A model to design recreational boat mooring fields

This article develops a mathematical model and heuristic algorithm to design recreational boating mooring fields. The boating industry is important to the Florida economy, and boat storage is becoming a concern among those in the industry. The mooring field design problem is formulated to maximize the total number of boat feet moored in the mooring field. In the model, we allow two adjacent moorings to overlap, which introduces a risk that under certain conditions the boats on these moorings could contact each other. We identify the conditions when contact is possible and quantify the probability of contact. The mooring field design problem is formulated as a nonlinear mixed‐integer programming problem. To solve the problem, we decompose it into two separate models, a mooring radii assignment model and a mooring layout model, which are solved sequentially. The first is solved via exhaustive enumeration and the second via a depth‐first search algorithm. Two actual mooring fields are evaluated, and in both cases our model leads to better layouts than ones experts developed manually. The mooring field design model rationalizes the mooring field design and shows that in one case by increasing the risk from 0 to 1%, the mooring efficiency increases from 74.8% to 96.2%. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

Optimizing fishbone aisles for dual‐command operations in a warehouse

Unit‐load warehouses store and retrieve unit‐loads, typically pallets. When storage and retrieval operations are not coordinated, travel is from a pickup and deposit (P&D) point to a pallet location and back again. In some facilities, workers interleave storage and retrieval operations to form a dual‐command cycle. Two new aisle designs proposed by Gue and Meller (“Improving the unit‐load warehouse.” In Progress in Material Handling Research: 2006. Material Handling Industry of America, Charlotte, NC, 2006) use diagonal aisles to reduce the travel distance to a single pallet location by approximately 10 and 20[percnt] for the two designs, respectively. We develop analytical expressions for travel between pallet locations for one of these—the fishbone design. We then compare fishbone warehouses that have been optimized for dual‐command to traditional warehouses that have been optimized in the same manner, and show that an optimal fishbone design reduces dual‐command travel by 10–15%. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 54: 389–403, 2009     

Design and control of agile automated CONWIP production lines

In this article, we study the design and control of manufacturing cells with a mix of manual and automated equipment, operating under a CONWIP pull protocol, and staffed by a single agile (cross‐trained) worker. For a three‐station line with one automated station, we fully characterize the structure of the optimal control policy for the worker and show that it is a static priority policy. Using analytical models and extensive simulation experiments, we also evaluate the effectiveness of practical heuristic control policies and provide managerial insights on automation configuration design of the line. This characterization of the worker control policy enables us to develop managerial insights into the design issues of how best to locate and concentrate automation in the line. Finally, we show that, in addition to ease of control and greater design flexibility, the CONWIP protocol also offers higher efficiency and robustness than does the push protocol. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2009     

On compounded bivariate poisson distributions

A unified treatment is given for a class of discrete distributions derived by compounding a bivariate Poisson with a bivariate discrete or continuous distribution. Using generating functions a number of interesting results are obtained for probabilities, moments, cumulants, factorial moments, and factorial cumulants. Conditional distributions and regression functions are also examined. Five illustrative examples are presented in detail. © 1994 John Wiley & Sons, Inc.     

Nonpreemptive scheduling of independent tasks with prespecified processor allocations

In this article we study the problem of scheduling independent tasks, each of which requires the simultaneous availability of a set of prespecified processors, with the objective of minimizing the maximum completion time. We propose a graph-theoretical approach and identify a class of polynomial instances, corresponding to comparability graphs. We show that the scheduling problem is polynomially equivalent to the problem of extending a graph to a comparability graph whose maximum weighted clique has minimum weight. Using this formulation we show that in some cases it is possible to decompose the problem according to the canonical decomposition of the graph. Finally, a general solution procedure is given that includes a branch-and-bound algorithm for the solution of subproblems which can be neither decomposed nor solved in polynomial time. Some examples and computational results are presented. © 1994 John Wiley & Sons, Inc.     

An exact ceiling point algorithm for general integer linear programming

We present an algorithm called the exact ceiling point algorithm (XCPA) for solving the pure, general integer linear programming problem (P). A recent report by the authors demonstrates that, if the set of feasible integer solutions for (P) is nonempty and bounded, all optimal solutions for (P) are “feasible 1-ceiling points,” roughly, feasible integer solutions lying on or near the boundary of the feasible region for the LP-relaxation associated with (P). Consequently, the XCPA solves (P) by implicitly enumerating only feasible 1-ceiling points, making use of conditional bounds and “double backtracking.” We discuss the results of computational testing on a set of 48 problems taken from the literature.     

Bounds for circular error probabilities

Bounds for P(X + X ⩽ k²σ) are given where X₁ and X₂ are independent normal variables having zero means and variances σ, σ, respectively. This is generalized when X₁ and X₂ are dependent variables with known covariance matrix.     

Minimizing flow time on a single machine with job classes and setup times

We examine the static sequencing problem of ordering the processing of jobs on a single machine so as to minimize the average weighted flow time. It is assumed that all jobs have zero ready times, and that the jobs are grouped into classes with the property that setup tasks are only required when processing switches from jobs of one class to jobs of another class. The time required for each setup task is given by the sum of a setdown time from the previous class and a setup time for the new class. We show that an algorithm presented in the literature for solving a special case of this problem gives suboptimal solutions. A number of properties of the optimal solution are derived, and their use in algorithms is evaluated. Computational results are presented for both a branch-and-bound procedure and a simpler depth-first search.     

Optimal sequential replenishment of ships during combat

A carrier battle group is operating in an area where it is subject to attack by enemy aircraft. It is anticipated that air raids will occur in large waves. The uncertain time between raids is available for the replenishment of supplies. We consider the problem of how best to schedule ammunition replenishment during this period. The theory of Gittins indices provides the technical background to the development of a range of models which yield a hierarchy of index-based heuristics for replenishment. One such heuristic is assessed computationally in a more realistic scenario than is explicitly allowed for by the models.