Index policies for the routing of background jobs

Arriving (generic) jobs may be processed at one of several service stations, but only when no other (dedicated) jobs are waiting there. We consider the problem of how to route these incoming background jobs to make best use of the spare service capacity available at the stations. We develop an approximative approach to Whittle's proposal for restless bandits to obtain an index policy for routing. The indices concerned are increasing and nonlinear in the station workload. A numerical study testifies to the strong performance of the index policies developed. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

A balancing problem for mixed model assembly lines with a paced moving conveyor

We state a balancing problem for mixed model assembly lines with a paced moving conveyor as: Given the daily assembling sequence of the models, the tasks of each model, the precedence relations among the tasks, and the operations parameters of the assembly line, assign the tasks of the models to the workstations so as to minimize the total overload time. Several characteristics of the problem are investigated. A line‐balancing heuristic is proposed based on a lower bound of the total overload time. A practical procedure is provided for estimating the deviation of any given line‐balance solution from the theoretical optimum. Numerical examples are given to illustrate the methodology. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

On the uncapacitated K‐commodity network design problem with zero flow‐costs

Extending Sastry's result on the uncapacitated two‐commodity network design problem, we completely characterize the optimal solution of the uncapacitated K‐commodity network design problem with zero flow costs for the case when K = 3. By solving a set of shortest‐path problems on related graphs, we show that the optimal solutions can be found in O(n³) time when K = 3, where n is the number of nodes in the network. The algorithm depends on identifying a list of “basic patterns”; the number of basic patterns grows exponentially with K. We also show that the uncapacitated K‐commodity network design problem can be solved in O(n³) time for general K if K is fixed; otherwise, the time for solving the problem is exponential. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Higher‐order Markov chain models for categorical data sequences*

In this paper we study higher‐order Markov chain models for analyzing categorical data sequences. We propose an efficient estimation method for the model parameters. Data sequences such as DNA and sales demand are used to illustrate the predicting power of our proposed models. In particular, we apply the developed higher‐order Markov chain model to the server logs data. The objective here is to model the users' behavior in accessing information and to predict their behavior in the future. Our tests are based on a realistic web log and our model shows an improvement in prediction. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Strategies for managing the flexible capacity in the airline industry

The ability to effectively match supply and demand under uncertainty can result in significant revenue benefits in the airline industry. We study the benefits of a Demand Driven Swapping (DDS) approach that takes advantage of the flexibilities in the system and dynamically swaps aircraft as departures near and more accurate demand information is obtained. We analyze the effectiveness of different DDS strategies, characterized by their frequency (how often the swapping decision is revised), in hedging against demand uncertainty. Swapping aircraft several weeks prior to departures will not cause much disturbance to revenue management and operations, but will be based on highly uncertain demands. On the other hand, revising the swapping decision later will decrease the possibility of bad swaps, but at a higher cost of disrupting airport services and operations. Our objective is to provide guidelines on how the flexible (swappable) capacity should be managed in the system. We study analytical models to gain insights into the critical parameters that affect the revenue benefits of the different swapping strategies. Our study determines the conditions under which each of the different DDS strategies is effective. We complement our analysis by testing the proposed DDS strategies on a set of flight legs, using data obtained from United Airlines. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

An algorithm for the solution of a location problem with metric constraints

In many location problems, the solution is constrained to lie within a closed set. In this paper, optimal solutions to a special type of constrained location problem are characterized. In particular, the location problem with the solution constrained to be within a maximum distance of each demand point is considered, and an algorithm for its solution is developed and discussed.     

Optimal location of a single service center of certain types

Hakimi has considered the problem of finding an optimal location for a single service center, such as a hospital or a police station. He used a graph theoretic model to represent the region being serviced. The communities are represented by the nodes while the road network is represented by the ares of the graph. In his work, the objective is one of minimizing the maximum of the shortest distances between the vertices and the service center. In the present work, the region being serviced is represented by a convex polygon and communities are spread over the entire region. The objective is to minimize the maximum of Euclidian distances between the service center and any point in the polygon. Two methods of solution presented are (i) a geometric method, and (ii) a quadratic programming formulation. Of these, the geometric method is simpler and more efficient. It is seen that for a class of problems, the geometric method is well suited and very efficient while the graph theoretic method, in general, will give only approximate solutions in spite of the increased efforts involved. But, for a different class of problems, the graph theoretic approach will be more appropriate while the geometric method will provide only approximate solutions though with ease. Finally, some feasible applications of importance are outlined and a few meaningful extensions are indicated.     

Deterministic inventory lot‐size models under inflation with shortages and deterioration for fluctuating demand

In this paper, we extend the inventory lot‐size models to allow for inflation and fluctuating demand (which is more general than constant, increasing, decreasing, and log‐concave demand patterns). We prove that the optimal replenishment schedule not only exists but is also unique. Furthermore, we show that the total cost associated with the inventory system is a convex function of the number of replenishments. Hence, the search for the optimal number of replenishments is simplified to finding a local minimum. Finally, several numerical examples are provided to illustrate the results. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 144–158, 2001     

Computational analysis of MMAP[K]/PH[K]/1 queues with a mixed FCFS and LCFS service discipline

This paper studies a queueing system with a Markov arrival process with marked arrivals and PH‐distribution service times for each type of customer. Customers (regardless of their types) are served on a mixed first‐come‐first‐served (FCFS) and last‐come‐first‐served (LCFS) nonpreemptive basis. That is, when the queue length is N (a positive integer) or less, customers are served on an FCFS basis; otherwise, customers are served on an LCFS basis. The focus is on the stationary distribution of queue strings, busy periods, and waiting times of individual types of customers. A computational approach is developed for computing the stationary distribution of queue strings, the mean of busy period, and the means and variances of waiting times. The relationship between these performance measures and the threshold number N is analyzed in depth numerically. It is found that the variance of the virtual (actual) waiting time of an arbitrary customer can be reduced by increasing N. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 399–421, 2000     

Explicit solution of partitioning problems over a 1‐dimensional parameter space

We consider a class of partitioning problems where the partitioned set is a finite set of real numbers and the objective function of a partition is a function of the vector whose coordinates are the sums of the elements in each part of the given partition (the number of such parts is assumed given). We obtain an explicit solution of such partitioning problem with polynomial complexity bounds. © John Wiley & Sons, Inc. Naval Research Logistics 47: 531–540, 2000