Accounting for the tongue-and-groove effect using a robust direct aperture optimization approach

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98733/1/MPH001266.pd

Capacity expansion and cost efficiency improvement in the warehouse problem

The warehouse problem with deterministic production cost, selling prices, and demand was introduced in the 1950s and there is a renewed interest recently due to its applications in energy storage and arbitrage. In this paper, we consider two extensions of the warehouse problem and develop efficient computational algorithms for finding their optimal solutions. First, we consider a model where the firm can invest in capacity expansion projects for the warehouse while simultaneously making production and sales decisions in each period. We show that this problem can be solved with a computational complexity that is linear in the product of the length of the planning horizon and the number of capacity expansion projects. We then consider a problem in which the firm can invest to improve production cost efficiency while simultaneously making production and sales decisions in each period. The resulting optimization problem is nonâ convex with integer decision variables. We show that, under some mild conditions on the cost data, the problem can be solved in linear computational time. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 367â 373, 2016Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/134190/1/nav21703_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/134190/2/nav21703.pd

Decision Support for Optimal Adaptation of Product and Supply Chain Systems based on Real Options Theory

In order to remain profitable in the highly competitive global market, a manufacturing enterprise is expected to proactively adapt itself in anticipation of unplanned, but foreseeable high impact events. This paper presents a decision model for optimal adaptation of product and supply chain systems subject to sudden, severe changes in the operating environment. Extending our previous work, decision-tree based framework is developed for optimally choosing design-supplier alternatives in multi-product, multi-echelon product and supply chain systems based on the real options theory. A case study on a two-component, two-echelon supply chain is presented which highlights unique characteristics of product quality as compared to cost and time.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87256/4/Saitou57.pd

Simplex Algorithm for Countable-state Discounted Markov Decision Processes

Submitted to Operations Research; preliminary version.We consider discounted Markov Decision Processes (MDPs) with countably-infinite state spaces, finite action spaces, and unbounded rewards. Typical examples of such MDPs are inventory management and queueing control problems in which there is no specific limit on the size of inventory or queue. Existing solution methods obtain a sequence of policies that converges to optimality in value but may not improve monotonically, i.e., a policy in the sequence may be worse than preceding policies. Our proposed approach considers countably-infinite linear programming (CILP) formulations of the MDPs (a CILP is defined as a linear program (LP) with countably-infinite numbers of variables and constraints). Under standard assumptions for analyzing MDPs with countably-infinite state spaces and unbounded rewards, we extend the major theoretical extreme point and duality results to the resulting CILPs. Under an additional technical assumption which is satisfied by several applications of interest, we present a simplex-type algorithm that is implementable in the sense that each of its iterations requires only a finite amount of data and computation. We show that the algorithm finds a sequence of policies which improves monotonically and converges to optimality in value. Unlike existing simplex-type algorithms for CILPs, our proposed algorithm solves a class of CILPs in which each constraint may contain an infinite number of variables and each variable may appear in an infinite number of constraints. A numerical illustration for inventory management problems is also presented.National Science Foundation grant CMMI-1333260A research grant from the University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/109413/1/CountableStateMDP-MAE.pdfDescription of CountableStateMDP-MAE.pdf : Main article (preliminary version

A new column-generation-based algorithm for VMAT treatment plan optimization

We study the treatment plan optimization problem for volumetric modulated arc therapy (VMAT). We propose a new column-generation-based algorithm that takes into account bounds on the gantry speed and dose rate, as well as an upper bound on the rate of change of the gantry speed, in addition to MLC constraints. The algorithm iteratively adds one aperture at each control point along the treatment arc. In each iteration, a restricted problem optimizing intensities at previously selected apertures is solved, and its solution is used to formulate a pricing problem, which selects an aperture at another control point that is compatible with previously selected apertures and leads to the largest rate of improvement in the objective function value of the restricted problem. Once a complete set of apertures is obtained, their intensities are optimized and the gantry speeds and dose rates are adjusted to minimize treatment time while satisfying all machine restrictions. Comparisons of treatment plans obtained by our algorithm to idealized IMRT plans of 177 beams on five clinical prostate cancer cases demonstrate high quality with respect to clinical dose–volume criteria. For all cases, our algorithm yields treatment plans that can be delivered in around 2 min. Implementation on a graphic processing unit enables us to finish the optimization of a VMAT plan in 25–55 s.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98593/1/0031-9155_57_14_4569.pd

Duality in infinite dimensional linear programming

We consider the class of linear programs with infinitely many variables and constraints having the property that every constraint contains at most finitely many variables while every variable appears in at most finitely many constraints. Examples include production planning and equipment replacement over an infinite horizon. We form the natural dual linear programming problem and prove strong duality under a transversality condition that dual prices are asymptotically zero. That is, we show, under this transversality condition, that optimal solutions are attained in both primal and dual problems and their optimal values are equal. The transversality condition, and hence strong duality, is established for an infinite horizon production planning problem.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47922/1/10107_2005_Article_BF01585695.pd

A DVH‐guided IMRT optimization algorithm for automatic treatment planning and adaptive radiotherapy replanning

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135098/1/mp5700.pd

Ultrafast treatment plan optimization for volumetric modulated arc therapy (VMAT)

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/134981/1/mp1675.pd

Improving Hit-and-Run for global optimization

Improving Hit-and-Run is a random search algorithm for global optimization that at each iteration generates a candidate point for improvement that is uniformly distributed along a randomly chosen direction within the feasible region. The candidate point is accepted as the next iterate if it offers an improvement over the current iterate. We show that for positive definite quadratic programs, the expected number of function evaluations needed to arbitrarily well approximate the optimal solution is at most O(n 5/2 ) where n is the dimension of the problem. Improving Hit-and-Run when applied to global optimization problems can therefore be expected to converge polynomially fast as it approaches the global optimum.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44932/1/10898_2005_Article_BF01096737.pd

FusionArc optimization: A hybrid volumetric modulated arc therapy (VMAT) and intensity modulated radiation therapy (IMRT) planning strategy

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/134837/1/mp8153.pd