optimal solutions to large instances with a considerable number of time periods. Furthermore, the solution found by the proposed algorithm can be used as a starting solution for the direct method to the original problem delivering a global optimal solution.

An Efficient Multiperiod MINLP Model for Optimal Planning of Offshore Oil and Gas Field Infrastructure

In this paper, we present an efficient strategic/tactical planning model for offshore oilfield development problem that is fairly generic and can be extended to include other complexities. The proposed multiperiod nonconvex MINLP (mixed integer nonlinear programming) model for multifield site includes three components (oil, water, and gas) explicitly in the formulation using higher order polynomials, avoiding bilinear and other nonlinear terms. With the objective of maximizing total NPV for long-term planning horizon, the model involves decisions related to FPSO (floating production, storage, and offloading) installation and expansions, field–FPSO connections, well drilling, and production rates in each time period. The model can be solved effectively with DICOPT for realistic instances and gives good quality solutions. Furthermore, it can be reformulated into an MILP after piecewise linearization and exact linearization techniques that can be solved globally in an efficient way. Solutions of realistic in...

Minimisation of a heat exchanger networks' cost over its lifetime

The optimal design of heat exchanger networks (HENs) has a great influence on the profitability of a plant. The optimisation is based on trade-offs between investment and operational cost. The full lifetime of the HEN and future utility prices have to be considered rather than optimising HEN on a yearly basis using current utility prices. Single-period optimisation and synthesis models for HENs reflect current utility prices only. These prices can fluctuate rather quickly and the optimal solution may be very different from a year to year. Deterministic and stochastic multi-period mixed-integer nonlinear programming (MINLP) models for HEN synthesis have been developed to account for future price projections, where the utility cost coefficients are forecasted for the lifetime of the process. An optimal design is then determined for each projection and these designs are compared against a design with fixed current prices by applying the Incremental Net Present Value and other economic measures. In case studies the difference between utility consumption, using previous optimisation methods and new, were significant; e.g. in Case Study 2 the utility savings were 18.4% for hot and 32.6% for cold utility yielding an increase of the Net Present Value (NPV) by 7.8%.

Multi-period Optimal Operational Planning of Boiler Steam System Based on Line-up Competition Algorithm

In this paper, a multi-period mixed integer nonlinear programming (MINLP) model for boiler steam system, which accounts for both the operating cost for each period and the changeover cost each between periods of operation, is presented. To find an exact solution for the MINLP problem within an allowable computation time, a new hybrid algorithm combining the line-up competition algorithm (LCA) with nonlinear programming is proposed. A boiler steam system contains six boilers is used for case study. And the results show a significant potential for cost saving.

Decomposition Based Stochastic Programming Approach for Polygeneration Energy Systems Design under Uncertainty

Polygeneration, a multi-input multioutput energy conversion process which typically involves the coproduction of electricity and liquid synthetic fuels, is a promising technology which offers real potential toward the reduction of excessive energy consumption and consequent greenhouse gas emissions. The optimal design of such a complex and nonlinear process system under inevitable and unpredictable future uncertainty poses great challenges in terms of both modeling and corresponding solution strategies. In this paper, we propose a stochastic programming framework for the optimal design under uncertainty of polygeneration energy systems. On the basis of a detailed mixed-integer nonlinear programming (MINLP) model, proposed in our previous work, a two-stage stochastic programming problem is formulated, which is then converted into a large-scale multiperiod MINLP problem by employing cubature based integration and sampling techniques. A decomposition algorithm is utilized for the efficient solution of the multiperiod problem, which involves iterations between a set of nonlinear subproblems of much smaller size and a master mixed-integer linear programming problem. A case study is then presented, where detailed computational results and comparisons between optimal designs obtained for both the stochastic and deterministic cases are shown.

Design of responsive supply chains under demand uncertainty

This paper addresses the optimization of supply chain design and planning under responsive criterion and economic criterion with the presence of demand uncertainty. The supply chain consists of multi-site processing facilities and corresponds to a multi-echelon production network with both dedicated and multiproduct plants. The economic criterion is measured in terms of net present value, while the criterion for responsiveness accounts for transportation times, residence times, cyclic schedules in multiproduct plants and inventory management. By using a probabilistic model for stock-out, the expected lead time is proposed as the quantitative measure of supply chain responsiveness. The probabilistic model can also predict the safety stock levels by integrating stock-out probability with demand uncertainty. These are all incorporated into a multi-period mixed-integer nonlinear programming (MINLP) model, which takes into account the selection of manufacturing sites and distribution centers, process technology, production levels, scheduling and inventory levels. The problem is formulated as a bi-criterion optimization model that maximizes the net present value and minimizes the expected lead time. The model is solved with the ɛ-constraint method and produces a Pareto-optimal curve that reveals how the optimal net present value, supply chain network structure and safety stock levels change with different values of the expected lead time. A hierarchical algorithm is also proposed based on the decoupling of different decision-making levels (strategic and operational) in the problem. The application of this model and the proposed algorithm are illustrated with two examples of polystyrene supply chains.

Multiperiod Investment Models for the Gradual Reconstruction of Chemical Processes

AbstractA multiperiod mixed‐integer nonlinear programming (MINLP) model is presented for the planning of an optimal investment policy for the gradual retrofit of chemical plants over a specified time frame. This approach can be applied when the available funds are insufficient to perform the optimal reconstruction in one step. Through gradual improvements, the process progressively approaches its optimum with considerably lower requirements for new capital, while still exhibiting an attractive increase in economic performance. In the proposed multiperiod problem for gradual retrofit, certain amounts of capital enter into the time periods for the gradual increase of equipment in order to improve the performance of the process, e.g., to lead to an increase in conversion or energy recovery. This capital may arise from internal sources within the company or can be borrowed. The financial benefits resulting from the improvements at the end of the time period can be reinvested for the additional reconstruction over the next development phases. In this way, self‐sustained capital generation for future reconstruction is achieved, and any additional funds required are minimized. The objective function of the proposed problem is formulated as the net present worth of the gradually retrofitted system. This enables several techno‐economic analyses to be performed. The proposed multiperiod investment strategies are illustrated by an investment planning example for the retrofit of a heat‐exchanger network.

Synthesis of multi-stream heat exchanger network for multi-period operation with genetic/simulated annealing algorithms

The multi-period synthesis of multi-stream heat exchanger network (MSHEN) can be formulated as a mixed integer nonlinear programming (MINLP) model and the obtained MSHEN is over-synthesized for all operational period. In this paper a novel strategy for synthesizing flexible MSHEN under multi-period operation that involves specified changes in stream temperatures and flow rates is presented. In the first stage, the multi-period MSHEN is over-synthesized by the temperature–enthalpy ( T– H) diagram method based on the stream pseudo-temperature. Compared with the superstructure-based multi-period MINLP model, the decision variables of the simultaneous multi-period NLP model proposed are only the stream heat transfer temperature difference contributions. The model features that the size and the complexity of the problem are reduced significantly and the feasibility of the initial feasible solutions are guaranteed, which will enhance the calculation efficiency of the problem. In the second stage, the optimal MSHEN obtained in the first stage is improved to overcome the problem of over-synthesis. The structure of the over-synthesis MSHEN is retained and each heat exchanger area is optimized considering the multi-period operation in order to make the MSHEN less costly. The objective in both stages is the total annual cost of MSHEN and the global solution can be guaranteed by genetic/simulated annealing algorithm (GA/SA) at high probability. Finally, two examples are illustrated to demonstrate the performance of the strategy for multi-period MSHEN synthesis.

Design of flexible heat exchanger network for multi-period operation

Heat exchanger networks (HENs) increase heat recovery from industrial processes by matching hot and cold streams to exchange heat and reducing utility consumption. The design of HENs is a very complex task which generally involves mixed-integer non-linear programming (MINLP). This work evaluates and critically compares existing HEN design methods. It then presents a systematic methodology in the design of HENs under multiple periods of operation. The model presented in this work is a superstructure-based MINLP model which minimises the total annualised cost containing heat exchanger area cost and utility costs. The model is based on the superstructure by Yee and Grossmann [1990. Simultaneous optimisation models for heat integration—II, heat exchanger network synthesis. Computer & Chemical Engineering 14(10), 1165–1184], which was later formulated for multiple periods by Aaltola [2002. Simultaneous synthesis of flexible heat exchanger network. Applied Thermal Engineering 22, 907–918]. It includes a multi-period simultaneous MINLP model to design the HEN structure, and an NLP model to improve the solution and allow for non-isothermal mixing. Modifications to Aaltola's model include the use of maximum area per period in the area cost calculation of the MINLP objective function, and the removal of slack variables and weighed parameters from the existing NLP improvement model. The new model has been applied to one industrial case study, demonstrating that the new combined MINLP–NLP model can obtain better solutions by not relying on the average area assumption in the MINLP stage.

Optimal production and scheduling of a process with decaying catalyst

AbstractA multiperiod mixed‐integer nonlinear programming (MINLP) optimization model is presented to schedule catalyst changeovers and determine the best operating policy for a chemical process with decaying performance. Two solution strategies are proposed to reduce the effect of nonconvexities and to reduce the solution time: (1) a search strategy that relies on partitioning the time horizon and (2) a strategy that makes use of the Generalized Benders Decomposition (GBD). Examples are presented for different time horizons to illustrate the performance of the proposed methods. The same objective value is reached with both strategies, which find better solutions than the full‐space MINLP. For small models, the GBD algorithm is faster than the partitioning search strategy, whereas the latter method is faster for larger models. Comparison with the operating strategy used in a real plant is also presented. © 2005 American Institute of Chemical Engineers AIChE J, 51:909–921, 2005

A strategy for the integration of production planning and reactive scheduling in the optimization of a hydrogen supply network

In this paper, we address the integration of production planning and reactive scheduling for the optimization of a hydrogen supply network consisting of five plants, four inter-connected pipelines and 20 customers. We present multiperiod mixed integer nonlinear programming (MINLP) models for both the planning and scheduling levels. The planning model includes complex pricing functions resulting from deregulation, with a simplified pipeline description and determines feed and energy prices, as well as production levels, for a monthly horizon divided into 12-h time periods. Prices are fixed on the scheduling level, while a detailed pipeline model is included, to determine the on/off status and load steps of compressors on an hourly basis, in order to satisfy the actual demands as they become known while adhering to pressure constraints. In addition, we propose a solution methodology where the demand forecast is updated and the planning model is rerun every 12 h, while the scheduling model is run every hour and information is passed between the two levels to facilitate integration. We show that the planning model quickly becomes intractable and propose a heuristic solution method for this level based on Lagrangean decomposition. Results show that the proposed Lagrangean decomposition heuristic reduces the computational effort for solving the planning model by more than an order of magnitude compared to the commercial MINLP solver DICOPT++. It is also shown that for the majority of the plants, the power consumption and hydrogen production from the scheduling level agrees with the planning level. In some cases, however, the integration is hampered by the presence of nonlinearities, especially on the scheduling level, that lead to suboptimal or infeasible solutions. These nonlinearities need to be further addressed before the proposed methodology can be implemented in practice.

A Lagrangean Decomposition Heuristic for the Design and Planning of Offshore Hydrocarbon Field Infrastructures with Complex Economic Objectives

In this work, we present a multiperiod mixed-integer nonlinear programming model for the long-term design and planning of offshore hydrocarbon field infrastructures with complex economic objectives. We show that when complex fiscal rules, such as tariff, tax, and royalty calculations are added to the model, substantial increases in the net present value of the project are obtained. However, including these calculations leads to more than an order of magnitude increase in the computational effort required. To address this problem, we propose a specialized heuristic algorithm that relies on the concept of Lagrangean decomposition. We present an iterative scheme where feasible solutions are postulated from the Lagrangean decomposition, and multipliers are updated through a subgradient method. Results show that for moderately sized models up to 2 orders of magnitude of reduction in solution time is obtained compared to the full-space solution. Larger problems that could not be solved in 5 days of computation ...

An Iterative Aggregation/Disaggregation Approach for the Solution of a Mixed-Integer Nonlinear Oilfield Infrastructure Planning Model

A multiperiod mixed-integer nonlinear programming model for offshore oilfield infrastructure planning is presented where nonlinear reservoir behavior is incorporated directly into the formulation. Discrete decisions include the selection of production platforms, well platforms and wells to be installed/drilled, and the drilling schedule for the wells over the planning horizon. Continuous decisions include the capacities of the platforms and the production profile for each well in each time period. For the solution of this model, an iterative aggregation/disaggregation algorithm is proposed in which logic-based methods, a bilevel decomposition technique, the use of convex envelopes, and aggregation of time periods are integrated. Furthermore, a novel dynamic programming subproblem is proposed to improve the aggregation scheme at each iteration in order to obtain an aggregate problem that resembles the disaggregate problem more closely. A number of examples are presented to illustrate the performance of the proposed method.

Robust investment model for long-range capacity expansion of chemical processing networks under uncertain demand forecast scenarios

The problem of long-range capacity expansion planning for chemical processing networks under uncertain demand forecast scenarios is addressed. This optimization problem involves capacity expansion timing and sizing of each chemical processing unit to maximize the expected net present value while considering the deviation of net present values and the excess capacity over a given time horizon. A multiperiod mixed integer nonlinear programming optimization model that is both solution and model robust for any realization of demand scenarios is developed using the two-stage stochastic programming modeling framework. Two example problems are considered to illustrate the effectiveness of the model. Especially, the use of the model is illustrated on a real problem arising from investment planning in Korean petrochemical industry.

A multiperiod MINLP model for the synthesis of flexible heat and mass exchange networks

This paper addresses the problem of how to synthesize mass and heat exchange processes, in which stream flowrates and their inlet compositions and temperatures may vary according to a set of discrete values. A unified hyperstructure representation of mass and heat exchange alternatives is introduced to account for all mass and heat integration possibilities. A multiperiod mixed integer nonlinear programming (MINLP) model is then developed, where a total annualized cost is minimized by balancing capital investment cost (of the heat and mass exchange equipment and their interconnections) to operating cost (of the hot-cold utilities, mass separating agents, etc.). As illustrated with the example problems, the proposed model can be effectively employed for the synthesis of flexible heat exchanger networks (HENs) and mass exchanger networks (MENs) separately or, for the synthesis of separation processes involving both heat and mass transfer.