Stochastic Capacity Planning Research Articles

Risk-averse stochastic capacity planning and P2P trading collaborative optimization for multi-energy microgrids considering carbon emission limitations: An asymmetric Nash bargaining approach

The increasing penetration of renewable energy with stochastic characteristics and continuous refinement of carbon emission policies put forward higher requirements for the construction of new power systems. This paper proposes a risk-averse stochastic capacity planning and peer-to-peer (P2P) trading collaborative optimization method for multi-energy microgrids (MEMGs) considering carbon emission limitations. First, a cooperative operation model for MEMGs considering the capacity planning of distributed generation units, uncertainty from renewable energy generations, carbon emission limitations and P2P electricity trading among MEMGs is formulated. Second, a risk-averse stochastic programming method is applied to avoid the potential risk losses caused by randomness and intermittence of renewable energy. Third, an asymmetric Nash bargaining approach is adopted to ensure the fair allocation of benefits and maintain the willingness of individual MEMGs to participate in cooperation. Then, to protect the privacy of individual MEMGs belonging to different stakeholders, the alternating direction method of multipliers is used to solve the two subproblems in a distributed manner. Meanwhile, to further alleviate the computation burdens, a diagonal quadratic approximation method is applied to linearize the quadratic penalty term in the augmented Lagrangian function and realize the parallel solution of all optimization subproblems. Moreover, the influence of different carbon emission targets on the optimal resource combination strategy of the system is investigated by introducing carbon emission factors. Simulations on different models, strategies, and distributed algorithms are conducted to verify the effectiveness and superiority of the proposed method.

Multistage stochastic capacity planning of partially upgraded bitumen production with hybrid solution method

Partial upgrading technologies have received a great amount of attention as a promising and economic solution for Canadian oil sands bitumen processing. In this paper, the optimal planning of capital and expansion capacities for partial upgrading of bitumen is studied. We propose a multistage stochastic planning model with consideration of various sources of uncertainties. The main challenge of the stochastic model is the presence of terms in which an uncertain parameter is multiplied by an adjustable dynamic decision variable. To solve the problem, two hybrid methods are proposed: in method 1, the uncertain parameter is modeled with an uncertainty set and the dynamic variable is modeled as scenario dependent variables; in method 2, the uncertain parameter is modeled with samples and the dynamic variable is modeled using the decision rule-based approximation. Finally, results obtained from both hybrid models are compared based on different criteria: (1) computational time, (2) solution performance, and (3) solutions for representative scenarios.

Stochastic capacity planning and dynamic network design

Abstract The present paper proposes a mathematical model and a solution approach to the Stochastic Capacity Planning and Dynamic Network Design Problem. Here, strategic decisions usually comprise developing the necessary capacity — through either incrementing capacity on existing assets (facilities or logistics channels) or establishing new capacity in the form of new assets — in order to satisfy increasing demand. Hence, throughout the planning horizon, decisions on which new assets to establish and where to increment capacity must be taken at minimal cost and in a timely manner. However, when demand varies nonmonotonically, decisions on which assets to temporarily shut down in times of decreasing demand and which of those to reopen when market conditions improve must also be taken into account. We propose a multi-stage stochastic mixed-integer programming approach to the problem as well as a Lagrangian Heuristic procedure to attain reasonably well bounded feasible solutions. The proposed method is evaluated in a Global Mining Supply Chain context which, due to the inherently large capital expenses, could have the outcome of its strategic decision making process significantly improved.

Stochastic multi-site capacity planning of TFT-LCD manufacturing using expected shadow-price based decomposition

This paper presents a stochastic optimization model and efficient decomposition algorithm for multi-site capacity planning under the uncertainty of the TFT-LCD industry. The objective of the stochastic capacity planning is to determine a robust capacity allocation and expansion policy hedged against demand uncertainties because the demand forecasts faced by TFT-LCD manufacturers are usually inaccurate and vary rapidly over time. A two-stage scenario-based stochastic mixed integer programming model that extends the deterministic multi-site capacity planning model proposed by Chen et al. (2010) [1] is developed to discuss the multi-site capacity planning problem in the face of uncertain demands. In addition a three-step methodology is proposed to generate discrete demand scenarios within the stochastic optimization model by approximating the stochastic continuous demand process fitted from the historical data. An expected shadow-price based decomposition, a novel algorithm for the stage decomposition approach, is developed to obtain a near-optimal solution efficiently through iterative procedures and parallel computing. Preliminary computational study shows that the proposed decomposition algorithm successfully addresses the large-scale stochastic capacity planning model in terms of solution quality and computation time. The proposed algorithm also outperforms the plain use of the CPLEX MIP solver as the problem size becomes larger and the number of demand scenarios increases.

Contributors

Contributors

A two-level interior-point decomposition algorithm for multi-stage stochastic capacity planning and technology acquisition

Manufacturing flexibility is recognised as one of the key strategies to address uncertain future products demand. Therefore, a growing need exists to investigate the strategic aspect of flexibility. To capture the different aspects of market flexibility in the face of this dynamic demand, this paper focuses on the role of product, volume, and expansion flexibility in the context of the multi-stage stochastic program. Moreover, we implement a two-level, interior-point decomposition algorithm based on the Analytic Center Cutting Plane Method (ACCPM) to solve the model. The central prices obtained by the ACCPM provides a fast convergence and promising computational results in terms of the number of iterations.

Scenario-based Stochastic Capacity Planning Model and Decision Risk Analysis

Abstract To study the capacity planning problem under uncertainty in which market demand and product price are stochastic, multi period capacity planning model based on scenario was investigated in this paper. Two models were proposed: one is a prearranged planning model in which the capacity investment plan do not change with the stochastic market demand, and the other is an adaptive planning model in which capacity investment plan could trace the evolution progress of the stochastic market demand. The computational study compared the decision results of both models, which reveals that the adaptive planning model could suggest better decision. Moreover, based on downside risk analysis, the investment risk of stochastic capacity planning has been investigated, and a prearranged capacity planning model considering the expected downside risk of the objective revenue was proposed. In the model, a constraint of expected downside risk is added to the initial stochastic model to reflect the decision-maker's risk preference. Whether to consider the risk or not will result in different decisions, which, in the computational study, were compared.

The application of reliability constrained stochastic capacity planning models to the service sector

Emphasis on quality management has recently permeated not only the manufacturing sector, but the service sector as well. Consequently, quality service and consumer satisfaction have become realities for many monopolistic service oriented industries facing competition. In order to effectively implement timely service within these industries (i) capacity plans must be developed which provide adequate staffing during both peakload and offpeak hours, as well as optimal (ii) prices and (iii) reliability of service. This paper builds on the results of Boronico (1992) in illustrating how reliability constrained marginal cost, within which optimal price is embodied, and minimum cost capacity plans may be determined for a service provider facing stochastic demand. Excess demand is not lost, but is deferred: a characteristic that typifies the operation of many delivery systems, such as postal services. Results indicate that marginal costs are convex with respect to reliability of service, while changes in the demand distribution's variability may impact optimal capacity by either increasing or decreasing required capacity.

A multivariate utility function approach to stochastic capacity planning

The problem being considered is the expansion of a single capacity when the installation cost is large and there are neither absolescence nor spatial effects on the expansion. Demand is assumed to follow an evolving process; in particular, the demand increments are normally distributed with linearly increasing mean and variance in time (i.e., a Wiener process). Selecting the optimum size and timing of capacity additions in the face of uncertain demand forecasts involves both the minimization of cost as well as the minimization of risk. For the situation where demand acts as a Wiener process, Kang and Park have derived the expectation of the “equivalent cost rate.” Using the standard deviation of the equivalent cost rate as a measure of the risk of expansion, Kang and Park then minimized an objective function that was a linear combination of cost and risk. The purpose of this paper is to extend this line of research. Using standard decision analysis procedures, a multiattribute utility function is constructed that reflects the decision maker's trade-off for cost and risk. A significant advantage of the utility function approach is that it allows for nonlinear trade-offs of cost and risk.