Optimal Priority Rule Research Articles

Understanding Customers’ Insights Using Attribution Theory: A Text Mining and Rule-Based Machine Learning Two-Step Multifaceted Method

By looking at complaints made by guests of different star-rated hotels, this study attempts to detect associations between complaint attributions and specific consequences. A multifaceted approach is applied. First, a content analysis is conducted to transform textual complaints into categorically structured data. Furthermore, a web graph analysis and rule-based machine learning method are applied to discover potential relationships among complaint antecedents and consequences. These are validated using a qualitative projective technique. Using an Apriori rule-based machine learning algorithm, optimal priority rules for this study were determined for the respective complaining attributions for both the antecedents and consequences. Based on attribution theory, we found that Customer Service, Room Space, and Miscellaneous Issues received more attention from guests staying at higher star-rated hotels. Conversely, cleanliness was a consideration more prevalent amongst guests staying at lower star-rated hotels. Qualitative research was conducted to corroborate the findings. Other machine learning techniques (i.e., Decision Tree) build rules based on only a single conclusion, while association rules attempt to determine many rules, each of which may lead to a different conclusion. The main contributions of this study lie in the fact that this is one of the first attempts to detect correlations within the online complaining behaviors of guests of different star-rated hotels by utilizing rule-based machine learning.

Optimal deadline scheduling for electric vehicle charging with energy storage and random supply

Motivated by the potential of utilizing used electric vehicle (EV) batteries as the battery energy storage system (BESS) in EV charging stations, we study the joint scheduling of BESS operation and deferrable EV charging load (with the same deadline) in the presence of random renewable generation, EV arrivals, and electricity prices. We formulate the cost-minimizing scheduling problem faced by an EV charging station operator as a dynamic program. When the number of EVs is large, the formulated dynamic program cannot be exactly solved by brute-force methods due to the curse of dimensionality. We characterize a complete, optimal priority rule on energy allocation among EVs. For an important special case with full charging/discharging efficiency and all EVs available for charging at the initial period, we propose a new methodological approach to establish full characterizations of an optimal scheduling policy that enable the development of scalable computational approaches. The proposed approach achieves close-to-optimal performance in numerical experiments with real-world electricity pricing and solar generation data.

The multi-armed bandit, with constraints

The colorfully-named and much-studied multi-armed bandit is the following Markov decision problem: At epochs 1, 2, ... , a decision maker observes the current state of each of several Markov chains with rewards (bandits) and plays one of them. The Markov chains that are not played remain in their current states. The Markov chain that is played evolves for one transition according to its transition probabilities, earning an immediate reward (possibly negative) that can depend upon its current state and on the state to which transition occurs. Henceforth, to distinguish the states of the individual Markov chains from those of the Markov decision problem, the latter are called multi-states. Each multi-state prescribes a state for each of the Markov chains. This version of the multi-armed bandit problem was originally solved by John Gittins. It has a large range of operations research applications including applications to resource allocation, scheduling, project management, and search. A key result for the multi-armed bandit is that attention can be restricted to a simple class of decision procedures. A label is assigned to each state of each bandit such that no two states have the same label, even if they are in different bandits. A priority rule is a policy that, given each multistate, plays the Markov chain whose current state has the lowest label. The literature includes several different proofs of the optimality of a priority rule. Nearly all of these proofs rest on a family of optimal stopping times, one for each state of each bandit. A different approach is taken here. Pair-wise comparison, rather than optimal stopping, is used to demonstrate the optimality of a priority rule. This is accomplished for models having linear and exponential utility functions. Elementary row operations are used to identify an optimal priority rule and to compute its expected utility for a given starting state. Our analysis covers the cases of linear and exponential utilities. In the case of a linear utility function, the model is generalized to include constraints that link the bandits. With C constraints, an optimal policy is shown to take the form of an initial randomization over C + 1 priority rules, and column generation is proposed as a solution method. The proposed computational methods are based on several matrix algorithms. First, an algorithm, called the Triangularizer, transforms the one-step rewards and transition probability matrixes for individual bandits by applying elementary row operations. The transformed matrixes, called finalized, are triangle: all their elements on diagonals and below diagonals are equal to zero. For a given index policy, running the transformed bandits is equivalent to running the original bandits. Second, the transition probabilities and one-step rewards of the transformed bandits are used to compute the performance characteristics of index policies in polynomial times. These computations are used by the column generation algorithm for multi-armed bandits with constraints.

An evolutionary multi-objective optimization of trading rules in call markets

SUMMARY We evaluate an agent-based model featuring near-zero-intelligence traders operating in a call market with a wide range of trading rules governing the determination of prices and which orders are executed, as well as a range of parameters regarding market intervention by market makers and the presence of informed traders. We optimize these trading rules using a multi-objective population-based incremental learning algorithm seeking to maximize the trading volume and minimize the bid–ask spread. Our results suggest that markets should choose a small tick size if concerns about the bid–ask spread are dominating and a large tick size if maximizing trading volume is the main aim. We also find that unless concerns about trading volume dominate, time priority is the optimal priority rule. Copyright © 2011 John Wiley & Sons, Ltd.

Efficient Solution of a Stochastic Scheduling Problem on an Out-Forest—Revisited

We consider the problem of scheduling tasks subject to out-forest precedence constraints, where the tasks are identified with the edges. Initially only the tasks with no predecessors are available. At each step, an available task is selected and processed, resulting in either (a) termination, or (b) the replacement of the selected task in the available set by a random subset of its immediate successors. Also, an outcome-dependent reward is gained. The goal is to maximize the expected utility, which can be either linear or exponential. Denardo, Rothblum, and Van der Heyden [Math. Oper. Res., 29 (2004), pp. 162–181] (DRV) study a special version of the above problem. DRV use a leaf-to-stem induction to demonstrate the optimality of a priority rule and to compute it, the latter with work that is quadratic in the number of edges in the application that motivated their paper. Sethuraman and Tsitsiklis [Math. Oper. Res., 32 (2007), pp. 589–593] (ST) treat the general model and demonstrate optimality of a priority rule by employing an idea of Tsisiklis [Ann. Appl. Probab., 4 (1994), pp. 194–199] to successively eliminate nodes, from highest to lowest priority. ST report a work bound that is exponential in the size of the data. In the current paper, we adapt the leaf-to-stem methodology of DRV to show how to compute optimal priority rules for the general model, with work that is polynomial in the size of the data.

On almost optimal priority rules for preemptive scheduling of stochastic jobs on parallel machines

We consider scheduling a batch of jobs with stochastic processing times on single or parallel machines, with the objective of minimizing the expected holding costs. Preemption of jobs is allowed, and the holding costs of preempted jobs may depend on the stage of completion. We provide a new proof of the optimality of a Gittins priority rule for the single machine and use the same proof to show that the Gittins priority rule is nearly optimal for parallel machines.

On almost optimal priority rules for preemptive scheduling of stochastic jobs on parallel machines

We consider scheduling a batch of jobs with stochastic processing times on single or parallel machines, with the objective of minimizing the expected holding costs. Preemption of jobs is allowed, and the holding costs of preempted jobs may depend on the stage of completion. We provide a new proof of the optimality of a Gittins priority rule for the single machine and use the same proof to show that the Gittins priority rule is nearly optimal for parallel machines.

Aircraft Flow Management under Congestion

Airport congestion is one of the main causes of costly aircraft delays. Sometimes costs may be reduced by imposing on some aircraft a delay at take off time in order to later avoid a more expensive airborne delay. The objective of the Flow Management Problem (F.M.P.) is to find an optimal delay strategy so that the total expected delay cost is minimized. In this paper an idealized and greatly simplified version of F.M.P. is investigated. In particular the airways network considered is star-shaped and congestion is allowed only in the central (arrival) airport. For this particular version a model is presented and a polynomial solution algorithm is derived. Landing priorities among aircraft can also influence the total expected delay cost: the optimal priority rule for our version of the F.M.P. is derived. Another algorithm is presented for the case where the number of aircraft not to be delayed on the ground is given a priori. Possible extensions of the proposed model to more realistic situations are mentioned.

Repair Priority Effect on Availability of a 2-unit System

This paper is concerned with a 2-unit parallel system with priority repair. The priority rule is a mixture of several disciplines. The optimal priority rule minimizes the s-expected total discounted time in which the system is failed. The optimality of Late Preemption Rule is shown and the effect of the rule on the availability of the system is investigated.

Determining Priority-Rules for Underground Rail-Transport by Computer Simulation

Automation of underground rail-transport systems seems to be somewhat more difficult than automation of belt-bunker-systems. However, at least certain aspects of operation of an underground rail-transport system are promising fields for improving the efficiency of the system by automation.One of these is the decision-making process during dispatching the trains, both empty and loaded; automation of this process will make it possible to use “optimal” priority rules which often cannot be applied by normal dispatching.The paper describes some results of studies which have been carried out in order to determine both optimal priority rules and the likely effect of these rules to the efficiency of the system.

Dynamic Scheduling of a Two-Class Queue: Small Interest Rates

We consider a single server queuing system with two classes of customers who arrive according to independent Poisson processes. The two service time distributions are arbitrary, and we assume a linear holding cost and fixed service reward for each class. The problem is to decide, at the completion of each service and given the state of the system, which class (if any) to admit next into service. We seek a policy, called Blackwell optimal, which will maximize for all sufficiently small interest rates the expected net present value of service rewards received minus holding costs incurred over an infinite planning horizon. For a variety of different cases, it is shown that there exists a Blackwell optimal policy which simply enforces a static priority ranking of the classes, choosing idleness only when the system is empty. Criteria for ranking the classes are derived, extending classical results on optimal priority rules. For other cases, involving one zero holding cost and/or an unstable system, it is shown that there exists a Blackwell optimal policy which serves only one class. Attention is largely restricted to nondegenerate cases. It is shown, however, that lexicographic ranking criteria can be derived to deal with degeneracies.