A new approximation algorithm for the multilevel facility location problem

In this paper we propose a new integer programming formulation for the multi-level facility location problem and a novel 3-approximation algorithm based on LP rounding. The linear program we are using has a polynomial number of variables and constraints, being thus more efficient than the one commonly used in the approximation algorithms for this type of problems

Increasing network lifetime by battery-aware master selection in radio networks

Mobile wireless communication systems often need to maximize their network lifetime (defined as the time until the first node runs out of energy). In the broadcast network lifetime problem, all nodes are sending broadcast traffic, and one asks for an assignment of transmit powers to nodes, and for sets of relay nodes so that the network lifetime is maximized. The selection of a relay set consisting of a single node (the ‘master’), can be regarded as a special case of this problem. We provide a mean value analysis of algorithms controlling the selection of a master node with the objective of maximizing the network lifetime. The results show that already for small networks simple algorithms can extend the average network lifetime considerably

Optimal staffing under an annualized hours regime using Cross-Entropy optimization

This paper discusses staffing under annualized hours. Staffing is the selection of the most cost-efficient workforce to cover workforce demand. Annualized hours measure working time per year instead of per week, relaxing the restriction for employees to work the same number of hours every week. To solve the underlying combinatorial optimization problem this paper develops a Cross-Entropy optimization implementation that includes a penalty function and a repair function to guarantee feasible solutions. Our experimental results show Cross-Entropy optimization is efficient across a broad range of instances, where real-life sized instances are solved in seconds, which significantly outperforms an MILP formulation solved with CPLEX. In addition, the solution quality of Cross-Entropy closely approaches the optimal solutions obtained by CPLEX. Our Cross-Entropy implementation offers an outstanding method for real-time decision making, for example in response to unexpected staff illnesses, and scenario analysis

A polling model with an autonomous server

Polling models are used as an analytical performance tool in several application areas. In these models, the focus often is on controlling the operation of the server as to optimize some performance measure. For several applications, controlling the server is not an issue as the server moves independently in the system. We present the analysis for such a polling model with a so-called autonomous server. In this model, the server remains for an exogenous random time at a queue, which also implies that service is preemptive. Moreover, in contrast to most of the previous research on polling models, the server does not immediately switch to a next queue when the current queue becomes empty, but rather remains for an exponentially distributed time at a queue. The analysis is based on considering imbedded Markov chains at specific instants. A system of equations for the queue-length distributions at these instant is given and solved for. Besides, we study to which extent the queues in the polling model are independent and identify parameter settings for which this is indeed the case. These results may be used to approximate performance measures for complex multi-queue models by analyzing a simple single-queue model

Threshold Queueing to Describe the Fundamental Diagram of Uninterrupted Traffic

Queueing because of congestion is an important aspect of road traffic. This paper provides a novel threshold queue that models the empirical shape of the fundamental diagram. In particular, we show that our threshold queue with two service phases captures the capacity drop that is eminent in the fundamental diagram of modern traffic. We use measurements on a Danish highway to illustrate that our threshold queue is indeed capable of capturing the fundamental diagram of real-world traffic systems. We furthermore indicate the modelling power of our threshold queue via a sensitivity study showing that our model is able to capture a wide range of shapes for the fundamental diagram

An analytical comparison of the patient-to-doctor policy and the doctor-to-patient policy in the outpatient clinic

Outpatient clinics traditionally organize processes such that the doctor remains in a consultation room, while patients visit for consultation, we call this the Patient-to-Doctor policy. A different approach is the Doctor-to-Patient policy, whereby the doctor travels between multiple consultation rooms, in which patients prepare for their consultation. In the latter approach, the doctor saves time by consulting fully prepared patients. We compare the two policies via a queueing theoretic and a discrete-event simulation approach. We analytically show that the Doctor-to-Patient policy is superior to the Patient-to-Doctor policy under the condition that the doctor’s travel time between rooms is lower than the patient’s preparation time. Simulation results indicate that the same applies when the average travel time is lower than the average preparation time. In addition, to calculate the required number of consultation rooms in the Doctor-to-Patient policy, we provide an expression for the fraction of consultations that are in immediate succession; or, in other words, the fraction of time the next patient is prepared and ready, immediately after a doctor finishes a consultation.We apply our methods for a range of distributions and parameters and to a case study in a medium-sized general hospital that inspired this research

Approximation algorithms for facility location problems with a special class of subadditive cost functions

In this article we focus on approximation algorithms for facility location problems with subadditive costs. As examples of such problems, we present three facility location problems with stochastic demand and exponential servers, respectively inventory. We present a $(1+\varepsilon, 1)$-reduction of the facility location problem with subadditive costs to the soft capacitated facility location problem, which implies the existence of a $2(1 + \varepsilon)$-approximation algorithm. For a special subclass of subadditive functions, we obtain a 2-approximation algorithm by reduction to the linear cost facility location problem

A new approximation algorithm for the multilevel facility location problem

In this paper we propose a new integer programming formulation for the multilevel facility location problem and a novel 3-approximation algorithm based on LP-rounding. The linear program that we use has a polynomial number of variables and constraints, thus being more efficient than the one commonly used in the approximation algorithms for these types of problems.\ud \u

Note on a class of admission control policies for the stochastic knapsack problem

In this note we discuss a class of exponential penalty function policies recently proposed by Iyengar and Sigman for controlling a stochastic knapsack. These policies are based on the optimal solution of some related deterministic linear programs. By finding explicitly their optimal solution, we reinterpret the exponential penalty function policies and show that they belong to the class of threshold policies. This explains their good practical behavior, facilitates the comparison with the thinning policy, simplifies considerably their analysis and improves the bounds previously proposed

An approximation algorithm for a facility location problem with inventories and stochastic demands

In this article we propose, for any ε > 0, a 2(1 + ε)-approximation algorithm for a facility location problem with stochastic demands. At open facilities, inventory is kept such that arriving requests find a zero inventory with (at most) some pre-specified probability. The incurred costs are the expected transportation costs from the demand points to the facilities, the operating costs of the facilities and the investment in inventory