CIM PROGRAMS AND ACTIVITIES

Kai Huang (McMaster University) (slides)
Benchmarking Non-First-Come-First-Served Component Allocation in an Assemble-To-Order System

In a multi-product, multi-component Assemble-To-Order (ATO) system, component allocation policy has significant influence on the service and cost performance measures. In this paper, we study a series of simple non-First-Come-First-Served (non-FCFS) component allocation rules in a periodic review ATO system with component base stock policy, i.e. the Last-Come-First-Served (LCFS) rule, the Product-Based-Priority-Within-Time-Windows (PTW) rule, and the Myopic Optimization (MO) rule. For the LCFS rule and the PTW rule, we express the demand fulfillment rates analytically. Based on these representations, we can optimize the base stock levels. Moreover, to test the non-FCFS allocation rules, we propose to use three mathematical programs as benchmarks. These mathematical programs maximize the average cycle service level, maximize the aggregate fill rate, and minimize the operational cost per period separately under the FCFS rule. Our computational study shows that the proposed simple non-FCFS rules can significantly increase the service measures or decrease the cost measure, and outperform the benchmarks. Moreover, the values of the LCFS rule and the PTW rule increase when there is a greater need for customer service differentiation.

Giles Laurier (Capstone Technology) (slides)
Industrial Plant Optimization in Reduced Dimensional Spaces

The implementation history of real time optimization (RTO) in the refining industry is a sobering case study of a failed product launch. Starting from a heady beginning in the early 1990's, rapid adoption, and published successes, many of these projects have been abandoned. It is a cautionary tale to the optimization community that the ability to successfully go "live" in an operating plant may depend more on industrial psychology than algorithms. This seminar discusses the math and methods of the early RTO efforts, and proposes an alternative approach based on latent space methods which may prove to be more commercially viable.

Vlad Mahalec (McMaster)
Inventory Pinch Algorithms for Gasoline Blending (slides)

Optimal gasoline blending requires optimization of blend recipes and scheduling of blends in a manner that minimizes switching between grades and minimizes total cost of the blends. Rigorous computation of blend properties requires solution of complex non-linear models (e.g. EPA reformulated gasoline). MINLP models with such nonlinear constraints often involve large computational times. This work introduces a decomposition of the blend planning models into optimization of blend recipes and allocation of volumes to be produced based on these optimal blend recipes. It is shown that a specific blend recipe is optimal for a region delineated by inventory pinch points, or sometimes by its sub region which can be found iteratively. The top level of the algorithm minimizes the number of periods which have different blend recipes by solving a multiperiod NLP (periods delimited by the pinch points). The lower level computes the blend plan via fixed-recipe MILP. The algorithm leads to a much smaller number of blend recipes than the current paradigm. We also introduce a variation of the algorithm, where only single period NLP model is solved in order to optimize the blend recipes.

Dimitrios Varvarezos (Aspen Technology, Inc.) (slides)
Refinery Optimization - Recent Advances in Planning and Blending Operations

In this seminar we discuss recent advances made in the area of refinery optimization. Two very prominent and challenging large-scale mixed integer optimization problems are discussed: the optimization of crude purchasing decisions and the optimal blending of refinery streams without intermediate storage. For the crude acquisition problem, we present a robust optimization framework based on a combination of Pareto-type analysis, parametric optimization, and goal programming. This approach allows users to evaluate a range of options close to the optimal solution that preserve the economic optimization but also take account important strategic and operational goals. Together with novel global optimization techniques for non-convex models, this methodology offers actionable information to refinery planners and traders. This presentation describes the techniques employed and demonstrates their potential value to refinery planning and trading organizations. For the rundown blending problem, we present a novel modeling and optimization approach that determines the optimal sequence and timing of blend events, as well as rundown component tank switches in order to handle the blending of "hot" streams into a finished product tank. This solution incorporates multiple blend headers and multiple blends in a multi-period, event-driven campaign, using open-equation based optimization and modeling technology. The proposed approach is both comprehensive and practical and much superior to the current practice.

Ricardo Fukasawa (Waterloo) (slides) (video archive of the talk)
MIP reformulations of some chance-constrained mathematical programs

In mathematical programs, an often used assumption is that the problem data is deterministic, or in other words it is known in advance. This simplifying assumption may be reasonable in many situations, but it may be too strong in others. In this talk we will focus on a specific type of model that addresses uncertain data, namely chance-constrained mathematical programs with discrete random right-hand sides.
Chance-constrained mathematical programs are optimization problems where some of the data is assumed to be random and we are interested in an optimal solution satisfying constraints with a pre-specified high probability. Luedtke, Ahmed and Nemhauser (2010) proposed a mixed-integer programming (MIP) model for dealing with the case where the randomness is solely on the right-hand side of the inequalities and the distribution is discrete. They were able to obtain some strong inequalities for the model by studying the polyhedral structure of a mixing-type set subject to an additional constraint. Later, Kucukyavuz (2012) extended and improved on their results. However, the results on both of these papers are mostly for the case where the distribution is uniform.
In this talk, we will give some background on the problem and present some of our results in extending and generalizing the results of these papers to the case of general probabilities.
Based on joint work with Ahmad Abdi.

In this presentation, we will describe the approach and experience gained in the development of a suite of fully integrated optimization models for water and power optimization that has been implemented over many different hydro systems in North America and various parts of the world. In particular, the handling of large size problems through various decomposition schemes and integration of multiple time scales over the entire planning process will be discussed. The representation of hydrologic, market and load uncertainty and the challenges of solving for discrete decisions as related to reserve allocation and the unit commitment problem within the short term scheduling problem will be reviewed.

Robert McCann (University of Toronto) (video archive of the talk)
Pricing multidimensional products and contracts facing informational asymmetry

The monopolist's problem of deciding what types of products to manufacture and how much to charge for each of them, knowing only statistical information about the preferences of an anonymous field of potential buyers, is one of the basic problems analyzed in economic theory. The solution to this problem when the space of products and of buyers can each be parameterized by a single variable (say quality X, and income Y) garnered Mirrlees (1971) and Spence (1974) their Nobel prizes in 1996 and 2001. The multidimensional version of this question is a largely open problem, which arises when pricing products or contracts parameterized by several variables. It is of both theoretical and computational interest to know when this optimization problem is convex, and when it is not.
I describe joint work with A Figalli and Y-H Kim (JET 2011), identifying structural conditions on the value b(X,Y) of product X to buyer Y which are sufficient (and nearly necessary) to reduce this problem to a convex program in a Banach space. This leads to uniqueness and stability results for its solution, confirms the robustness of certain economic phenomena observed by Armstrong (1996) such as the desirability for the monopolist to raise prices enough to drive a positive fraction of buyers out of the market, and yields conjectures concerning the robustness of other phenomena observed Rochet and Chone (1998), such as the clumping together of products marketed into subsets of various dimension. The passage to several dimensions relies on ideas from differential geometry / general relativity, optimal transportation, and nonlinear partial differential equations.

To find a suitable interest rate curve construction method is one of the basic but crucial components for building a sophisticated interest rate pricing and risk management framework in today’s banking industry. In this post-crisis era, building interest rate curves is no longer a trivial task: financial engineers are working on new curves that are smooth, stable and fast to compute in order to meet the increasingly complicated and time-critical requirements from the business and financial regulators. One of the most challenging problems is to build a smooth curve from a set of crowded forward interest rate instruments. We have mapped this problem to an interval-based interpolation, and assigned a penalty measure to the problem. Under a trivial condition, we have proved that this problem has a unique solution which is given by a piecewise quadratic and continuously differentiable function.