scholarly journals Trading Plan Cost for Timeliness in Situated Temporal Planning

2020 ◽  
Author(s):  
Shahaf Shperberg ◽  
Andrew Coles ◽  
Erez Karpas ◽  
Eyal Shimony ◽  
Wheeler Ruml
Keyword(s):  
Empirical Evaluation ◽  
Optimal Solution ◽  
Search Trees ◽  
Expected Cost ◽  
Temporal Planning ◽  
Scheduling Scheme ◽  
Special Cases ◽  
Sequential Schedule ◽  
Deliberation Scheduling

If a planning agent is considering taking a bus, for example, the time that passes during its planning can affect the feasibility of its plans, as the bus may depart before the agent has found a complete plan. Previous work on this situated temporal planning setting proposed an abstract deliberation scheduling scheme for maximizing the probability of finding a plan that is still feasible at the time it is found. In this paper, we extend the deliberation scheduling approach to address problems in which plans can differ in their cost. Like the planning deadlines, these costs can be uncertain until a complete plan has been found. We show that finding a deliberation policy that minimizes expected cost is PSPACE-hard and that even for known costs and deadlines the optimal solution is a contingent, rather than sequential, schedule. We then analyze special cases of the problem and use these results to propose a greedy scheme that considers both the uncertain deadlines and costs. Our empirical evaluation shows that the greedy scheme performs well in practice on a variety of problems, including some generated from planner search trees.

Optimal Consumption and Insurance: A Continuous-time Markov Chain Approach

2008 ◽  
Vol 38 (01) ◽  
pp. 231-257 ◽  
Author(s):  
Holger Kraft ◽  
Mogens Steffensen
Keyword(s):  
Continuous Time ◽  
Optimal Solution ◽  
Decision Problems ◽  
Optimal Consumption ◽  
Continuous Time Markov Chain ◽  
Financial Decision Making ◽  
Markov Chain Approach ◽  
Special Cases ◽  
Financial Decision ◽  
The Individual

Personal financial decision making plays an important role in modern finance. Decision problems about consumption and insurance are in this article modelled in a continuous-time multi-state Markovian framework. The optimal solution is derived and studied. The model, the problem, and its solution are exemplified by two special cases: In one model the individual takes optimal positions against the risk of dying; in another model the individual takes optimal positions against the risk of losing income as a consequence of disability or unemployment.

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 Optimizing preservation strategies for deteriorating items with time-varying holding cost and stock-dependent demand

2020 ◽  
Vol 30 (2) ◽  
pp. 237-250
Author(s):  
Aditi Khanna ◽  
P Priyamvada ◽  
Chandra Jaggi
Keyword(s):  
Optimal Solution ◽  
Optimal Investment ◽  
Deteriorating Items ◽  
Time Varying ◽  
Preservation Technology ◽  
Special Cases ◽  
Stock Dependent Demand ◽  
Managerial Implications ◽  
Holding Cost ◽  
Dependent Demand

Organizations are keen on rethinking and optimizing their existing inventory strategies so as to attain profitability. The phenomenon of deterioration is a common phenomenon while managing any inventory system. However, it could become a major challenge for the business if not dealt carefully. An investment in preservation technology is by far the most inuential move towards dealing with deterioration proficiently. Additionally, it is noticed that the demand pattern of many products is reliant on its availability and usability. Thus, considering demand of the product to be ?stock-dependent" is a more practical approach. Further, in case of deteriorating items, it is observed that the longer an item stays in the system the higher is its holding cost. Therefore, the model assumes the holding cost to be time varying. Hence, the proposed framework aims to develop an inventory model for deteriorating items with stock-dependent demand and time-varying holding cost under an investment in preservation technology. The objective is to determine the optimal investment in preservation technology and the optimal cycle length so as to minimize the total cost. Numerical example with various special cases have been discussed which signifies the effect of preservation technology investment in controlling the loss due to deterioration. Finally, the effect of key model features on the optimal solution is studied through sensitivity analysis which provides some important managerial implications.

Inductive graph invariants and approximation algorithms

2021 ◽  
Author(s):  
C. R. Subramanian
Keyword(s):  
Optimization Problems ◽  
Independence Number ◽  
Optimal Solution ◽  
Maximum Size ◽  
Chordal Graphs ◽  
Minimum Size ◽  
Optimal Size ◽  
Induced Subgraph ◽  
Special Cases ◽  
Optimal Formula

We introduce and study an inductively defined analogue [Formula: see text] of any increasing graph invariant [Formula: see text]. An invariant [Formula: see text] is increasing if [Formula: see text] whenever [Formula: see text] is an induced subgraph of [Formula: see text]. This inductive analogue simultaneously generalizes and unifies known notions like degeneracy, inductive independence number, etc., into a single generic notion. For any given increasing [Formula: see text], this gets us several new invariants and many of which are also increasing. It is also shown that [Formula: see text] is the minimum (over all orderings) of a value associated with each ordering. We also explore the possibility of computing [Formula: see text] (and a corresponding optimal vertex ordering) and identify some pairs [Formula: see text] for which [Formula: see text] can be computed efficiently for members of [Formula: see text]. In particular, it includes graphs of bounded [Formula: see text] values. Some specific examples (like the class of chordal graphs) have already been studied extensively. We further extend this new notion by (i) allowing vertex weighted graphs, (ii) allowing [Formula: see text] to take values from a totally ordered universe with a minimum and (iii) allowing the consideration of [Formula: see text]-neighborhoods for arbitrary but fixed [Formula: see text]. Such a generalization is employed in designing efficient approximations of some graph optimization problems. Precisely, we obtain efficient algorithms (by generalizing the known algorithm of Ye and Borodin [Y. Ye and A. Borodin, Elimination graphs, ACM Trans. Algorithms 8(2) (2012) 1–23] for special cases) for approximating optimal weighted induced [Formula: see text]-subgraphs and optimal [Formula: see text]-colorings (for hereditary [Formula: see text]’s) within multiplicative factors of (essentially) [Formula: see text] and [Formula: see text] respectively, where [Formula: see text] denotes the inductive analogue (as defined in this work) of optimal size of an unweighted induced [Formula: see text]-subgraph of the input and [Formula: see text] is the minimum size of a forbidden induced subgraph of [Formula: see text]. Our results generalize the previous result on efficiently approximating maximum independent sets and minimum colorings on graphs of bounded inductive independence number to optimal [Formula: see text]-subgraphs and [Formula: see text]-colorings for arbitrary hereditary classes [Formula: see text]. As a corollary, it is also shown that any maximal [Formula: see text]-subgraph approximates an optimal solution within a factor of [Formula: see text] for unweighted graphs, where [Formula: see text] is maximum size of any induced [Formula: see text]-subgraph in any local neighborhood [Formula: see text].

Optimum replacement policies with delay

1974 ◽  
Vol 11 (01) ◽  
pp. 102-110 ◽  
Author(s):  
Toshio Nakagawa ◽  
Shunji Osaki
Keyword(s):  
Delay Time ◽  
Expected Cost ◽  
Numerical Examples ◽  
Special Cases ◽  
Replacement Theory

Replacement theory for equipment has been investigated by several authors. This paper introduces the ‘delay’ time preparing for replacement, derives the expected cost per unit time, and discusses the optimum replacement policies under several conditions. Three special cases are discussed and numerical examples are presented.

An optimal inspection–repair–replacement policy for standby systems

1995 ◽  
Vol 32 (1) ◽  
pp. 212-223 ◽  
Author(s):  
Lam Yeh
Keyword(s):  
Geometric Model ◽  
Optimal Solution ◽  
Simple Algorithm ◽  
Replacement Policy ◽  
System State ◽  
Expected Cost ◽  
Long Run ◽  
Optimal Maintenance ◽  
Maintenance Model

In this paper, an optimal maintenance model for standby systems is studied. An inspection–repair–replacement policy is employed. Assume that the state of the system can only be determined through an inspection which may incorrectly identify the system state. After each inspection, if the system is identified as in the down state, a repair action will be taken. It will be replaced some time later by a new and identical one. The problem is to determine an optimal policy so that the availability of the system is high enough at any time and the long-run expected cost per unit time is minimized. An explicit expression for the long-run expected cost per unit time is derived. For a geometric model, a simple algorithm for the determination of an optimal solution is suggested.

scholarly journals A Generalized Process Targeting Model and an Application Involving a Production Process with Multiple Products

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 699
Author(s):  
Mohammad A. M. Abdel-Aal ◽  
Shokri Z. Selim
Keyword(s):  
Lower Limit ◽  
Optimal Solution ◽  
Solution Procedure ◽  
Quality Characteristic ◽  
Specification Limits ◽  
Common Mean ◽  
Multiple Products ◽  
Upper Limit ◽  
Proposed Model ◽  
Special Cases

This paper presents a generalized targeting model that subsumes most known targeting problems. In this paper, a recurrent state is defined as a condition that requires reprocessing or rework. The generalized model can accommodate one or two specifications limits and can be used for the following quality characteristics: The nominal-the-better, the larger-the-better, and the smaller-the-better. This model can be used to find the optimal mean of a quality characteristic, as well as the optimal specification limits. In addition, the paper studies the conditions under which the solution to the proposed model can provide a global solution. The paper shows that, for some of the special cases and under very general conditions, the optimal lower limit should be zero and the optimal upper limit should be infinity. This paper proves that the expected profits improve for the case where only a lower limit on the quality characteristic is used, if a recurrent state is included by adding an optimized upper limit. A special case of the model is used to study the problem of determining a common mean for multiple products, as well as the optimal upper specification limits for each product. A solution procedure for maximizing the expected profits and obtaining the optimal solution is introduced. A numerical example is presented.

Warehousing operation optimization model of one storey new dangerous goods warehouse based on warehousing chain and its application

2020 ◽  
Vol 01 ◽  
Author(s):  
Xiaguang Li ◽  
Xiefang Lin ◽  
Fangwei Zhang ◽  
Xufeng Tang ◽  
Ruolin Qiu ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Evaluation Model ◽  
Optimal Solution ◽  
The Novel ◽  
Allocation Model ◽  
Scheduling Scheme ◽  
Dangerous Goods ◽  
Novel Theory ◽  
Time Optimal ◽  
Scheme Evaluation

Introduction: In order to ensure the efficiency and cost of dangerous goods warehouse under the premise of safety, this study takes the dangerous goods warehouse as the research object and implements multitask for dangerous goods warehouse with two forklifts. Methods: This study takes traversal calculation, novel safety calculation formula and scheduling scheme evaluation model as tools to research the forklift scheduling scheme of one-stoery packed dangerous goods warehouse. Results: Optimal scheme and allocation decision model are obtained through numerical simulation. The innovation of this study is giving the safety formula of forklift operation in dangerous goods warehouse and using numerical simulation to obtain the global optimal solution. Furthermore, this study draws on the concept of travel chain to propose the idea of warehousing chain. At the same time, optimal schemes for multiple dangerous goods inbound and outbound the warehouse are studied. Conclusion: With the application of actual data in Shanghai Lingang dangerous goods warehouse, this study combines with the simulation technology to verify the allocation model of warehousing operations and forklift scheduling model. The validity and feasibility of the novel theory are also verified.

Scheduling jobs on non-identical IFR processors to minimize general cost functions

1991 ◽  
Vol 23 (04) ◽  
pp. 909-924 ◽  
Author(s):  
Rhonda Righter ◽  
Susan H. Xu
Keyword(s):  
Cost Function ◽  
Optimal Policy ◽  
Expected Number ◽  
Expected Cost ◽  
Processing Times ◽  
Special Cases ◽  
The Cost ◽  
General Cost Functions ◽  
Tardy Jobs ◽  
Completion Times

We consider the problem of scheduling n jobs non-preemptively on m parallel, non-identical processors to minimize a weighted expected cost function of job completion times, where the weights are associated with the jobs. The cost function is assumed to be increasing and concave but otherwise arbitrary. Processing times are IFR with different distributions for different processors. Jobs may be processed on any processor and there are no precedences. We show that the optimal policy orders the jobs in decreasing order of their weights and then uses the individually optimal policy for each job. In other words, processors are offered to jobs in order, and each job considers its own expected cost function for its completion time to decide whether to accept or reject a processor. Therefore, the optimal policy does not depend on the weights of the jobs except through their order. Special cases of our objective function are weighted expected flowtime, weighted discounted expected flowtime, and weighted expected number of tardy jobs.

THE PERIODIC MAINTENANCE POLICY FOR A WEIBULL LIFE-TIME SYSTEM WITH DEGRADATION RATE REDUCTION UNDER RELIABILITY LIMIT

2008 ◽  
Vol 25 (06) ◽  
pp. 793-805 ◽  
Author(s):  
CHUN-YUAN CHENG ◽  
MINGCHIH CHEN
Keyword(s):  
Failure Rate ◽  
Degradation Rate ◽  
Life Time ◽  
Repairable Systems ◽  
Maintenance Policy ◽  
Rate Reduction ◽  
Expected Cost ◽  
Cost Rate ◽  
Special Cases ◽  
Reduction Effect

From the literature, it is known that preventive maintenance (PM) can reduce the deterioration of system or equipment to a younger level. Researchers usually develop optimal PM policies based on the assumption that the PM can reduce system's age or failure rate. However, the PM actions, such as cleaning, adjustment, alignment, and lubrication work, may not always reduce system's age or failure rate. Instead, it may only reduce the degradation rate of the system to a certain level. In addition, most of the existing optimal PM policies are developed by minimizing the expected cost rate only. Yet, as demonstrated in this paper, the system will have very low reliability at the time of preventive replacement if the reliability limit is not considered. Hence, this paper is to develop an optimal periodic PM model by minimizing the expected cost rate per unit time with the consideration of reliability limit for repairable systems with degradation rate reduction after each PM. The improvement factor method is used to measure the reduction effect of the degradation rate. The algorithm for searching the optimal solutions for this PM model is developed. Examples are also presented with discussions of parameter sensitivity and special cases.

Sign in / Sign up

Export Citation Format

Share Document