Scenario-based Model Research Articles

Resilient facility location against the risk of disruptions

In this paper, we consider an uncapacitated facility location problem (RUFL) with random facility disruptions. We develop risk-averse optimization formulations to compute resilient location and customer assignment solutions for two cases (i.e., under either independent or correlated disruptions), where the risks are expressed through a family of risk measures including conditional value-at-risk (CVaR) and absolute-semideviation (ASD). The risk-averse RUFL with independent facility disruptions is to control the risks at each individual customer and modeled as a mixed-integer nonlinear programming, which is challenging to be solved. In response, we develop a branch-and-cut algorithm combined with augmented Lagrangian decomposition for globally optimizing the problem. As for the risk-averse RUFL with correlated facility disruptions, we propose a scenario-based model to minimize the total fixed costs and risks across the entire customer set. The resulting formulation is a pure MILP and a Lagrangian decomposition scheme is proposed for computational aspects in large-scale cases. Our numerical results show that the risk-averse models outperform the classic risk-neutral models in improving the reliability. Experiments demonstrate that our proposed algorithms perform well. To conclude, we extract managerial insights that suggest important guidelines for controlling risk in the face of disruption.

Dynamic Safety Constraints by Scenario-Based Economic Model Predictive Control of Marine Electric Power Plants

This paper studies scenario-based model predictive control (MPC) for dynamic safety constraints. For marine electric power plant with direct current distribution and variable speed generator set, the speed of the generator sets should be as low as possible to increase the efficiency of the diesel engines. However, a safety margin toward underspeed is necessary. In this paper, a dynamical safety constraint is achieved by including a fault scenario in the MPC formulation. This is done using a nominal trajectory of the predicted states for the fault-free operation, and adding fault trajectories starting from the samples of the nominal trajectory. The fault trajectories simulate the fault scenario and dynamically constrain the nominal trajectory. The controller is shown to be effective using closed-loop simulations of a marine electric power plant.

Modeling sustainable long-term electricity supply-demand in Africa

This paper develops a scenario-based model to identify and provide an array of electricity demand in Africa, and to derive them from the African power system of development. A system-based approach is performed by applying the scenario methodology developed by Schwartz in the context of the energy-economic modeling platform ‘Long-range Energy Alternative Planning’. Four scenarios are investigated. The Business as Usual scenario (BAU) replicates the regional and national Master Plans. The renewable-promotion scenario increases the share of renewable energy in the electricity mix. The demand and supply side efficiency scenarios investigate the impact of energy efficiency measures on the power system. The results show an increase in electricity demand by 4% by 2040, supply shortages and high emissions of Greenhouse Gases. Contrary to expectations, the renewable energy scenario did not emerge as the best solution to a sustainable electrification of the region. The energy efficiency scenarios have allowed us to draw a sustainable pathway for electrification.

Accelerated Model Predictive Control for Electric Vehicle Integrated Microgrid Energy Management: A Hybrid Robust and Stochastic Approach

A microgrid with an advanced energy management approach is a feasible solution for accommodating the development of distributed generators (DGs) and electric vehicles (EVs). At the primary stage of development, the total number of EVs in a microgrid is fairly small but increases promptly. Thus, it makes most prediction models for EV charging demand difficult to apply at present. To overcome the inadaptability, a novel robust approach is proposed to handle EV charging demand predictions along with demand-side management (DSM) on the condition of satisfying each EV user’s demand. Variables with stochastic forecast models join the objective function in the form of probability-constrained scenarios. This paper proposes a scenario-based model predictive control (MPC) approach combining both robust and stochastic models to minimize the total operational cost for energy management. To overcome the concern about the convergence time increasing from the combination of scenarios, the Benders decomposition (BD) technique is further adopted to improve computational efficiency. Simulation results on a combined heat and power microgrid indicate that the proposed scenario-based MPC approach achieves a better economic performance than a traditional deterministic MPC (DMPC) approach, while ensuring EV charging demands, as well as minimizing the trade-off between optimal solutions and computing times.

Scenario-based model predictive control for multi-echelon supply chain management

Policies for managing multi-echelon supply chains can be considered mathematically as large-scale dynamic programs, affected by uncertainty and incomplete information. Except for a few special cases, optimal solutions are computationally intractable for systems of realistic size. This paper proposes a novel approximation scheme using scenario-based model predictive control (SCMPC), based on recent results in scenario-based optimization. The presented SCMPC approach can handle supply chains with stochastic planning uncertainties from various sources (demands, lead times, prices, etc.) and of a very general nature (distributions, correlations, etc.). Moreover, it guarantees a specified customer service level, when applied in a rolling horizon fashion. At the same time, SCMPC is computationally efficient and able to tackle problems of a similar scale as manageable by deterministic optimization. For a large class of supply chain models, SCMPC may therefore offer substantial advantages over robust or stochastic optimization.

Block Erection in the Event of Delays in Shipbuilding: A Scenario-Based Approach

Ships are constructed from individual steel structural units called blocks, which are typically erected into the ship one by one in a sequence. This sequence, the block erection schedule, is the main schedule in shipbuilding, and it is followed in other production phases. However, the problems in the production of the blocks can delay the arrival of the blocks in comparison to what was initially scheduled. To deal with these delays, this article studies five different planning methods: erecting blocks unfinished; the use of inventories; the use of rush jobs; sequence changes; and, if the delays cannot be dealt with, delaying the completion of the ship. In order to do that, a mathematical, scenario-based mixed-integer linear programming model is formed. The model is used with numerical results to show that the block structure, delay conditions, and the tardiness costs have significant effect on the optimal use of planning methods. Results show that inventories should be used when delays are probable, whereas blocks should be erected unfinished if the delays are very uncertain and there are high tardiness penalties. The uses of rush jobs and sequence changes depend on the structure of the ship.

Block Erection in the Event of Delays in Shipbuilding: A Scenario-Based Approach

Ships are constructed from individual steel structural units called blocks, which are typically erected into the ship one by one in a sequence. This sequence, the block erection schedule, is the main schedule in shipbuilding, and it is followed in other production phases. However, the problems in the production of the blocks can delay the arrival of the blocks in comparison to what was initially scheduled. To deal with these delays, this article studies five different planning methods: erecting blocks unfinished; the use of inventories; the use of rush jobs; sequence changes; and, if the delays cannot be dealt with, delaying the completion of the ship. In order to do that, a mathematical, scenario-based mixed-integer linear programming model is formed. The model is used with numerical results to show that the block structure, delay conditions, and the tardiness costs have significant effect on the optimal use of planning methods. Results show that inventories should be used when delays are probable, whereas blocks should be erected unfinished if the delays are very uncertain and there are high tardiness penalties. The uses of rush jobs and sequence changes depend on the structure of the ship.

Evaluating and ranking sustainable suppliers by robust dynamic data envelopment analysis

One of the advantages of data envelopment analysis (DEA) is to determine benchmarks for inefficient decision making units (DMUs). However, determination of the benchmarks is the result of past performance of DMUs. In other words, the benchmarks do not provide any recommendation for improvement of future efficiency of DMUs. On the other hand, in dynamic DEA models often no DMU gets the efficiency score of unity. In this case, although we can rank the DMUs, we cannot introduce an efficient DMU and benchmarks. To overcome these shortcomings we propose a dynamic ideal DMU using dynamic DEA and scenario-based model of robust. A case study showing the model in use provided.

Newsvendor Models for Innovative Products with Inventory Inaccuracies

In recent years, there has been growing interest in the inventory inaccuracies in the newsvendor problems, which are costly and prevalent in many industries. Innovative products, which are characterized with short lifecycle and unpredictable demand, are especially suffered by the inventory inaccuracies. Based on the one-shot decision theory (OSDT), a scenario-based inventory model (newsvendor-OSDT) has been proposed for the newsvendor problems for innovative products. In this article, within the framework of newsvendor-OSDT, we consider two cases: (a) the retailer ignores the inventory errors; (b) RFID technology is used to reduce or eliminate the errors. Based on the theoretical analysis and computational simulation, the article aims at addressing the questions: does the inventory inaccuracy tackled using newsvendor-OSDT? Within the framework of newsvendor-OSDT, does the RFID contribute to the inventory inaccuracies? This article will construct the newsvendor models for innovative products with inventory inaccuracies and put forward managerial implications.

Toward A scenario-based Model of Culture Transformation building upon the Competing values Framework

In this paper we develop a culture-sensitive framework for managing culture change. Building upon the Competing values Framework (Cameron & Quinn, 1999), we investigated each of the four culture types consisting of the framework and identified the major resistance forces associated with each individual culture. Then we propose how these resistance forces could be addressed with appropriate interventions. In addition, we analyzed twelve likely culture change scenarios coming out of the competing values framework based typology in search of possible interventions that can facilitate the culture transformation of each specific culture change scenario. Twelve propositions are developed as a result of the analysis. Our study shows that competing values framework could be used as a blueprint for guiding culture change, in addition to mapping out organizational culture.

A hospital staff scheduling problem under stochastic operation times

This paper is concerned with a hospital staff scheduling problem wherein surgical operation times are stochastic. We formulate a complete recourse, scenario-based model for this problem, and develop a branch-and-cut (B&C) algorithm that is further hybridised with the Monte Carlo method (MCM). The proposed hybrid MCM-based approach is demonstrated to substantially reduce the required computational effort over a purely branch-and-cut methodology while producing near-optimal solutions having relatively small optimality gaps.

Bi-criterion procedures to support logistics decision making: cost and uncertainty

In practical decision making, one often is interested in solutions that balance multiple objectives. In this study we focus on generating efficient solutions for optimization problems with two objectives and a large but finite number of feasible solutions. Two classical approaches exist, being the constraint method and the weighting method, for which a specific implementation is required for this problem class. This paper elaborates specific straightforward implementations and applies them to a practical allocation problem, in which transportation cost and risk of shortage in supplied livestock quality are balanced. The variability in delivered quality is modelled using a scenario-based model that exploits historical farmer quality delivery data. The behaviour of both implementations is illustrated on this specific case, providing insight in (i) the obtained solutions, (ii) their computational efficiency. Our results indicate how efficient trade-offs in bi-criterion problems can be found in practical problems.

Review of models for carbon accounting in harvested wood products

Carbon storage in harvested wood products (HWPs) is seen as a measure to mitigate climate change. The increased use of long-life wood products, however, should be thoroughly analysed before being promoted as a climate mitigation strategy. The national carbon pool of HWPs is very dynamic, due to changing patterns of wood product consumption and trade. Carbon accounting models are a common tool for estimating and projecting carbon pools. The purpose of this study is to analyse and find the relevant features of existing models that are related to the carbon pool in HWPs. From the many existing models, we have selected several representative models. We have analysed these selected models in depth by looking at their features, components and application. The models have variable features, depending on their scope and the modelling objectives. Significant modelling components for assessing the climate change mitigation potential of wood products are often missing. For example, the material substitution effect in the construction sector is rarely quantified, even if it would result in a significant reduction of greenhouse gas emissions. In this paper, we propose modelling components for a scenario-based model capable of using country-specific data for major groups of HWPs that would allow improved assessments of the climate change mitigation potential of alternative forest resource utilisation scenarios.

Joint service capacity planning and dynamic container routing in shipping network with uncertain demands

Service capacity planning is a key tactic decision in container shipping, which has a significant impact on daily operations of shipping company. On the other hand, operational decisions such as demand fulfilment and shipment routing will impact on service capacity requirements and utilisation, particularly in the presence of demand uncertainty. This article proposes a two stage stochastic programming model with recourse to deal with the problem of joint service capacity planning and dynamic container routing in liner shipping. The first stage of the model concerns how to determine the optimal service capacity, and the second focuses on the optimal routing of shipments in stochastic and dynamic environments under a given service capacity plan. Initially, SAA (Sample Average Approximation) is employed to solve the model. Noting the computational complexity of the problem, Progressive Hedging Algorithm (PHA) is employed to decompose the SAA model into a number of scenario-based models so that reasonably large scale problems can be solved. To handle larger scale problems, we develop a new solution procedure termed as APHA (Adapted Progressive Hedging Algorithm) that further decomposes the scenario-based model into job (customer order) based models with measurable error bounds. Numerical experiments are conducted to illustrate the effectiveness of the proposed APHA in solving the problems under consideration.

Scenario-based Model Predictive Control: Recursive Feasibility and Stability

Many processes are influenced by uncertain parameters or external disturbances, such as temperature changes. The control of such systems is in general challenging. In this work, we consider robust multi-scenario Model Predictive Control (MPC). Its central idea is to assume a finite number of possible values for the uncertainties and to model their combinations in a scenario tree. We adapt the classical dual mode approach of nominal MPC to establish recursive feasibility and stability for the multi-scenario case, using a common terminal region and common terminal cost function for all uncertainty realizations. For linear systems, the computation of these ingredients can be formulated as a semidefinite program. In a simulation, we apply the suggested approach to building climate control and show that it robustly stabilizes the system while a standard MPC controller violates state constraints and becomes infeasible.

Progresses in on-body channel models for wireless body area networks

On-body communication channels are a physical basis for the establishment of an effective and reliable wireless link between on-body nodes in wireless body area networks (WBANs).Due to normally strict limitations in transmit power and power consumptions of on-body nodes as well as the human-centered characteristics of WBANs,on-body channels are prone to be affected by the electromagnetic properties of human tissues,human movements,application environments and transceiver antennas,which increase greatly the complexity of the research on channel models.The paper discusses the developments,mathematical expressions and application characteristics of five types of on-body channel models,such as the simple path loss model,the hybrid path loss model,the small-scale fading model,the scenario-based model and the ultra-wideband model,and reviews the current progress on the modeling on-body channels. Key words: Wireless body area network; On-body channel; Path loss; Fading

The scenario approach for Stochastic Model Predictive Control with bounds on closed-loop constraint violations

Many practical applications in control require that constraints on the inputs and states of the system are respected, while some performance criterion is optimized. In the presence of model uncertainties or disturbances, it is often sufficient to satisfy the state constraints for at least a prescribed share of the time, such as in building climate control or load mitigation for wind turbines. For such systems, this paper presents a new method of Scenario-Based Model Predictive Control (SCMPC). The basic idea is to optimize the control inputs over a finite horizon, subject to robust constraint satisfaction under a finite number of random scenarios of the uncertainty and/or disturbances. Previous SCMPC approaches have suffered from a substantial gap between the rate of constraint violations specified in the optimal control problem and that actually observed in closed-loop operation of the controlled system. This paper identifies the two theoretical explanations for this gap. First, accounting for the special structure of the optimal control problem leads to a substantial reduction of the problem dimension. Second, the probabilistic constraints have to be interpreted as average-in-time, rather than pointwise-in-time. Based on these insights, a novel SCMPC method can be devised for general linear systems with additive and multiplicative disturbances, for which the number of scenarios is significantly reduced. The presented method retains the essential advantages of the general SCMPC approach, namely a low computational complexity and the ability to handle arbitrary probability distributions. Moreover, the computational complexity can be adjusted by a sample-and-remove strategy.

Stochastic vs deterministic programming in water management: the value of flexibility

In the paper we develop a two stage scenario-based stochastic programming model for water management in the Indus Basin Irrigation System (IBIS). We present a comparison between the deterministic and scenario-based stochastic programming model. Our model takes stochastic inputs on hydrologic data i.e. inflow and rainfall. We divide the basin into three rainfall zones which overlap on 44 canal commands. Data on crop characteristics are taken on canal command levels. We then use ten-daily and monthly time intervals to analyze the policies. This system has two major reservoirs and a complex network of rivers, canal head works, canals, sub canals and distributaries. All the decisions on hydrologic aspects are governed by irrigation and agricultural development policies. Storage levels are maintained within the minimum and maximum bounds for every time interval according to a power generation policy. The objective function is to maximize the expected revenue from crops production. We discuss the flexibility of two stochastic optimization models with varying time horizon.

Stochastic scenario-based model and investigating size of battery energy storage and thermal energy storage for micro-grid

Energy storage systems (ESS) are designed to accumulate energy when production exceeds demand and to make it available at the user’s request. They can help match energy supply and demand, exploit the variable production of renewable energy sources (e.g. solar and wind), increase the overall efficiency of the energy system and reduce CO2 emissions. This paper presents a unit commitment formulation for micro-grid that includes a significant number of grid parallel PEM-Fuel Cell Power Plants (PEM-FCPPs) with ramping rate and minimum up and down time constraints. The aim of this problem is to determine the optimum size of energy storage devices like hydrogen, thermal energy and battery energy storages in order to schedule the committed units’ output power while satisfying practical constraints and electrical/thermal load demand over one day with 15min time step. In order to best use of multiple PEM-FCPPs, hydrogen storage management is carried out. Also, since the electrical and heat load demand are not synchronized, it could be useful to store the extra heat of PEM-FCPPs in the peak electrical load in order to satisfy delayed heat demands. Due to uncertainty nature of electrical/thermal load, photovoltaic and wind turbine output power and market price, a two-stage scenario-based stochastic programming model, where the first stage prescribes the here-and-now variables and the second stage determines the optima value of wait-and-see variables under cost minimization. Quantitative results show the usefulness and viability of the suggested approach.

Nonlinear Production Planning of Oil-Refinery Units for the Future Fuel Market in Brazil: Process Design Scenario-Based Model

The oil industry in Brazil has accounted for US$300 billion in investments over the past 10 years, and further expansions are planned to supply the needs of the future fuel market in terms of both quantity and quality. In this paper we analyze the Brazilian fuel production and market scenarios considering the country’s planned investments to prevent a fuel deficit of around 30% in 2020. A nonlinear programming model is proposed to predict the national overall capacity for different oil-refinery units considering four future market scenarios. Single-period operational planning cases for the present and intermediate scenarios and those considered in 2020 are proposed by changing demands, costumer preference, and planned investments to calculate fuel production and import figures for the current and future production and market scenarios in the country. The results indicate a different processing outline in the national overall unit capacity planning.