The Master Surgery Scheduling problem consists of finding a suitable allocation of operating resources to surgical groups. A myriad of variants of the problem has been addressed in literature. Here we focus on two maj...
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The Master Surgery Scheduling problem consists of finding a suitable allocation of operating resources to surgical groups. A myriad of variants of the problem has been addressed in literature. Here we focus on two major variants, arising during a cooperation with Sykehuset Asker og B'rum HF, a large hospital in the city of Oslo. The first variant asks for balancing patient queue lengths among different specialties, whereas the second for minimizing resort to overtime. To cope with these problems we introduce a new mixedinteger linear formulation and show its beneficial properties. Both problems require the estimation of demand levels. As such estimation is affected by uncertainty, we also develop a light robustness approach to the second variant. Finally we present computational results on a number of real-world instances provided by our reference hospital.
The Flow-Refueling Location Model (FRLM) locates a given number of refueling stations on a network to maximize the traffic flow among origin-destination pairs that can be refueled given the driving range of alternativ...
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The Flow-Refueling Location Model (FRLM) locates a given number of refueling stations on a network to maximize the traffic flow among origin-destination pairs that can be refueled given the driving range of alternative-fuel vehicles. Traditionally, the FRLM has been formulated using a two-stage approach: the first stage generates combinations of locations capable of serving the round trip on each route, and then a mixed-integer programming approach is used to locate p facilities to maximize the flow refueled given the feasible combinations created in the first stage. Unfortunately, generating these combinations can be computationally burdensome and heuristics may be necessary to solve large-scale networks. This article presents a radically different mixed-binary-integerprogramming formulation that does not require pre-generation of feasible station combinations. Using several networks of different sizes, it is shown that the proposed model solves the FRLM to optimality as fast as or faster than currently utilized greedy and genetic heuristic algorithms. The ability to solve real-world problems in reasonable time using commercial math programming software offers flexibility for infrastructure providers to customize the FRLM to their particular fuel type and business model, which is demonstrated in the formulation of several FRLM extensions.
We develop a finite-horizon discrete-time constrained Markov decision process (MDP) to model diagnostic decisions after mammography where we maximize the total expected quality-adjusted life years (QALYs) of a patient...
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We develop a finite-horizon discrete-time constrained Markov decision process (MDP) to model diagnostic decisions after mammography where we maximize the total expected quality-adjusted life years (QALYs) of a patient under resource constraints. We use clinical data to estimate the parameters of the MDP model and solve it as a mixed-integer program. By repeating optimization for a sequence of budget levels, we calculate incremental cost-effectiveness ratios attributable to consecutive levels of funding and compare actual clinical practice with optimal decisions. We prove that the optimal value function is concave in the allocated budget. Comparing to actual clinical practice, using optimal thresholds for decision making may result in approximately 22% cost savings without sacrificing QALYs. Our analysis indicates short-term follow-ups are the immediate target for elimination when budget becomes a concern. Policy change is more drastic in the older age group with the increasing budget, yet the gains in total expected QALYs related to larger budgets are predominantly seen in younger women along with modest gains for older women.
Combined heat and power (CHP) plants are characterized by high fuel efficiency and are therefore usually the thermal power producing units of choice within a district heating network. The operation of CHP units is typ...
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Combined heat and power (CHP) plants are characterized by high fuel efficiency and are therefore usually the thermal power producing units of choice within a district heating network. The operation of CHP units is typically controlled by the current heat demand and thus delimits the range of electricity production. Heat storage devices are a promising alternative to uncouple the heat load of the district heating network from the commitment of the units and to allow for price-oriented electricity production. In this paper we present numerical results for the combined optimization of the operation of nineteen existing power plant units and the design of six proposed heat accumulators which supply the district heating network of Berlin. A mixed-integer programming problem (MIP) is formulated in GAMS and solved with CPLEX. This paper focuses on the potential for increasing profitability through the addition of heat accumulators in the energy system described above, on the optimal storage capacities for different price scenarios (variation of fuel costs, prices for carbon dioxide emission certificates, and electricity price time series) as well as on the adjustment of the operation of the power plants due to heat storage. (C) 2011 Elsevier Ltd. All rights reserved.
Enterprise-wide Optimization (EWO) 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 supply, manufacturi...
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Enterprise-wide Optimization (EWO) 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 supply, manufacturing and distribution activities of a company to reduce costs, inventories and environmental impact, and to maximize profits and responsiveness. Major operational items include planning, scheduling, real-time optimization and control. We provide an overview of EWO in terms of a mathematical programming framework. We first provide a brief overview of mathematical programming techniques (mixed-integer linear and nonlinear optimization methods), as well as decomposition methods, stochastic programming and modeling systems. We then address some of the major issues involved in the modeling and solution of these problems. Finally, based on the EWO program at the Center of Advanced Process Decision-making at Carnegie Mellon, we describe several applications to show the potential of this area. (C) 2012 Elsevier Ltd. All rights reserved.
The NP-hard problem of scheduling jobs on unrelated parallel machines, in the presence of machine-dependent and sequence-dependent setup times, with the objective of minimizing the makespan, is considered. A variable ...
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The NP-hard problem of scheduling jobs on unrelated parallel machines, in the presence of machine-dependent and sequence-dependent setup times, with the objective of minimizing the makespan, is considered. A variable neighborhood descent search algorithm, hybridized with mathematical programming elements, is presented and its performance is evaluated on a large set of benchmark problem instances. The extensive computational experiments show that the proposed algorithm outperforms previously proposed methods in terms of solution quality as well as computation time.
The mixing set with a knapsack constraint arises in deterministic equivalent of chance-constrained programming problems with finite discrete distributions. We first consider the case that the chance-constrained progra...
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The mixing set with a knapsack constraint arises in deterministic equivalent of chance-constrained programming problems with finite discrete distributions. We first consider the case that the chance-constrained program has equal probabilities for each scenario. We study the resulting mixing set with a cardinality constraint and propose facet-defining inequalities that subsume known explicit inequalities for this set. We extend these inequalities to obtain valid inequalities for the mixing set with a knapsack constraint. In addition, we propose a compact extended reformulation (with polynomial number of variables and constraints) that characterizes a linear programming equivalent of a single chance constraint with equal scenario probabilities. We introduce a blending procedure to find valid inequalities for intersection of multiple mixing sets. We propose a polynomial-size extended formulation for the intersection of multiple mixing sets with a knapsack constraint that is stronger than the original mixing formulation. We also give a compact extended linear program for the intersection of multiple mixing sets and a cardinality constraint for a special case. We illustrate the effectiveness of the proposed inequalities in our computational experiments with probabilistic lot-sizing problems.
Big events lead to temporary very high traffic volumes which usually exceed traffic capabilities of the existing infrastructure. Hence, it is necessary to control traffic in a way that helps to keep traffic congestion...
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Big events lead to temporary very high traffic volumes which usually exceed traffic capabilities of the existing infrastructure. Hence, it is necessary to control traffic in a way that helps to keep traffic congestion as low as possible. In this paper we introduce a traffic planning model for big events which optimizes traffic routing, allocates parking space, and defines locations for spot checks on traffic. We extend and modify a traffic flow model that has successfully been used in previous work on evacuation planning. A computational study demonstrates the model's applicability to a real world situation.
Even though biomass is attracting increasing interest as a raw material in the chemical and the fuel industries, only few biobased production processes are yet established. At the same time a lot of new catalytic rout...
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Even though biomass is attracting increasing interest as a raw material in the chemical and the fuel industries, only few biobased production processes are yet established. At the same time a lot of new catalytic routes are proposed, but their potential in biorefinery applications is hard to predict. Reaction network flux analysis (RNFA) is introduced as a novel, rapid screening method which bridges the gap between chemo- or biocatalysis and process design by (1) systematically identifying and (2) subsequently analyzing and ranking the large number of alternative reaction pathways based on limited data. This optimization-based method helps to detect promising production routes as well as bottlenecks in possible pathways. The potential and the application of the RNFA methodology will be demonstrated by means of a case study for the production of the potential biofuel 3-methyl-tetrahydrofuran (3-MTHF) from the platform chemical itaconic acid (IA). (C) 2011 American Institute of Chemical Engineers AIChE J, 58: 17881801, 2012
We extend recent work on nonlinear optimal control problems with integer restrictions on some of the control functions (mixed-integer optimal control problems, MIOCP). We improve a theorem (Sager et al. in Math Progra...
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We extend recent work on nonlinear optimal control problems with integer restrictions on some of the control functions (mixed-integer optimal control problems, MIOCP). We improve a theorem (Sager et al. in Math Program 118(1): 109-149, 2009) that states that the solution of a relaxed and convexified problem can be approximated with arbitrary precision by a solution fulfilling the integer requirements. Unlike in previous publications the new proof avoids the usage of the Krein-Milman theorem, which is undesirable as it only states the existence of a solution that may switch infinitely often. We present a constructive way to obtain an integer solution with a guaranteed bound on the performance loss in polynomial time. We prove that this bound depends linearly on the control discretization grid. A numerical benchmark example illustrates the procedure. As a byproduct, we obtain an estimate of the Hausdorff distance between reachable sets. We improve the approximation order to linear grid size instead of the previously known result with order (Hackl in Reachable sets, control sets and their computation, augsburger mathematisch-naturwissenschaftliche schriften. Dr. Bernd Winer, Augsburg, 1996). We are able to include a Special Ordered Set condition which will allow for a transfer of the results to a more general, multi-dimensional and nonlinear case compared to the Theorems in Pietrus and Veliov in (Syst Control Lett 58:395-399, 2009).
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