Puzzle‐based storage systems

We introduce and develop models for a physical goods storage system based on the 15‐puzzle, a classic children's game in which 15 numbered tiles slide within a 4 × 4 grid. The objective of the game is to arrange the tiles in numerical sequence, starting from a random arrangement. For our purposes, the tiles represent totes, pallets, or even containers that must be stored very densely, and the objective is to maneuver items to an input–output point for retrieval or processing. We develop analytical results for storage configurations having a single empty location (as in the game) and experimental results for configurations with multiple empty locations. Designs with many empty locations can be made to form aisles, allowing us to compare puzzle‐based designs with traditional aisle‐based designs found in warehousing systems. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Kurtosis correction method for X̄ and R control charts for long‐tailed symmetrical distributions

This paper proposes a kurtosis correction (KC) method for constructing the X? and R control charts for symmetrical long‐tailed (leptokurtic) distributions. The control charts are similar to the Shewhart control charts and are very easy to use. The control limits are derived based on the degree of kurtosis estimated from the actual (subgroup) data. It is assumed that the underlying quality characteristic is symmetrically distributed and no other distributional and/or parameter assumptions are made. The control chart constants are tabulated and the performance of these charts is compared with that of the Shewhart control charts. For the case of the logistic distribution, the exact control limits are derived and are compared with the KC method and the Shewhart method. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

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 experimental comparison of solution algorithms for the single-machine tardiness problem

A basic problem in scheduling involves the sequencing of a set of independent tasks at a single facility with the objective of minimizing mean tardiness. Although the problem is relatively simple, the determination of an optimal sequence remains a challenging combinatorial problem. A number of algorithms have been developed for finding solutions, and this paper reports a comparative evaluation of these procedures. Computer programs for five separate algorithms were written and all were run on a data base designed to highlight computational differences. Optimizing algorithms developed by Emmons and by Srinivasan appeared to be particularly efficient in the comparative study.     

Location of facilities with rectangular distances among point and area destinations

This article is concerned with the optimal location of any number (n) of facilities in relation to any number (m) of destinations on the Euclidean plane. The criterion to be satisfied is the minimization of total weighted distances where the distances are rectangular. The destinations may be either single points, lines or rectangular areas. A gradient reduction solution procedure is described which has the property that the direction of descent is determined by the geometrical properties of the problem.     

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.