Aiying Rong

Fuzzy chance constrained linear programming model for optimizing the scrap charge in steel production

Optimizing the charge in secondary steel production is challenging because the chemical composition of the scrap is highly uncertain. The uncertainty can cause a considerable risk of the scrap mix failing to satisfy the composition requirements for the final product. In this paper, we represent the uncertainty based on fuzzy set theory and constrain the failure risk based on a possibility measure. Consequently, the scrap charge optimization problem is modeled as a fuzzy chance constrained linear programming problem. Since the constraints of the model mainly address the specification of the product, the crisp equivalent of the fuzzy constraints should be less relaxed than that purely based on the concept of soft constraints. Based on the application context we adopt a strengthened version of soft constraints to interpret fuzzy constraints and form a crisp model with consistent and compact constraints for solution. Simulation results based on realistic data show that the failure risk can be managed by proper combination of aspiration levels and confidence factors for defining fuzzy numbers. There is a tradeoff between failure risk and material cost. The presented approach applies also for other scrap-based production processes.

CO2 emissions trading planning in combined heat and power production via multi-period stochastic optimization

Abstract The EU emissions trading scheme (ETS) taking effect in 2005 covers CO2 emissions from specific large-scale industrial activities and combustion installations. A large number of existing and potential future combined heat and power (CHP) installations are subject to ETS and targeted for emissions reduction. CHP production is an important technology for efficient and clean provision of energy because of its superior carbon efficiency. The proper planning of emissions trading can help its potential into full play, making it become a true “winning technology” under ETS. Fuel mix or fuel switch will be the reasonable choices for fossil fuel based CHP producers to achieve their emissions targets at the lowest possible cost. In this paper we formulate CO2 emissions trading planning of a CHP producer as a multi-period stochastic optimization problem and propose a stochastic simulation and coordination approach for considering the risk attitude of the producer, penalty for excessive emissions, and the confidence interval for emission estimates. In test runs with a realistic CHP production model, the proposed solution approach demonstrates good trading efficiency in terms of profit-to-turnover ratio. Considering the confidence interval for emission estimates can help the producer to reduce the transaction costs in emissions trading. Comparisons between fuel switch and fuel mix strategies show that fuel mix can provide good tradeoff between profit-making and emissions reduction.

Efficient algorithms for combined heat and power production planning under the deregulated electricity market

Combined heat and power (CHP) production is an important energy production technology that can yield much higher total energy efficiency than separate heat and power generation. In CHP production, the heat and power production follows a joint characteristic, which means that the production planning must be done in coordination. Cost-efficient operation of a CHP system can be planned by using an optimization model. A long-term planning model decomposes into thousands of hourly models. Earlier, in the regulated electric power market, the planning problem was symmetrically driven by heat and power demand. The liberalization of the power market has created an asymmetrical planning problem, where heat production responds to the demand and power production to the volatile market price. In this paper, we utilize this asymmetry to develop novel envelope-based dual algorithms for solving the hourly CHP models efficiently. The basic idea is to transform the three-dimensional characteristic operating region for heat and power production of each CHP plant into a two-dimensional envelope by taking the power price as a parameter. Then the envelopes of each plant are used for looking up the optimal solution rapidly. We propose two versions of the algorithm: the on-line envelope construction algorithm (ECON) where the envelopes are constructed for each hour based on the power price and the off-line envelope construction algorithm (ECOFF) where envelopes are pre-computed for all different power price ranges. We derive the theoretical time complexity of the two algorithms and compare their performance empirically with realistic test models against the ILOG CPLEX solver and the Power Simplex (PS) algorithm. PS is an extremely efficient specialized primal algorithm developed for the symmetrical CHP planning problem under the regulated market. On average, when reusing previous basic solutions, ECON is 603 times faster than CPLEX and 1.3 times faster than PS. ECOFF is 1860 times faster than CPLEX and four times faster than PS.

Lagrangian relaxation based algorithm for trigeneration planning with storages

Trigeneration is a booming power production technology where three energy commodities are simultaneously produced in a single integrated process. Electric power, heat (e.g. hot water) and cooling (e.g. chilled water) are three typical energy commodities in the trigeneration system. The production of three energy commodities follows a joint characteristic. This paper presents a Lagrangian relaxation (LR) based algorithm for trigeneration planning with storages based on deflected subgradient optimization method. The trigeneration planning problem is modeled as a linear programming (LP) problem. The linear cost function poses the convergence challenge to the LR algorithm and the joint characteristic of trigeneration plants makes the operating region of trigeneration system more complicated than that of power-only generation system and that of combined heat and power (CHP) system. We develop an effective method for the long-term planning problem based on the proper strategy to form Lagrangian subproblems and solve the Lagrangian dual (LD) problem based on deflected subgradient optimization method. We also develop a heuristic for restoring feasibility from the LD solution. Numerical results based on realistic production models show that the algorithm is efficient and near-optimal solutions are obtained.

An efficient envelope-based Branch and Bound algorithm for non-convex combined heat and power production planning

Combined heat and power (CHP) production is universally accepted as one of the most energy-efficient technologies to produce energy with lower fuel consumption and fewer emissions. In CHP technology, heat and power generation follow a joint characteristic. Traditional CHP production is usually applied in backpressure plants, where the joint characteristic can often be represented by a convex model. Advanced CHP production technologies such as backpressure plants with condensing and auxiliary cooling options, gas turbines, and combined gas and steam cycles may require non-convex models. Cost-efficient operation of a CHP system can be planned using an optimization model based on forecasts for heat load and power price. A long-term planning model decomposes into thousands of single-period models, which can be formulated in the convex case as linear programming (LP) problems, and in the non-convex case as mixed integer programming (MIP) problems. In this paper, we introduce EBB algorithm, for solving the non-convex single-period CHP models of a long-term planning problem under the deregulated power market. EBB is based on the Branch and Bound (B&B) algorithm where tight lower bounds are computed analytically for pruning the search tree and the LP sub-problems are solved through an efficient envelope-based dual algorithm. We compare the performance of EBB with realistic models against the ILOG CPLEX 9.0 MIP solver and the Power Simplex (PS)-based B&B algorithm (PBB). PS is an efficient specialized primal-based Simplex algorithm developed for convex CHP planning problems. EBB is from 661 to 955 times (with average 785) faster than CPLEX and from 11 to 31 times (with average 24) faster than PBB.

An efficient linear model and optimisation algorithm for multi-site combined heat and power production

Abstract Combined heat and power (CHP) production is an important energy production technology which can help to improve the efficiency of energy production and to reduce the emission of CO2. Cost-efficient operation of a CHP system can be planned using an optimisation model based on hourly load forecasts. A long-term planning model decomposes into hourly models, which can be formulated as linear programming (LP) problems. Such problems can be solved efficiently using the specialized Power Simplex algorithm. However, Power Simplex can only manage one heat and one power balance. Since heat cannot be transported over long distances, Power Simplex applies only for local CHP planning. In this paper we formulate the hourly multi-site CHP planning problem with multiple heat balances as an LP model with a special structure. We then develop the Extended Power Simplex (EPS) algorithm for solving such models efficiently. Even though the problem can be quite large as the number of demand sites increases, EPS demonstrates very good efficiency. In test runs with realistic models, EPS is from 29 to 85 times faster than an efficient sparse Simplex code using the product form of inverse (PFI). Furthermore, the relative efficiency of EPS improves as the problem size grows.

A variant of the dynamic programming algorithm for unit commitment of combined heat and power systems

The paper addresses the unit commitment in multi-period combined heat and power (CHP) production planning under the deregulated power market. In CHP plants (units), generation of heat and power follows joint characteristics, which means that production planning must be done in coordination. We introduce in this paper the DP-RSC1 algorithm, which is a variant of the dynamic programming (DP) algorithm based on linear relaxation of the ON/OFF states of the units and sequential commitment of units one by one. The time complexity of DP-RSC1 is proportional to the number of generating units in the system, the number of periods over the planning horizon and the time for solving a single-period economic dispatch problem. We have compared the DP-RSC1 algorithm with realistic power plants against the unit decommitment algorithm and the traditional priority listing method. The results show that the DP-RSC1 algorithm gives somewhat more accurate results (0.08-0.5% on average, maximum 10% for the individual sub-case) and executes 3-5 times faster on average than the unit decommitment algorithm. It is not surprising that the solution quality of the DP-RSC1 algorithm is much better than that of the priority listing method.

A methodology for controlling dispersion in food production and distribution

After a number of food safety crises, the design and implementation of traceability systems became an important tool for managing safety risks in the food industry. In the literature, numerous studies deal with traceability from the viewpoint of information system and technology development. However, traceability and its implications for food safety receive less attention in literature on production and distribution planning. From the viewpoint of operations management, an efficient management of food safety risks requires the consideration of the amounts of potentially recalled products, affected regions/customers, and logistics efforts connected to solving the safety problem. In this paper we are developing a production and distribution planning model for food supply chains to address these issues. We also present heuristics for solving the resulting mixed-integer linear programming model and demonstrate the effectiveness of the developed methodology in a numerical investigation.

An improved unit decommitment algorithm for combined heat and power systems

This paper addresses the unit commitment in multi-period combined heat and power (CHP) production planning, considering the possibility to trade power on the spot market. In CHP plants (units), generation of heat and power follows joint characteristics, which means that production planning for both heat and power must be done in coordination. We present an improved unit decommitment (IUD) algorithm that starts with an improved initial solution with less heat surplus so that the relative cost-efficiency of the plants can be determined more accurately. Then the subsequent decommitment procedures can decommit (switch off) the least cost-efficient plants properly. The improved initial solution for the committed plants is generated by a heuristic procedure. The heuristic procedure utilizes both the Lagrangian relaxation principle that relaxes the system-wide (heat and power) demand constraints and a linear relaxation of the ON/OFF states of the plants. We compare the IUD algorithm with realistic test data against a generic unit decommitment (UD) algorithm. Numerical results show that IUD is an overall improvement of UD. The solution quality of IUD is better than that of UD for almost all of tested cases. The maximum improvement is 11.3% and the maximum degradation is only 0.04% (only two sub-cases out of 216 sub-cases) with an average improvement of 0.3-0.5% for different planning horizons. Moreover, IUD is more efficient (1.1-3 times faster on average) than UD.

Dynamic programming based algorithms for the discounted {0–1} knapsack problem

Abstract The discounted {0–1} knapsack problem (DKP) is an extension of the classical {0–1} knapsack problem (KP) that consists of selecting a set of item groups where each group includes three items and at most one of the three items can be selected. The DKP is more challenging than the KP because four choices of items in an item group diversify the selection of the items. Consequently, it is not possible to solve the DKP based on a classical definition of a core consisting of a small number of relevant variables. This paper partitions the DKP into several easier sub-problems to achieve problem reductions by imitating the core concept of the KP to derive an alternative core for the DKP. Numerical experiments with DP-based algorithms are conducted to evaluate the effectiveness of the problem partition by solving the partitioned problem and the original problem based on different types of DKP instances.