Kevin C. Furman

Global optimization for scheduling refinery crude oil operations

In this work we present an outer-approximation algorithm to obtain the global optimum of a nonconvex mixed-integer nonlinear programming (MINLP) model that is used to represent the scheduling of crude oil movement at the front-end of a petroleum refinery. The model relies on a continuous time representation making use of transfer events. The proposed algorithm focuses on effectively solving a mixed-integer linear programming (MILP) relaxation of the nonconvex MINLP to obtain a rigorous lower bound (LB) on the global optimum. Cutting planes derived by spatially decomposing the network are added to the MILP relaxation of the original nonconvex MINLP in order to reduce the solution time for the MILP relaxation. The solution of this relaxation is used as a heuristic to obtain a feasible solution to the MINLP which serves as an upper bound (UB). The lower and upper bounds are made to converge to within a specified tolerance in the proposed outer-approximation algorithm. On applying the proposed technique to test examples, significant savings are realized in the computational effort required to obtain provably global optimal solutions.

A maritime inventory routing problem: Practical approach

Despite of the practicality of the motivation of the inventory routing problem (IRP), there are few successful implementation stories of IRP based decision support systems which utilize optimization algorithms. Besides the fact that the IRP is an extremely challenging optimization problem, simplifications and assumptions made in the definition of typical IRP in the literature make it even more difficult to take advantage of the developed technologies for IRP in practice. This paper introduces a flexible modeling framework for IRP, which can accommodate various practical features. A simple algorithmic framework of an optimization based heuristic method is also proposed. A case study on a practical maritime inventory routing problem (MIRP) shows that the proposed modeling and algorithmic framework is flexible and effective enough to be a choice of model and solution method for practical inventory routing problems.

A discretization-based approach for the optimization of the multiperiod blend scheduling problem

Abstract In this paper, we introduce a new generalized multiperiod scheduling version of the pooling problem to represent time varying blending systems. A general nonconvex MINLP formulation of the problem is presented. The primary difficulties in solving this optimization problem are the presence of bilinear terms, as well as binary decision variables required to impose operational constraints. An illustrative example is presented to provide unique insight into the difficulties faced by conventional MINLP approaches to this problem, specifically in finding feasible solutions. Based on recent work, a new radix-based discretization scheme is developed with which the problem can be reformulated approximately as an MILP, which is incorporated in a heuristic procedure and in two rigorous global optimization methods, and requires much less computational time than existing global optimization solvers. Detailed computational results of each approach are presented on a set of examples, including a comparison with other global optimization solvers.

A Branch-Price-and-Cut Algorithm for Single-Product Maritime Inventory Routing

A branch-price-and-cut algorithm is developed for a complex maritime inventory-routing problem with varying storage capacities and production/consumption rates at facilities. The resulting mixed-integer pricing problem is solved exactly and efficiently using a dynamic program that exploits certain “extremal” characteristics of the pricing problem. The formulation is tightened by using the problems boundary conditions in preprocessing and to restrict the set of columns that are produced by the pricing problem. Branching schemes and cuts are introduced that can be implemented efficiently and that preserve the structure of the pricing problem. Some of the cuts are inspired by the capacity cuts known for the vehicle-routing problem, whereas others specifically target fractional solutions brought about by individual vessels “competing” for limited inventory at load ports and limited storage capacity at discharge ports. The branch-price-and-cut approach solves practically sized problems motivated by the operations of an oil company to optimality, and it provides reasonable bounds for larger instances.

Feedstock Routing in the ExxonMobil Downstream Sector

ExxonMobil annually transports significant volumes of vacuum gas oil (VGO) from supply points in Europe to refineries in the United States. Optimizing these transportation costs by using modern mathematical programming technology can provide significant cost savings. We developed a mixed-integer programming formulation for VGO routing and inventory management, and we integrated it into a decision support tool to enable experienced traders and schedulers to further improve the performance of ExxonMobils downstream supply chain.

Maritime crude oil transportation – A split pickup and split delivery problem

The maritime oil tanker routing and scheduling problem is known to the literature since before 1950. In the presented problem, oil tankers transport crude oil from supply points to demand locations around the globe. The objective is to find ship routes, load sizes, as well as port arrival and departure times, in a way that minimizes transportation costs. We introduce a path flow model where paths are ship routes. Continuous variables distribute the cargo between the different routes. Multiple products are transported by a heterogeneous fleet of tankers. Pickup and delivery requirements are not paired to cargos beforehand and arbitrary split of amounts is allowed. Small realistic test instances can be solved with route pre-generation for this model. The results indicate possible simplifications and stimulate further research.

Constraint Programming for LNG Ship Scheduling and Inventory Management

We propose a constraint programming approach for the optimization of inventory routing in the liquefied natural gas industry. We present two constraint programming models that rely on a disjunctive scheduling representation of the problem. We also propose an iterative search heuristic to generate good feasible solutions for these models. Computational results on a set of large-scale test instances demonstrate that our approach can find better solutions than existing approaches based on mixed integer programming, while being 4–10 times faster on average.

Optimization and logistics challenges in the enterprise

Preface.- List of Contributors.- Part I: Process Industry.- 1. Challenges in Enterprisewide Optimization for the Process Industries (Ignacio E. Grossmann, Kevin C. Furman).- 2. Multiproduct Inventory Logistics Modeling in the Process Industries (Danielle Zyngier, Jeffrey D. Kelly).- 3. Modeling and Managing Uncertainty in Process Planning and Scheduling (Marianthi Ierapetritou, Zukui Li).- 4. A Relative Robust Optimization Approach for Full Factorial Scenario Design of Data Uncertainty and Ambiguity (Tiravat Assavapokee, Matthew J. Realff, Jane C. Ammons).- Part II: Supply Chain and Logistics Design.- 5. An Enterprise Risk Management Model for Supply Chains (John M. Mulvey, Hafize G. Erkan).- 6. Notes of using Optimization and DSS Techniques to Support Supply Chain and Logistics Operations (Tan Miller).- 7. On the Quadratic Programming Approach for Hub Location Problems (Xiaoz He, Anthony Chen, Wanpracha Art Chaovalitwongse, Henry Liu).- 8. Nested Partitions and its Applications to the Intermodal Hub Location Problem (Weiwei Chen, Liang Pi, Leyuan Shi).- Part III: Supply Chain Operation.- 9. Event-Time Models for Supply Chain Scheduling (Omer S. Benli).- 10. A Dynamic and Data-Driven Approach to the News Vendor Problem Under Cyclical Demand(Gokhan Metan, Aurelie Thiele).- 11. Logic-based Multiobjective Optimization for Restoration Planning (Jing Gong, Earl E. Lee, John E Mitchell, William A. Wallace).- Part IV: Network and Transportation 12. The Aircraft Maintenance Routing Problem (Zhe Liang, Wanpracha Art Chaovalitwongse).- 13. The Stochastic Vehicle Routing Problem for Minimum Unmet Demand (Zhihong Shen, Fernando Ordonez, Maged M. Dessouky).- 14. Collaboration in Cargo Transportation (Richa Agarwal, Ozlem Ergun, Lori Houghtalen, Okan Orsan Ozener).- 15. Communication Models for a Cooperative Network of Autonomous Agents (Ashwin Arulselvan, Clayton W. Commander, Michael J. Hirsch, Panos M. Pardalos).

Challenges in Enterprise Wide Optimization for the Process Industries

Enterprisewide optimization (EWO) is a new emerging area that lies at the interface of chemical engineering and operations research, and has become a major goal in the process industries due to the increasing pressures for remaining competitive in the global marketplace. EWO involves optimizing the operations of supply, manufacturing, and distribution activities of a company to reduce costs and inventories. A major focus in EWO is the optimal operation of manufacturing facilities, which often requires the use of nonlinear process models. Major operational items include planning, scheduling, real-time optimization, and inventory control. This chapter provides an overview of major challenges in the development of deterministic and stochastic linear/nonlinear optimization models and algorithms for the optimization of entire supply chains that are involved in EWO problems. We specifically review three major challenges: (a) modeling of planning and scheduling, (b) multiscale optimization, and (c) handling of uncertainties. Finally, we also discuss briefly the algorithmic methods and tools that are required for tackling these problems, and we conclude with future research needs in this area.

Using diversification, communication and parallelism to solve mixed-integer linear programs

Performance variability of modern mixed-integer programming solvers and possible ways of exploiting this phenomenon present an interesting opportunity in the development of algorithms to solve mixed-integer linear programs (MILPs). We propose a framework using multiple branch-and-bound trees to solve MILPs while allowing them to share information in a parallel execution. We present computational results on instances from MIPLIB 2010 illustrating the benefits of this framework.