Mehmet A. Begen

Appointment Scheduling with Discrete Random Durations

We consider the problem of determining optimal appointment schedule for a given sequence of jobs (e.g., medical procedures) on a single processor (e.g., operating room, examination facility), to minimize the expected total underage and overage costs when each job has a random processing duration given by a joint discrete probability distribution. Simple conditions on the cost rates imply that the objective function is submodular and L-convex. Then there exists an optimal appointment schedule which is integer and can be found in polynomial time. Our model can handle a given due date for the total processing (e.g., end of day for an operating room) after which overtime is incurred and, no-shows and emergencies.

Technical Note---A Sampling-Based Approach to Appointment Scheduling

We consider the problem of appointment scheduling with discrete random durations but under the more realistic assumption that the duration probability distributions are not known and only a set of independent samples is available, e.g., historical data. For a given sequence of appointments (jobs, tasks), the goal is to determine the planned starting time of each appointment such that the expected total underage and overage costs due to the mismatch between allocated and realized durations is minimized. We use the convexity and subdifferential of the objective function of the appointment scheduling problem to determine bounds on the number of independent samples required to obtain a provably near-optimal solution with high probability.

Rate-distortion optimized on-demand media streaming with server diversity

This paper studies the streaming of packetized media from multiple servers to a client over a lossy network. In particular, we propose a client-driven rate-distortion optimal packet scheduling algorithm that decides which packet(s) to be requested from which server(s) at a given request opportunity. In doing so, the proposed scheduling algorithm not only attains the maximal presentation quality but also conforms to the rate constraints dictated by the flow, window and congestion control mechanisms. The simulation results clearly demonstrate the efficacy of the proposed algorithm over the single-server rate-distortion optimized streaming.

A branch and bound based heuristic for makespan minimization of washing operations in hospital sterilization services

In this paper, we address the problem of parallel batching of jobs on identical machines to minimize makespan. The problem is motivated from the washing step of hospital sterilization services where jobs have different sizes, different release dates and equal processing times. Machines can process more than one job at the same time as long as the total size of jobs in a batch does not exceed the machine capacity. We present a branch and bound based heuristic method and compare it to a linear model and two other heuristics from the literature. Computational experiments show that our method can find high quality solutions within short computation time.

Predictive Modeling of Video Packet Delay in IP Networks

This paper studies linear prediction algorithms for packet-delay modeling. A detailed examination of the delay traces collected from video streams encoded at different bitrates, suggests that autoregressive (AR) models can exploit the correlation among the delay samples and produce the best estimates in terms of the mean-squared error criterion. Simulation results show that AR prediction can reduce the average prediction-error power significantly as compared to the exponentially-weighted moving average prediction as well as the recursive weighted median filtering. This is a promising result since many layers in the multimedia communication protocol stack, e.g., rate control, error control and network adaptation, can greatly benefit from accurate packet-delay prediction.

Optimization in Healthcare Delivery Modeling: Methods and Applications

Optimization methods have been applied to a wide variety of problems in healthcare ranging from operational level scheduling decisions to the design of national healthcare policies. In this chapter, we provide an overview of several practical optimization applications in the domain of healthcare operations management, including appointment scheduling, operating room scheduling, capacity planning, workforce scheduling, healthcare facility location, organ allocation and transplantation, disease screening, and vaccine design. We provide detailed examples to illustrate the use of different optimization techniques such as discrete convex analysis, stochastic programming, and approximate dynamic programming in these areas.

Real-time multiple description and layered encoded video streaming with optimal diverse routing

Multiple description (MD) and layered coding (LC) are two source-coding approaches proposed for adaptive and robust video streaming over lossy networks. Both streaming methods aim to improve the streaming quality by transmitting the generated multiple sub-bitstreams over partially link-disjoint paths. However, the achieved qualities heavily depend on the media characteristics, path conditions and application requirements. In order to attain the highest quality, we study optimal multi-path selection methods for both MD and LC streaming. The simulations run over an overlay infrastructure show 9.0 - 12.5 dB peak signal-to-noise ratio (PSNR) improvement when the video is streamed over intelligently selected multiple paths instead of the shortest path or maximally link-disjoint paths. By the help of the proposed path selection methods, the end users estimate the expected qualities of MD and LC streaming for the given network conditions and application requirements prior to the streaming, which allows the users to make a choice accordingly.

A branch and bound algorithm for scheduling unit size jobs on parallel batching machines to minimize makespan

In this paper, we present a branch and bound algorithm for the parallel batch scheduling of jobs having different processing times, release dates and unit sizes. There are identical machines with a fixed capacity and the number of jobs in a batch cannot exceed the machine capacity. All batched jobs are processed together and the processing time of a batch is given by the greatest processing time of jobs in that batch. We compare our method to a mixed integer program as well as a method from the literature that is capable of optimally solving instances with a single machine. Computational experiments show that our method is much more efficient than the other two methods in terms of solution time for finding the optimal solution.

Proxy Selection for Interactive Video

Transmission of time-critical video traffic over the networks with large end-to-end delays poses two main difficulties: slow adaptation to changing network conditions and inability of timely recovery from lost packets. Previously, we proposed a proxy-based solution that enabled us to cope with these problems. Our Internet experiments with a single proxy system showed that the QoS delivered by interactive video applications could be greatly improved by the Intermediate-Proxy approach. In multi-proxy systems, however, the availability of a large number of proxies throughout the Internet will bring the proxy selection problem to the fore. This is an important problem since the benefits of the intermediate-proxy approach can be best exploited with a proper proxy selection. In this study, our goal is to model the dynamics involved in the networks with proxies, and investigate mathematical and practical proxy selection methods.

Development Of A Catch Allocation Tool Design For Production Planning At Js Mcmillan Fisheries

Abstract JS McMillan Fisheries Ltd. (JSM) is a Vancouver-based commercial fishing, production and distribution company. As the operations of JSM evolved, the process of allocating a commereial salmon catch to a set of final products has become complex and time-consuming. We developed a linear programming based decision support tool to assist JSM management with this allocation decision. The decision support tool yields a production plan that maximizes the profit potential of the catch and allows management to carry out “what if” analyses. Moreover, this paper explores implementation issues such as modeling fish quality deterioration, measuring the effect of by-product and addressing catch-size uncertainty.