Appointment Scheduling Under Time-Dependent Patient No-Show Behavior

2020 ◽  
Vol 66 (8) ◽  
pp. 3480-3500 ◽  
Author(s):  
Qingxia Kong ◽  
Shan Li ◽  
Nan Liu ◽  
Chung-Piaw Teo ◽  
Zhenzhen Yan
Keyword(s):  
Optimal Solution ◽  
Time Of Day ◽  
Time Dependent ◽  
Worst Case ◽  
Arrival Times ◽  
Functional Relationships ◽  
Robust Model ◽  
Distributionally Robust ◽  
The Right ◽  
Dependent Patient

This paper studies how to schedule medical appointments with time-dependent patient no-show behavior and random service times. The problem is motivated by our studies of independent datasets from countries in two continents that unanimously identify a significant time-of-day effect on patient show-up probabilities. We deploy a distributionally robust model, which minimizes the worst-case total expected costs of patient waiting and service provider’s idling and overtime, by optimizing the scheduled arrival times of patients. This model is challenging because evaluating the total cost for a given schedule involves a linear program with uncertainties present in both the objective function and the right-hand side of the constraints. In addition, the ambiguity set considered contains discrete uncertainties and complementary functional relationships among these uncertainties (namely, patient no-shows and service durations). We show that when patient no-shows are exogenous (i.e., time-independent), the problem can be reformulated as a copositive program and then be approximated by semidefinite programs. When patient no-shows are endogenous on time (and hence on the schedule), the problem becomes a bilinear copositive program. We construct a set of dual prices to guide the search for a good schedule and use the technique iteratively to obtain a near-optimal solution. Our computational studies reveal a significant reduction in total expected cost by taking into account the time-of-day variation in patient show-up probabilities as opposed to ignoring it. This paper was accepted by David Simchi-Levi, optimization.

scholarly journals Robust Optimization Model with Shared Uncertain Parameters in Multi-Stage Logistics Production and Inventory Process

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 211
Author(s):  
Lijun Xu ◽  
Yijia Zhou ◽  
Bo Yu
Keyword(s):  
Robust Optimization ◽  
Optimization Model ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Uncertain Parameters ◽  
Worst Case ◽  
Robust Model ◽  
Multi Stage ◽  
Proposed Model ◽  
Dual Forms

In this paper, we focus on a class of robust optimization problems whose objectives and constraints share the same uncertain parameters. The existing approaches separately address the worst cases of each objective and each constraint, and then reformulate the model by their respective dual forms in their worst cases. These approaches may result in that the value of uncertain parameters in the optimal solution may not be the same one as in the worst case of each constraint, since it is highly improbable to reach their worst cases simultaneously. In terms of being too conservative for this kind of robust model, we propose a new robust optimization model with shared uncertain parameters involving only the worst case of objectives. The proposed model is evaluated for the multi-stage logistics production and inventory process problem. The numerical experiment shows that the proposed robust optimization model can give a valid and reasonable decision in practice.

scholarly journals Distribution-Free Inventory Risk Pooling in a Multilocation Newsvendor

2020 ◽  
Author(s):  
Aravind Govindarajan ◽  
Amitabh Sinha ◽  
Joline Uichanco
Keyword(s):  
Upper Bound ◽  
Stochastic Approach ◽  
Distribution Networks ◽  
Semidefinite Program ◽  
Worst Case ◽  
Expected Cost ◽  
Demand Distribution ◽  
Cost Structures ◽  
Robust Model ◽  
Distributionally Robust

We study a multilocation newsvendor network when the only information available on the joint distribution of demands are the values of its mean vector and covariance matrix. We adopt a distributionally robust model to find inventory levels that minimize the worst-case expected cost among the distributions consistent with this information. This problem is NP-hard. We find a closed-form tight bound on the expected cost when there are only two locations. This bound is tight under a family of joint demand distributions with six support points. For the general case, we develop a computationally tractable upper bound on the worst-case expected cost if the costs of fulfilling demands have a nested structure. This upper bound is the optimal value of a semidefinite program whose dimensions are polynomial in the number of locations. We propose an algorithm that can approximate general fulfillment cost structures by nested structures, yielding a computationally tractable heuristic for distributionally robust inventory optimization on general newsvendor networks. We conduct experiments on networks resembling U.S. e-commerce distribution networks to show the value of a distributionally robust approach over a stochastic approach that assumes an incorrect demand distribution. This paper was accepted by Chung Piaw Teo, optimization.

Distributionally Robust Hub Location

2020 ◽  
Vol 54 (5) ◽  
pp. 1189-1210 ◽  
Author(s):  
Shuming Wang ◽  
Zhi Chen ◽  
Tianqi Liu
Keyword(s):  
Convex Hull ◽  
Mixed Integer ◽  
Hub Location ◽  
Hub Location Problem ◽  
Mixed Integer Linear Program ◽  
Worst Case ◽  
Data Set ◽  
Second Stage ◽  
Robust Model ◽  
Distributionally Robust

We study the adaptive distributionally robust hub location problem with multiple commodities under demand and cost uncertainty in both uncapacitated and capacitated cases. The hub location decision anticipates the worst-case expected cost over an ambiguity set of possible distributions of the uncertain demand and cost, and the routing policy, being adaptive to the uncertainty realization, ships commodities through selected hubs. We investigate the adaptivity and tractability of the distributionally robust model under different distributional information about uncertainty. In the uncapacitated case in which demand and cost are independent and costs of different commodities are also mutually independent, the adaptive distributionally robust model is equivalent to a nonadaptive classical robust model and the second-stage routing decision follows an optimal static policy. We then relax the independence assumption and show that the second-stage routing decision follows an optimal scenario-wise policy if either the demand or the cost is supported on a convex hull of given scenarios. We extend our analysis to the capacitated case and show that the second-stage routing decision still follows an optimal scenario-wise policy if the demand is supported on the convex hull of given scenarios. In terms of tractability, for all mentioned cases, we reformulate the distributionally robust model as a moderate-sized mixed-integer linear program, and we recover the associated worst-case distribution by solving a collection of linear programs. Through numerical studies using the Civil Aeronautics Board data set, we demonstrate the advantages of the distributionally robust model by examining its superior out-of-sample performance against the classical robust model and the stochastic model.

Payment Tracking System

2019 ◽  
Vol 1 (2) ◽  
pp. 43-50
Author(s):  
Sakthi Sree T ◽  
Rajagopal T.K.P. ◽  
Ananthi Priya S ◽  
Ganesh M ◽  
Venkatesh V ◽  
...  
Keyword(s):  
Social Welfare ◽  
Tracking System ◽  
Single Point ◽  
Optimal Solution ◽  
Constant Factor ◽  
Worst Case ◽  
Web Based ◽  
The Social ◽  
The Right ◽  
Management Capabilities

Payment Tracking System is a web-based application for tracking and managing the payments for various vendors. It provides a single point of contact that consolidates payment requests from the accounts department to the top management to deliver the supplier payments on time, using integrated best practices to manage operations and services. It offers integrated Transaction Management capabilities like Ledger view and Hold/Release Payments. It ensures visibility, insight, isolation and faster resolution of Payment related issues for any type of organization by providing the right information at the right time as required by the user. For both models, we design incentive resource allocation mechanisms to maximize the social welfare. Theoretically analysis shows that the proposed mechanisms are truthful for general monotonic pro?t functions and the worst-case performance on the social welfare are well-bounded within a constant factor of the optimal solution for linear pro?t functions. Simulation results also demonstrate that the performances of the proposed mechanisms are very close to the optimal solution, in terms of maximizing the social welfare.

Complexity Results and Effective Algorithms for Worst-Case Linear Optimization Under Uncertainties

2020 ◽  
Author(s):  
Hezhi Luo ◽  
Xiaodong Ding ◽  
Jiming Peng ◽  
Rujun Jiang ◽  
Duan Li
Keyword(s):  
Large Scale ◽  
Risk Estimation ◽  
Convex Relaxation ◽  
Linear Optimization ◽  
Optimal Solution ◽  
Optimization Method ◽  
Optimization Techniques ◽  
Worst Case ◽  
Uncertainty Set ◽  
The Right

In this paper, we consider the so-called worst-case linear optimization (WCLO) with uncertainties on the right-hand side of the constraints. Such a problem often arises in applications such as in systemic risk estimation in finance and stochastic optimization. We first show that the WCLO problem with the uncertainty set corresponding to the [Formula: see text]p-norm ((WCLOp)) is NP-hard for p ɛ (1,∞). Second, we combine several simple optimization techniques, such as the successive convex optimization method, quadratic convex relaxation, initialization, and branch-and-bound (B&B), to develop an algorithm for (WCLO2) that can find a globally optimal solution to (WCLO2) within a prespecified ε-tolerance. We establish the global convergence of the algorithm and estimate its complexity. We also develop a finite B&B algorithm for (WCLO∞) to identify a global optimal solution to the underlying problem, and establish the finite convergence of the algorithm. Numerical experiments are reported to illustrate the effectiveness of our proposed algorithms in finding globally optimal solutions to medium and large-scale WCLO instances.

Symmetrizable Difference Dchemes

2005 ◽  
Vol 5 (1) ◽  
pp. 3-50 ◽  
Author(s):  
Alexei A. Gulin
Keyword(s):  
Initial Data ◽  
Difference Scheme ◽  
Difference Schemes ◽  
Time Dependent ◽  
Stability Boundaries ◽  
Typical Representative ◽  
Variable Weight ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Right

AbstractA review of the stability theory of symmetrizable time-dependent difference schemes is represented. The notion of the operator-difference scheme is introduced and general ideas about stability in the sense of the initial data and in the sense of the right hand side are formulated. Further, the so-called symmetrizable difference schemes are considered in detail for which we manage to formulate the unimprovable necessary and su±cient conditions of stability in the sense of the initial data. The schemes with variable weight multipliers are a typical representative of symmetrizable difference schemes. For such schemes a numerical algorithm is proposed and realized for constructing stability boundaries.

scholarly journals A Fuzzy Optimization Model for the Berth Allocation Problem and Quay Crane Allocation Problem (BAP + QCAP) with n Quays

2021 ◽  
Vol 9 (2) ◽  
pp. 152
Author(s):  
Edwar Lujan ◽  
Edmundo Vergara ◽  
Jose Rodriguez-Melquiades ◽  
Miguel Jiménez-Carrión ◽  
Carlos Sabino-Escobar ◽  
...  
Keyword(s):  
Optimization Model ◽  
Fuzzy Optimization ◽  
Optimal Solution ◽  
Allocation Problem ◽  
Berth Allocation ◽  
Triangular Fuzzy Numbers ◽  
Berth Allocation Problem ◽  
Arrival Times ◽  
Decision Variables ◽  
Short Time

This work introduces a fuzzy optimization model, which solves in an integrated way the berth allocation problem (BAP) and the quay crane allocation problem (QCAP). The problem is solved for multiple quays, considering vessels’ imprecise arrival times. The model optimizes the use of the quays. The BAP + QCAP, is a NP-hard (Non-deterministic polynomial-time hardness) combinatorial optimization problem, where the decision to assign available quays for each vessel adds more complexity. The imprecise vessel arrival times and the decision variables—berth and departure times—are represented by triangular fuzzy numbers. The model obtains a robust berthing plan that supports early and late arrivals and also assigns cranes to each berth vessel. The model was implemented in the CPLEX solver (IBM ILOG CPLEX Optimization Studio); obtaining in a short time an optimal solution for very small instances. For medium instances, an undefined behavior was found, where a solution (optimal or not) may be found. For large instances, no solutions were found during the assigned processing time (60 min). Although the model was applied for n = 2 quays, it can be adapted to “n” quays. For medium and large instances, the model must be solved with metaheuristics.

scholarly journals Competitive Caching with Machine Learned Advice

2021 ◽  
Vol 68 (4) ◽  
pp. 1-25
Author(s):  
Thodoris Lykouris ◽  
Sergei Vassilvitskii
Keyword(s):  
Online Algorithms ◽  
Empirical Evaluation ◽  
Optimal Solution ◽  
Poor Performance ◽  
Machine Learning Algorithms ◽  
Average Error ◽  
Generalization Error ◽  
Worst Case ◽  
Future Events ◽  
Real World Datasets

Traditional online algorithms encapsulate decision making under uncertainty, and give ways to hedge against all possible future events, while guaranteeing a nearly optimal solution, as compared to an offline optimum. On the other hand, machine learning algorithms are in the business of extrapolating patterns found in the data to predict the future, and usually come with strong guarantees on the expected generalization error. In this work, we develop a framework for augmenting online algorithms with a machine learned predictor to achieve competitive ratios that provably improve upon unconditional worst-case lower bounds when the predictor has low error. Our approach treats the predictor as a complete black box and is not dependent on its inner workings or the exact distribution of its errors. We apply this framework to the traditional caching problem—creating an eviction strategy for a cache of size k . We demonstrate that naively following the oracle’s recommendations may lead to very poor performance, even when the average error is quite low. Instead, we show how to modify the Marker algorithm to take into account the predictions and prove that this combined approach achieves a competitive ratio that both (i) decreases as the predictor’s error decreases and (ii) is always capped by O (log k ), which can be achieved without any assistance from the predictor. We complement our results with an empirical evaluation of our algorithm on real-world datasets and show that it performs well empirically even when using simple off-the-shelf predictions.

scholarly journals Dislodgment of VDD Lead Connected to DR Pacer and Managed by Mode Switch

2012 ◽  
Vol 5 ◽  
pp. CCRep.S9625
Author(s):  
Antoine Kossaify ◽  
Nayla Nicolas
Keyword(s):  
Right Ventricle ◽  
Clinical Settings ◽  
Conservative Approach ◽  
Ventricular Pacing ◽  
Mode Switch ◽  
Dual Chamber ◽  
The Right ◽  
Dependent Patient

An 80-year-old patient having a dual chamber DR pacer connected to a VDD lead presented with chronic lead dislodgment with the atrial ring displaced into the right ventricle. There was no ventricular capture at maximal ventricular output, and given the clinical settings, the condition was managed with a conservative approach, the mode was switched to AAI ensuring a minimal adequate ventricular pacing backup in a non dependent patient.

Collision prediction and avoidance for satellite ultra-close relative motion with zonotope-based reachable sets

2018 ◽  
Vol 233 (11) ◽  
pp. 3920-3937
Author(s):  
Zhanpeng Xu ◽  
Xiaoqian Chen ◽  
Yiyong Huang ◽  
Yuzhu Bai ◽  
Qifeng Chen
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Control Method ◽  
Reachable Sets ◽  
Close Relative ◽  
Worst Case ◽  
Reference Orbit ◽  
Robust Model Predictive Control ◽  
Collision Prediction ◽  
Robust Model

Collision prediction and avoidance are critical for satellite proximity operations, and the key is the treatment of satellites' motion uncertainties and shapes, especially for ultra-close autonomous systems. In this paper, the zonotope-based reachable sets are utilized to propagate the uncertainties. For satellites with slender structures (such as solar panels), their shapes are simplified as cuboids which is a special class of zonotopes, instead of the classical sphere approach. The domains in position subspace influenced by the uncertainties and shapes are determined, and the relative distance is estimated to assess the safety of satellites. Moreover, with the approximation of the domains, the worst-case uncertainties for path constraints are determined, and a robust model predictive control method is proposed to deal with the line of sight and obstacle avoidance constraints. With zonotope representations of satellites, the proposed robust model predictive control is capable of handling the shapes of the satellite and obstacle simultaneously. Numerical simulations demonstrate the effectiveness of the proposed methods with an elliptic reference orbit. 1

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