Multi-period Scenario Research Articles

Reduction method for multi-period time series scenarios of wind power

In the planning and operation of power systems containing wind power, it is of great significance to use a small number of representative wind power time series scenarios to accurately portray the stochastic characteristics of wind power. With the increase of the number of scenarios, how to form representative typical scenarios to balance computational efficiency and accuracy is an urgent problem to be solved. In this study, a bi-directional optimization method is proposed to generate daily wind power time series scenarios based on a single-period optimal scenario generation strategy and a multi-period scenario reduction strategy. First, the Wasserstein probability distance index is used to form a scenario model that is best approximated to the probability distribution of wind power, and the optimal scenarios of each period are generated. Secondly, a wind power scenario reduction strategy that integrates spatial distance and stochastic features is proposed. The improved taboo search method is used to selectively connect the representative scenarios of each period to form the representative daily wind power time series scenarios. Finally, the effectiveness and practicality of the proposed wind power time series scenario generation method are verified by simulations.

Two-stage and multi-stage decompositions for the medium-term hydrothermal scheduling problem: A computational comparison of solution techniques

In hydro-based power systems, the Generation Scheduling (GS) problem is usually divided into a series of coupled models aiming to obtain an optimal operating policy over a multi-year planning horizon. The medium-term GS (MTGS) problem belongs to these models, linking the long-term GS (LTGS) with the short-term GS (STGS) problem. To carry out a proper coupling, we propose a stochastic MTGS model with a multi-period scenario tree with non-common samples, and hourly discretization in the first week to include the nonconvex thermal unit-commitment constraints. These considerations lead to solving a very challenging large-scale stochastic optimization problem with mixed-binary variables in the first week. In this context, efficient solution techniques must be explored to ensure a suitable trade-off between solution accuracy and computational performance. In this paper, we propose a two-stage decomposition for the MTGS that is solved by the extended level bundle method. Every second-stage subproblem is itself a multi-period stochastic problem involving only continuous variables. Numerical assessments on the large-scale Brazilian MTGS problem indicate that our approach significantly outperforms the Nested decomposition and Stochastic Dual Dynamic Programming (SDDP) algorithm in terms of computational burden, providing CPU time reductions in the order of 19%.

On pricing-based equilibrium for network expansion planning. A multi-period bilevel approach under uncertainty

This study focuses on the development of a mixed binary primal-dual bilinear model for multi-period bilevel network expansion planning under uncertainty, where pricing-based equilibrated strategic and operational decisions are to be made. The periodwise dependent parameters’ uncertainty is represented by a finite set of scenarios. Pricing-based equilibrium is required in the models to be optimized at the nodes of a multi-period scenario tree. Given the size of the models, it is unrealistic to seek an optimal solution. Several versions of a Stochastic Nested Decomposition matheuristic algorithm are presented for problem solving. Additionally, an approach based on a stagewise-related Stochastic Lagrangean Decomposition is also considered together with a Frank-Wolfe Progressive Hedging-based algorithm. The state step variables device is key for the performance of both approaches. The solution’s optimality gap is computed for three out of the four solution providers that are presented. An extension of the Toll Assignment Problem is considered as a pilot case. A broad computational experience is reported.

Multi-period multi-echelon inventory transportation problem considering stakeholders behavioural tendencies

An inventory transportation problem of manufacturing organization focusing on several stakeholders such as manufacturers, distributors, wholesalers, retailers and customers is addressed in this paper. The research study considered multi-echelon, multi-product, multi-modal and multi-period scenario. The mathematical model in the form of mixed integer non-linear programming is formulated to minimize the total cost associated with transportation, inventory holding and operational activities. A mathematical formulation based heuristic approach, which comprises of four algorithms, is proposed for solving purpose. The proposed heuristic approach considers the behavioural tendencies of stakeholders pertaining to the selection of shipment routes, transportation mode choice decisions and amount of products to be shipped. Fifteen practical problem instances are solved by using the developed heuristic approach while considering the behavioural aspects of stakeholders. Insights obtained from results will be beneficial for manufacturing organizations in making informed decisions related to transportation planning considering stakeholder's behavioural tendencies.

On dealing with strategic and tactical decision levels in forestry planning under uncertainty

A new scheme for dealing with the uncertainty in the scenario trees is considered in the presence of strategic and tactical stochastic parameters for a dynamic mixed 0–1 optimization model in a forest harvesting network along a time horizon under uncertainty. The strategic level of the model presented in this work is included by a several years time horizon, where the uncertainty lies in the timber production. It is represented in a multistage stochastic scenario tree, such that each stage comprises one or several years. Each node in the strategic tree has associated a multi-period scenario graph, where each period in the stages is related to a summer /winter season. The nodes in the graph represent the tactical uncertainty, whose stochastic parameters are the timber price and demand. The strategic decisions aim to the optimal design of the logistic timber harvesting and distribution network at each first period in the stages. The tactical decisions aim to timber harvesting, stocking and distribution from the stands until the markets at the periods in the stages. The model has been validated by using data from a real-life problem.

Dynamic supplier selection through optimal ranking under two-echelon system

PurposeWith the increasing competition among the industries, they remain under pressure as how to select the best set of suppliers for the competitive edge. Often, it has been challenging to develop an effective set of suppliers due to varied and asymmetric mode of criteria. The purpose of this paper is to develop a responsive chain under original equipment manufacturer (OEM).Design/methodology/approachThis study proposes a responsive chain under a two-echelon system (TES) of OEM, which needs to collaborate with a set of suppliers at each echelon through an integrated methodology of AHP and TOPSIS. According to the OEM’s criteria, demands and suppliers’ capacity vary with time, therefore they are not static for a longer period. Hence, supplier selection (SS) problem possesses dynamicity in real practice. For this, MILP is used for finding optimal order quantities based on the optimal ranking at each echelon in the multi-period scenario. Subsequently, sensitivity analysis (SA) is conducted through Taguchi method of parameter design (TMPD) to achieve an optimal ranking in the TES.FindingsThis study suggests optimal criteria’s weight, percentage contribution, and flexibility for the suppliers and manufacturers involving through maximum demand strategy at each echelon of OEM. It also provides robust group of suppliers and manufacturers in the TES through optimal ranking and simultaneously in the order allocations. Furthermore, it restricts the number of suppliers and manufactures at each echelon through proposed methodology to obtain the solution in a very short running time.Originality/valueTo validate this model, a real data set for the case of chain conveyor company is used. This adopted methodology can suggest the organization that how the approach should be implemented.

Multi-Period Planning With Actual Physical and Traffic Conditions

The common practice in optical networks is to deploy them statically in a future proof approach and to operate them with only traffic/fault driven changes. Lightpaths are overprovisioned with high quality of transmission (QoT) margins to anticipate future degradations, due to interference, aging, and maintenance operations, and to account for inaccuracies in QoT estimation. Such assumptions decrease network efficiency and increase the cost. Moreover, transponders and regenerators are assigned once to demands, yielding low efficiency if traffic varies significantly. Elastic optical technology, feedback from software monitors, and software defined networking enable the dynamic operation of the network. We propose an algorithm that takes into account the actual physical layer and traffic conditions and provisions new or adapts existing lightpaths with actual (just-enough) margins, optimizing placement and transmission parameter decisions for the transponders and regenerators. Using the proposed algorithm in a multi-period scenario, we quantify the benefits that can be achieved when planning with actual margins and varying levels of traffic dynamicity.

Scenario tree reduction methods through clustering nodes

To develop practical and efficient scenario tree reduction methods, we introduce a new methodology which depends on clustering nodes, and thus an easy-to-handle distance function to measure the difference between two scenario trees is designed. On the basis of minimizing the new distance, we construct a multiperiod scenario tree reduction model which is supported theoretically by the stability results of stochastic programs. By solving the model, we design a stage-wise scenario tree reduction algorithm which is superior to the simultaneous backward reduction method in terms of both computational complexity and solution results of stochastic programming problems, the corresponding reduction algorithm especially for fan-liked trees is also presented. We further design a multiperiod scenario tree reduction algorithm with a pre-specified distance by utilizing the stability results of stochastic programs. A series of numerical experiments with real trading data and the application to multiperiod portfolio selection problem demonstrate the practicality, efficiency and robustness of proposed reduction model and algorithms.

Point-in-time probability of default term structure models for multiperiod scenario loss projection

Point-in-time probability of default term structure models for multiperiod scenario loss projection

Scenario Analysis of Energy and Water Trade-Offs in the Expansion of a Dual Water System

AbstractUsing treated wastewater effluent (reclaimed water) for beneficial purposes can be a sustainable practice that reduces demand on potable networks. However, implementing reclaimed water networks can have unintended effects, specifically unintended increases in energy consumption. This case study employs multiperiod scenario analysis to examine energy consumption associated with the potable and reclaimed water systems for the Town of Cary, North Carolina. Using hydraulic planning models of both systems provided by the design engineers, the conveyance and additional treatment energy is tabulated. This method considers uncertainty in reclaimed water demand by varying the expected demand for each build out of the reclaimed water network. Differential electricity consumption is calculated as the difference between the electricity consumed to deliver reclaimed water through a secondary network compared to the electricity consumed to deliver the same volume through the potable water network. Demand uncert...

Techno-Economic Analysis of Fixed and Flexible Node Architectures in Multiperiod Scenarios [Invited

We analyze the capital expenditures (CapEx) and operational expenditures (OpEx) related to the power consumption and footprint requirements of fixed and flexible node architectures in a multiperiod scenario and under different traffic requirements. We consider fixed architectures based on muxponders, and nonblocking and partial nonblocking flexible architectures based on electrical cross connects (EXC) of different sizes. In flexible architectures, the impact of hitless traffic regrooming on the network CapEx and OpEx is also assessed. Results show that in spite of the initial higher investment required by flexible architectures, in the long term they tend to present lower CapEx and OpEx. Moreover, hitless regrooming can assist in postponing the need for increasing the footprint requirements in partial nonblocking EXCs.

A multiproduct batch plant design model incorporating production planning and scheduling decisions under a multiperiod scenario

In this study, we propose a multiperiod mixed-integer linear programming model, which integrates several decisions related to multistage multiproduct batch plants. In general, plant designs are solved without considering operation decisions, whereas the proposed approach considers production planning as well as scheduling decisions. The time horizon comprises several periods where deterministic variations in prices, product demand limits, costs, and the availability raw materials are considered. The plant operates using different production campaigns throughout each time period. The proposed model allows the optimal plant structure (unit sizes and its duplication in parallel at each stage) to be obtained, as well as the detailed production plan for every time period. Thus, the proposed method allows assessments of the trade-offs between the different decision levels involved by considering fluctuations throughout the time horizon.

Sourcing Decision in a Multi-Period Model under Demand and Supply Uncertainty

Determining the optimum number of suppliers and the optimum quantities to order from each of them is a critical problem for any supply chain. This paper has mathematically arrived at conditions to identify the appropriate sourcing strategy in a multi-period scenario for a stochastic supply and a stochastic demand environment. It has also obtained the total order quantity, optimum number of suppliers and order allocation to each of the suppliers under both uncertain demand and supply in the multiple-period context. Through a numerical analysis this work could bring interesting managerial insights about the sourcing strategies.

Risk-Averse Insider Trading in Multi-Asset Sequential Auction Markets

We extend Kyle's (Kyle, 1985) analysis of sequential auction markets to the case in which a risk-averse insider possesses private information on the liquidation value of a number of risky assets. We confirm: i) in a multi-asset setting, Holden and Subrahmanyam's counter-intuitive result that risk-aversion induces informed agents to consume more rapidly their long-lived private information vis-a-vis their risk-neutral counter-parts, so that with risk-averse insiders securities markets are more efficient; ii) in a multi-period scenario, Caballe and Krishnan's result that the insider operates in such a way that the price impact of signed volume (order flow) is symmetric across all risky assets.

New Alternatives in the Design and Planning of Multiproduct Batch Plants in a Multiperiod Scenario

New alternatives for the simultaneous design and planning of multiproduct batch plants in a multiperiod scenario are presented in this article. This formulation allows the flexible configuration of the plant in every time period for each product considering the assignment of parallel units of different sizes operating either in-phase or out-of-phase. Capacity expansion during the time horizon is also allowed in order to satisfy new variable requirements. For each batch stage, following the usual procurement policy, units are selected from a set of standard and discrete sizes that are available to perform each operation. The model is formulated through a mixed-integer linear programming (MILP) formulation that maximizes the net present value of profit. From the planning point of view, product sales, raw materials purchases, inventories, waste disposal, and late deliveries are taken into account. Thus, this model simultaneously solves both design and production planning for given forecasts of product demands and pricing in each time period.

Strategies for an Integrated Distribution Problem

The problems arising in the logistics of commercial distribution are complex and involve several players and decision levels. One important decision is related with the design of the routes to distribute the products, in an efficient and inexpensive way. This article explores three different distribution strategies: the first strategy corresponds to the classical vehicle routing problem; the second is a master route strategy with daily adaptations and the third is a strategy that takes into account the cross-functional planning through a multi-objective model with two objectives. All strategies are analyzed in a multi-period scenario. A metaheuristic based on the Iterated Local Search, is used to solve the models related with each strategy. A computational experiment is performed to evaluate the three strategies with respect to the two objectives. The cross functional planning strategy leads to solutions that put in practice the coordination between functional areas and better meet business objectives.