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13
Minimizing Service and Operation Costs of Periodic Scheduling
, 1998
"... We study the problem of scheduling activities of several types under the constraint that at most a fixed number of activities can be scheduled in any single timeslot. Any given activity type is associated with a service cost and an operating cost that increases linearly with the number of timeslot ..."
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Cited by 110 (11 self)
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We study the problem of scheduling activities of several types under the constraint that at most a fixed number of activities can be scheduled in any single timeslot. Any given activity type is associated with a service cost and an operating cost that increases linearly with the number of timeslots since the last service of this type. The problem is to find an optimal schedule that minimizes the longrun average cost per timeslot. Applications of such a model are the scheduling of maintenance service to machines, multiitem replenishment of stock, and minimizing the mean response time in Broadcast Disks. Broadcast Disks gained a lot of attention recently since they are used to model backbone communications in wireless systems, Teletext systems, and web caching in satellite systems. The first contribution of this paper is the definition of a general model that combines into one several important previous models. We prove that an optimal cyclic schedule for the general problem exists a...
The scheduling of maintenance service
 Discrete Appl. Math
, 1997
"... We study a discrete problem of scheduling activities of several types under the constraint that at most a single activity can be scheduled to any one period. Applications of such a model are the scheduling of maintenance service to machines and multiitem replenishment of stock. In this paper we ass ..."
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Cited by 32 (1 self)
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We study a discrete problem of scheduling activities of several types under the constraint that at most a single activity can be scheduled to any one period. Applications of such a model are the scheduling of maintenance service to machines and multiitem replenishment of stock. In this paper we assume that the cost associated with any given type of activity increases linearly with the number of periods since the last execution of this type. The problem is to find an optimal schedule specifying at which periods to execute each of the activity types in order to minimize the longrun average cost per period. We investigate properties of an optimal solution and show that there is always a cyclic optimal policy. We propose a greedy algorithm and report on computational comparison with the optimal. We also provide a heuristic, based on regular cycles for all but one activity type, with a guaranteed worse case bound.
Pricedirected replenishment of subsets: Methodology and its application to inventory routing
 Manufacturing & Service Operations Management
, 2003
"... The idea of pricedirected control is to use an operating policy that exploits optimal dual prices from a mathematical programming relaxation of the underlying control problem. We apply it to the problem of replenishing inventory to subsets of products/locations, such as in the distribution of indus ..."
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Cited by 24 (5 self)
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The idea of pricedirected control is to use an operating policy that exploits optimal dual prices from a mathematical programming relaxation of the underlying control problem. We apply it to the problem of replenishing inventory to subsets of products/locations, such as in the distribution of industrial gases, so as to minimize longrun time average replenishment costs.Given a marginal value for each product/location, whenever there is a stockout the dispatcher compares the total value of each feasible replenishment with its cost, and chooses one that maximizes the surplus.We derive this operating policy using a linear functional approximation to the optimal value function of a semiMarkov decision process on continuous spaces.This approximation also leads to a math program whose optimal dual prices yield values and whose optimal objective value gives a lower bound on system performance.We use duality theory to show that optimal prices satisfy several structural properties and can be interpreted as estimates of lowest achievable marginal costs.On realworld instances, the pricedirected policy achieves superior, near optimal performance as compared with other approaches.
Nearly Optimal PerfectlyPeriodic Schedules
 Proc. of the 20th ACM Symp. on Principles of Distr. Comp. (PODC
, 2001
"... We study the problem of scheduling infinitely ¢ often jobs, each with an associated demand probability, under the constraint that each job must be scheduled with a fixed period. That is, the number of time units between two consecutive occurrences of each job is constant (we assume that time is slot ..."
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Cited by 19 (6 self)
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We study the problem of scheduling infinitely ¢ often jobs, each with an associated demand probability, under the constraint that each job must be scheduled with a fixed period. That is, the number of time units between two consecutive occurrences of each job is constant (we assume that time is slotted and that each job can be scheduled in a single timeslot). The goal is to minimize the average time a random arriving client waits until its desired job is executed. This problem is a variant of the broadcast disks problem: the perfect periodicity allows clients to know exactly when their job is scheduled, rather than “busy waiting,” thus saving energy. The problem is known to be NPhard. The best known polynomial algorithm to date guarantees average waiting time of at ¦ §©¨�����������������¢� � most, ¨��© � where is the optimal waiting time. In this paper, we develop a treebased methodology for periodic scheduling, and using new general results, we derive algorithms with better bounds. A key quantity in our �������� � �� � ������������ � � methodology is. We compare the cost of a solution provided by our algorithms to the cost of a solution to a relaxed continuous (nonintegral) version of the problem. Our asymptotic treebased algorithm guarantees cost of ��������� at most times the cost of the relaxed problem; on the other hand, we prove that the cost of any integral solution is bounded from below by the cost of the continuous �������� � � solution times. We also provide three other treebased algorithms with cost bounded by the cost of the continuous solution ���� � times ���������������� � ,,
Optimal Broadcasting of Two Files over an Asymmetric Channel
 Journal of Parallel and Distributed Computing
, 1998
"... We study the problem of scheduling files over a broadcast channel in an asymmetric environment. The goal is to minimize the mean response time for clients who access the broadcast channel. Asymmetric channels gained a lot of attention since they are used to model wireless communication, Teletext sys ..."
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Cited by 14 (2 self)
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We study the problem of scheduling files over a broadcast channel in an asymmetric environment. The goal is to minimize the mean response time for clients who access the broadcast channel. Asymmetric channels gained a lot of attention since they are used to model wireless communication, Teletext systems, and web caching in satellite systems. This paper addresses the 2files case. We design a simple algorithm that defines the optimal schedule given the demand probability for each file. Our solution is extended to include other important factors, such as dependencies between files, variablelength files, and different priorities for the clients. Adding dependencies is important in the web caching environment since clients may wish to access more than one file in the broadcast channel. For all the above extensions, we prove the surprising result that there exists a simple optimal schedule. Such a schedule is composed of a repeated pattern of AA \Delta \Delta \Delta AB where A is the more ...
Broadcast Disks with Polynomial Cost Functions
, 2004
"... In broadcast disks systems, information is broadcasted in a shared medium. When a client needs an item from the disk, it waits until that item is broadcasted. Broadcast disks systems are particularly attractive in settings where the potential customers have a highlyasymmetric communication capabili ..."
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Cited by 13 (4 self)
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In broadcast disks systems, information is broadcasted in a shared medium. When a client needs an item from the disk, it waits until that item is broadcasted. Broadcast disks systems are particularly attractive in settings where the potential customers have a highlyasymmetric communication capabilities, i.e., receiving is significantly cheaper than transmitting. This is the case with satellite networks, mobile hosts in wireless networks, and Teletext system. The fundamental algorithmic problem for such systems is to determine the broadcast schedule based on the demand probability of items, and the cost incurred to the system by clients waiting. The goal is to minimize the mean access cost of a random client. Typically, it was assumed that the access cost is proportional to the waiting time. In this paper, we ask what are the best broadcast schedules for access costs which are arbitrary polynomials in the waiting time. These may serve as reasonable representations of reality in many cases, where the “patience” of a client is not necessarily proportional to its waiting time. We present an asymptotically optimal algorithm for a fractional model, where the bandwidth may be divided to allow for fractional concurrent broadcasting. This algorithm, besides being justified in its own right, also serves as a lower bound against which we test known discrete algorithms. We show that the Greedy algorithm has the best performance in most cases. Then we show that the performance of other algorithms deteriorate exponentially with the degree of the cost polynomial and approaches the fractional solution for sublinear cost. Finally, we study the quality of approximating the greedy schedule by a finite schedule.
Periodic Scheduling with Service Constraints
 Operations Research
, 1997
"... We consider the problem of servicing a number of objects in a discrete time environment. In each period, we may select an object that will receive a service in the period. Each time an object is serviced, we incur a servicing cost dependent on the time since the object’s last service. Problems of th ..."
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Cited by 5 (0 self)
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We consider the problem of servicing a number of objects in a discrete time environment. In each period, we may select an object that will receive a service in the period. Each time an object is serviced, we incur a servicing cost dependent on the time since the object’s last service. Problems of this type appear in many contexts, e.g., multiproduct lotsizing, machine maintenance, and several problems in telecommunications. We assume that at most one object can be serviced in a given period. For the general problem with m objects, which is known to be NPHard, we describe properties of an optimalpolicy; and for the speci c case of m = 2 objects, we determine an optimal policy. 1.
Duality and existence of optimal policies in generalized joint replenishment
 Mathematics of Operations Reserach
, 2003
"... We establish a duality theory for a broad class of deterministic inventory control problems on continuous spaces that includes the classical joint replenishment problem and inventory routing. Using this theory, we establish the existence of an optimal policy, which has been an open question. We show ..."
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Cited by 4 (2 self)
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We establish a duality theory for a broad class of deterministic inventory control problems on continuous spaces that includes the classical joint replenishment problem and inventory routing. Using this theory, we establish the existence of an optimal policy, which has been an open question. We show how a primaldual pair of infinite dimensional linear programs encode both cyclic and noncyclic schedules, and provide various results regarding cyclic schedules including an example showing that they need not be optimal.
A GlobalOptimization Algorithm for Solving the Maintenance Scheduling Problem for a Family
 of Machines,” Information and Management Sciences
, 2007
"... In this study, we propose a new solution approach for solving the Maintenance Scheduling Problem for a Family of Machines (MSPFM). After reviewing the literature, we found that Goyal and Kusy’s paper presented the only model that used a nonlinear function for the cost of operating a machine when stu ..."
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Cited by 2 (0 self)
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In this study, we propose a new solution approach for solving the Maintenance Scheduling Problem for a Family of Machines (MSPFM). After reviewing the literature, we found that Goyal and Kusy’s paper presented the only model that used a nonlinear function for the cost of operating a machine when studying the periodic maintenance scheduling problems. In our presentation of this paper, we first review Goyal and Kusy’s mathematical model and their heuristic for solving the MSPFM. By analyzing the mathematical model, we show that the objective function of the MSPFM is Lipschitz. Therefore, we propose to solve the MSPFM using a Lipschitz optimization algorithm with a dynamic Lipschitz constant. Based on our random experiments, we conclude that the proposed dynamic Lipschitz optimization algorithm outperforms Goyal and Kusy’s heuristic.
ON DETERMINING THE OPTIMAL MAINTENANCE FREQUENCY FOR A FAMILY OF MACHINES
"... In this study, we propose a new solution approach for solving the Maintenance Scheduling Problem for a Family of Machines (MSPFM). Goyal and Kusy (1985) presented the only model that used a nonlinear function for the cost of operating a machine in the literature of the periodic maintenance schedulin ..."
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Cited by 1 (0 self)
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In this study, we propose a new solution approach for solving the Maintenance Scheduling Problem for a Family of Machines (MSPFM). Goyal and Kusy (1985) presented the only model that used a nonlinear function for the cost of operating a machine in the literature of the periodic maintenance scheduling problems. Before presenting our solution approach, we first review Goyal and Kusy’s (1985) mathematical model for the MSPFM and their heuristic for determining the economic maintenance frequency of a family of machines. To solve the MSPFM, we conduct full analysis on the mathematical model for the MSPFM. By utilizing our theoretical results, we propose an efficient search algorithm that solves the optimal solution for the MSPFM within a very short run time. Based on our random experiments, we conclude that the proposed search algorithm outperforms Goyal and Kusy’s (1985) heuristic.