Data-driven distributionally robust optimization of shale gas supply chains under uncertainty

This article aims to leverage the big data in shale gas industry for better decision making in optimal design and operations of shale gas supply chains under uncertainty. We propose a two-stage distributionally robust optimization model, where uncertainties associated with both the upstream shale well estimated ultimate recovery and downstream market demand are simultaneously considered. In this model, decisions are classified into first-stage design decisions, which are related to drilling schedule, pipeline installment, and processing plant construction, as well as second-stage operational decisions associated with shale gas production, processing, transportation, and distribution. A data-driven approach is applied to construct the ambiguity set based on principal component analysis and first-order deviation functions. By taking advantage of affine decision rules, a tractable mixed-integer linear programming formulation can be obtained. The applicability of the proposed modeling framework is demonstrated through a small-scale illustrative example and a case study of Marcellus shale gas supply chain. Comparisons with alternative optimization models, including the deterministic and stochastic programming counterparts, are investigated as well. © 2018 American Institute of Chemical Engineers AIChE J, 65: 947–963, 2019     

Reloading Nuclear Reactor Fuel Using Mixed-Integer Nonlinear Optimization

A nodal nuclear reactor reload pattern optimization model is solved using mixed-integer nonlinear optimization techniques. Unlike currently used heuristic search methods, this method enables continuous optimization of the amount of Burnable Poisons in fresh fuel bundles in a natural way, which is shown in the first part of the article. The second part treats an algorithmic extension using dedicated cuts in a mixed-integer nonlinear optimization algorithm, which push the optimization towards solutions where local power peaks in parts of the core are avoided.     

Superstructure Optimization for Oil Refinery Design

Abstract

In this work, the optimal petroleum refinery topology is formulated as a conceptual process synthesis problem using the superstructure optimization approach. We begin with the development of a state–task network (STN)-based superstructure representation that is sufficiently rich to encompass all possible topology alternatives of a conventional oil refinery. Subsequently, a biobjective mixed-integer linear program (MILP) of maximization of profit and minimization of environmental impacts is formulated according to the constructed superstructure. Then, based on a given set of fixed amounts of desired products with available crude oil, the model is solved to generate an optimal topology. The proposed optimization framework also incorporates principles from life cycle analysis (LCA) to account for potential environmental impacts. A numerical example is illustrated to implement the modeling approach.     

A possibilistic programming approach for the location problem of multiple cross-docks and vehicle routing scheduling under uncertainty

This article considers the design of cross-docking systems under uncertainty in a model that consists of two phases: (1) a strategic-based decision-making process for selecting the location of cross-docks to operate, and (2) an operational-based decision-making process for vehicle routing scheduling with multiple cross-docks. This logistic system contains three echelons, namely suppliers, cross-docks and retailers, in an uncertain environment. In the first phase, a new multi-period cross-dock location model is introduced to determine the minimum number of cross-docks among a set of location sites so that each retailer demand should be met. Then, in the second phase, a new vehicle routing scheduling model with multiple cross-docks is formulated in which each vehicle is able to pickup from or deliver to more than one supplier or retailer, and the pickup and delivery routes start and end at the corresponding cross-dock. This article is the first attempt to introduce an integrated model for cross-docking systems design under a fuzzy environment. To solve the presented two-phase mixed-integer programming (MIP) model, a new fuzzy mathematical programming-based possibilistic approach is used. Furthermore, experimental tests are carried out to demonstrate the effectiveness of the presented model. The computational results reveal the applicability and suitability of the developed fuzzy possibilistic two-phase model in a variety of problems in the domain of cross-docking systems.     

Optimal design of an oil pipeline with a large-slope section

One of the important issues in the operation of a long-distance oil pipeline in a large-slope area is pressure control, especially for the section after the turning point. In this study, a method to optimally design an oil pipeline with a large-slope section is proposed. The method is based on a stochastic mixed-integer linear programming model with minimal total cost as the objective function to determine the size of the pipeline, the location, the operational plan of pump stations and the location of pressure reduction stations. Hydraulic calculations and different types of oil product are considered. The uncertainty in flow rates of the pipeline is studied by the proposed stochastic programming approach. This method is applied to a real case of designing an oil product pipeline in a large-slope area.     

Tackling perishability in multi-level process industries

The classical multi-level lot-sizing and scheduling problem formulations for process industries rarely address perishability issues, such as limited shelf lives of intermediate products. In some industries, ignoring this specificity may result in severe losses. In this paper, we start by extending a classical multi-level lot-sizing and scheduling problem formulation (MLGLSP) to incorporate perishability issues. We further demonstrate that with the objective of minimising the total costs (purchasing, inventory and setup), the production plans generated by classical models are often infeasible under a setting with perishable products. The model distinguishes different perishability characteristics of raw materials, intermediates and end products according to various industries. Finally, we provide quantitative insights on the importance of considering perishability for different production settings when solving integrated production planning and scheduling problems.     

On the robust decision-making in a supply chain under disruption risks

This paper considers a robust decision-making problem associated with supplies of parts and deliveries of finished products in a customer driven supply chain under disruption risks. The robustness refers to an equitably efficient performance of a supply chain in average-case as well as in the worst-case, which reflects the decision-makers common requirement to maintain an equally good performance of a supply chain under different conditions. Given a set of customer orders for products, the decision-maker needs to select suppliers of parts required to complete the orders, allocate the demand for parts among the selected suppliers and schedule the orders over the planning horizon, to equitably optimise average and worst-case performance of the supply chain. The supplies are subject to independent random local and regional disruptions. The obtained combinatorial stochastic optimisation problem is formulated as a mixed-integer program with conditional value-at-risk as a risk measure. The ordered weighted averaging aggregation of the expected value and the conditional value-at-risk of the selected optimality criterion is applied to obtain a robust solution. The risk-neutral, risk-averse and robust solutions that optimise, respectively average, worst-case and equitable average and worst-case performance of a supply chain are determined and compared for cost and customer service level objective functions. Numerical examples and computational results, in particular comparison with the mean-risk approach, are presented and some managerial insights are reported.     

Reactive scheduling in a make-to-order flexible job shop with re-entrant process and assembly: a mathematical programming approach

A mixed-integer linear programming model is presented for the scheduling of flexible job shops, a production mode characteristic of make-to-order industries. Re-entrant process (multiple visits to the same machine group) and a final assembly stage are simultaneously considered in the model. The formulation uses a continuous time representation and optimises an objective function that is a weighted sum of order earliness, order tardiness and in-process inventory. An algorithm for predictive-reactive scheduling is derived from the proposed model to deal with the arrival of new orders. This is illustrated with a realistic example based on data from the mould making industry. Different reactive scheduling scenarios, ranging from unchanged schedule to full re-scheduling, are optimally generated for order insertion in a predictive schedule. Since choosing the most suitable scenario requires balancing criteria of scheduling efficiency and stability, measures of schedule changes were computed for each re-scheduling solution. The short computational times obtained are promising regarding future application of this approach in the manufacturing environment studied.     

Supply chain optimisation with assembly line balancing

Supply chain management operates at three levels, strategic, tactical and operational. While the strategic approach generally pertains to the optimisation of network resources such as designing networks, location and determination of the number of facilities, etc., tactical decisions deal with the mid-term, including production levels at all plants, assembly policy, inventory levels and lot sizes, and operational decisions are related to how to make the tactical decisions happen in the short term, such as production planning and scheduling. This paper mainly discusses and explores how to realise the optimisation of strategic and tactical decisions together in the supply chain. Thus, a supply chain network (SCN) design problem is considered as a strategic decision and the assembly line balancing problem is handled as a tactical decision. The aim of this study is to optimise and design the SCN, including manufacturers, assemblers and customers, that minimises the transportation costs for determined periods while balancing the assembly lines in assemblers, which minimises the total fixed costs of stations, simultaneously. A nonlinear mixed-integer model is developed to minimise the total costs and the number of assembly stations while minimising the total fixed costs. For illustrative purposes, a numerical example is given, the results and the scenarios that are obtained under various conditions are discussed, and a sensitivity analysis is performed based on performance measures of the system, such as total cost, number of stations, cycle times and distribution amounts.     

Optimal Design of Electronic Components by Mixed-Integer Nonlinear Programming

Computer-aided design optimization of electronic components is a powerful tool to reduce development costs on one hand and to improve the performance of the components on the other. In this paper, a mathematical model of an electronic filter is outlined. It depends on certain parameters, some of them of being continuous, others of integer type. The purpose of the paper is to introduce an extension of the well-known sequential quadratic programming (SQP) method to solve the mixed-integer programming problem (MINLP). It is assumed that the integer variables cannot be relaxed to real ones, that the integer range is sufficiently large, and that they possess some physical meaning so that they basically behave like continuous ones. The general idea is to combine an SQP step with a direct search cycle in the integer space. Hessian information is updated based on difference formulae at neighbored grid points. Numerical results are included to show the feasibility of the mixed-integer nonlinear programming code for academic test examples and in addition for the optimal design of an electronic filter.