Two-stage stochastic mixed-integer linear programming (MILP) problems can arise naturally from a variety of process design and operation problems. These problems, with a scenario based formulation, lead to large-scale MILPs that are well structured. When firststage variables are mixed-integer and second-stage variables are continuous, these MILPs can be solved efficiently by classical decomposition methods, such as Dantzig-Wolfe decomposition (DWD), Lagrangian decomposition, and Benders decomposition (BD), or a cross decomposition strategy that combines some of the classical decomposition methods. This paper proposes a new cross decomposition method, where BD and DWD are combined in a unified framework to improve the solution of scenario based two-stage stochastic MILPs. This method alternates between DWD iterations and BD iterations, where DWD restricted master problems and BD primal problems yield a sequence of upper bounds, and BD relaxed master problems yield a sequence of lower bounds. The method terminates finitely to an optimal solution or an indication of the infeasibility of the original problem. Case study of two different supply chain systems, a bioproduct supply chain and an industrial chemical supply chain, show that the proposed cross decomposition method has significant computational advantage over BD and the monolith approach, when the number of scenarios is large.
Nigeria is endowed with huge proven gas reserves estimated to be 184 trillion cubic feet (Tcf). It ranks as the seventh holder of natural gas reserves in the world, and the largest in Africa. Nigeria also flares more natural gas than any other country; it accounts for 12.5% of the world's annual gas flared equivalent to $2.0 billion of annual revenue wasted. There is crucial need, therefore, to reduce gas flaring and its environmental impacts, and to derive maximum economic benefits from gas production.The purpose of this paper is to identify options for natural gas utilization and to develop a model for optimizing the natural gas utilization strategies using the Niger Delta as a case study. A Linear Programming model is proposed consisting of an objective function that is based on maximizing profit derived from the various utilization projects in the Niger Delta subject to several constraints. The optimal utilization/decision is determined from the solution of the optimization model. Results obtained indicate that the optimal utilization for maximum profit include both current and planned projects such as the Liquefied Natural gas project at Bonny, supply of gas for domestic use and power generation, transport to West African countries, transport of natural gas to Algeria through the TransSaharan Gas Pipeline (TSGP), and sales of EOR products to market. Upcoming project such as the Olokola LNG was only profitable as the gas price increases. Sensitivity analysis is carried out to evaluate impact of changes in the input parameters on the objective function. Paper also discusses the impact of gas pricing on the implementation of the Nigerian gas master plan (NGMP).The model can be used to select which set of projects would provide maximum profits (net income) from several competing natural gas projects.
This paper is concerned with strategic optimization of a typical industrial chemical supply chain, which involves a material purchase and transportation network, several manufacturing plants with on-site material and product inventories, a product transportation network, and several regional markets. In order to address large uncertainties in customer demands at the different regional markets, a novel robust scenario formulation, which has been recently developed by the authors, is tailored and applied for strategic optimization. Case study results show that the robust scenario formulation works well for this real industrial supply chain system, and it outperforms the deterministic formulation and the classical scenario-based stochastic programming formulation by generating better expected economic performance and solutions that are guaranteed to be feasible for all uncertainty realizations. The robust scenario problem exhibits a decomposable structure that can be taken advantage of by Benders decomposition for efficient solution, so the application of Benders decomposition to the solution of the strategic optimization is also discussed. The case study results show that Benders decomposition can reduce the solution time by almost an order of magnitude when the number of scenarios in the problem is large.Keywords: supply chain, uncertainty, stochastic programming, robust scenario formulation, Benders decomposition INTRODUCTION S upply chain optimization (SCO) is a set of approaches utilized to efficiently integrate suppliers, manufacturers, warehouses, and stores, so that merchandise is produced and distributed at the right quantities, to the right locations, and at the right time, in order to minimize system-wide costs while satisfying service level requirements.[1] SCO has emerged as a major research direction in the process systems engineering (PSE) community since the last decade; in the context of PSE, it is sometimes called enterprise-wide optimization if the emphasis is placed on the manufacturing stage. [2] In the PSE literature, SCO has been intensively studied for a variety of process industries, such as the petroleum industry, [3][4][5] bioenergy industry, [6][7][8] pharmaceutical industry, [9][10] and more. Papageorgiou gave a comprehensive summary and discussion of the advances and opportunities of supply chain optimization for the process industries. [11] Nikolopoulou and Ierapetritou presented a review on the optimization of sustainable chemical processes and supply chains for balanced economic, environmental, and social objectives. [12] SCO problems can be categorized into three levels: strategic, tactical, and operational problems, which are associated with the design, long-term/mid-term planning, and short-term operation of supply chains, respectively.[13] At any decision-making level in SCO, there may be factors that are not known exactly but can significantly impact supply chain performance, such as those related to raw material supplies, transportation and logistics, production and operation u...
The maximum concentration of hydrogen that can be commingled with or blended in natural gas has been a topic of discussion for many years. The reasons for blending hydrogen with natural gas are mainly twofold: to improve the renewable content of natural gas and to utilize the existing natural gas pipeline infrastructure for hydrogen distribution. This paper aims at addressing these issues by proposing an optimization model that considers blending hydrogen generated through a “power-to-gas” (PtG) technology pathway with natural gas. This paper develops a deterministic mixed-integer nonlinear programming network pressure-flowrate optimization model that captures the interaction between natural gas pipeline systems and the impact of hydrogen injections across multiple pipeline connections in the natural gas grid. A stochastic model is subsequently developed. The optimal quality/concentration of hydrogen in the natural gas pipelines and the optimal location of PtG units are realized while minimizing system-wide capital and operating costs. The design decisions obtained for the deterministic model differ from the stochastic model; the design decisions for the stochastic model varies across the different uncertainty realizations.
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