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Competitive solutions for online financial problems
 ACM Comput. Surv
, 1998
"... This article surveys results concerning online algorithms for solving problems related to the management of money and other assets. In particular, the survey focuses on search, replacement, and portfolio selection problems. ..."
Abstract

Cited by 14 (0 self)
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This article surveys results concerning online algorithms for solving problems related to the management of money and other assets. In particular, the survey focuses on search, replacement, and portfolio selection problems.
Nearly Optimal Competitive Online Replacement
"... This paper studies the following online replacement problem. There is a real function f(t), called the flow rate, defined over a finite time horizon [0; T ]. It is known that m f(t) M for some reals 0 m ! M . At time 0 an online player starts to pay money at the rate f(0). At each time 0 ! t T ..."
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Cited by 5 (2 self)
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This paper studies the following online replacement problem. There is a real function f(t), called the flow rate, defined over a finite time horizon [0; T ]. It is known that m f(t) M for some reals 0 m ! M . At time 0 an online player starts to pay money at the rate f(0). At each time 0 ! t T the player may changeover and continue paying money at the rate f(t). The complication is that each such changeover incurs some fixed penalty. The player is called online as at each time t the player knows f only over the time interval [0; t]. The goal of the player is to minimize the total cost comprised of cumulative payment flow plus changeover costs. This formulation of the replacement problem has various interesting applications among which are: equipment replacement, supplier replacement, the menu cost problem and mortgage refinancing.
OPTIMALITY OF CONTROL LIMIT MAINTENANCE POLICIES UNDER NONSTATIONARY DETERIORATION
 PROBABILITV IN THE ENGINEERING AND INFNRMATIONAL SCIENCES,13, 1999,5570. PRINTED IN THE U.S.A.
, 1999
"... Control limit type policies are widely discussed in the literature, particularly regarding the maintenance of deteriorating systems. Previous studies deal mainly with stationary deterioration processes, where costs and transition probabilities depend only on the state of the system, regardless of it ..."
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Control limit type policies are widely discussed in the literature, particularly regarding the maintenance of deteriorating systems. Previous studies deal mainly with stationary deterioration processes, where costs and transition probabilities depend only on the state of the system, regardless of its cumulative age. In this paper, we consider a nonstationary deterioration process, in which operation and maintenance costs, as well as transition probabilities "deteriorate " with both the system's state and its cumulative age. We discuss conditions under which control limit policies are optimal for such processes and compare them with thclse used in the analysis of stationary models. Two maintenance models are examined: in the first (as in the majority of classic studies), the only maintenance action allowed is the replacement of the system by a new one. In this case, we show that the nonstationary results are direct generalizations of their counterparts in stationary models. We propose an efficient algorithm for finding the optimal policy, utilizing its control limit form. In the second model we also allow for repairs to better states (without changing the age). In this case, the optimal policy is shown to have the form of a 3way control limit rule. However, conditions analogous to those used in the stationary problem do not suffice, so additional, more restrictive ones are suggested and discussed.