Optimal location of a facility relative to area demands

This paper deals with the Weber single-facility location problem where the demands are not only points but may be areas as well. It provides an iterative procedure for solving the problem with l^p distances when p > 1 (a method of obtaining the exact solution when p = 1 and distances are thus rectangular already exists). The special case where the weight densities in the areas are uniform and the areas are rectangles or circles results in a modified iterative process that is computationally much faster. This method can be extended to the simultaneous location of several facilities.     

Single machine parallel batch scheduling subject to precedence constraints

We consider the single machine parallel batch scheduling problems to minimize makespan and total completion time, respectively, under precedence relations. The complexities of these two problems are reported as open in the literature. In this paper, we settle these open questions by showing that both problems are strongly NP‐hard, even when the precedence relations are chains. When the processing times of jobs are directly agreeable or inversely agreeable with the precedence relations, there is an O(n²) time algorithm to minimize the makespan. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

An efficient SPH methodology for modelling mechanical characteristics of particulate composites

Particulate composites are one of the widely used materials in producing numerous state-of-the-art components in biomedical, automobile, aerospace including defence technology. Variety of modelling techniques have been adopted in the past to model mechanical behaviour of particulate composites. Due to their favourable properties, particle-based methods provide a convenient platform to model failure or fracture of these composites. Smooth particle hydrodynamics (SPH) is one of such methods which demonstrate excellent potential for modelling failure or fracture of particulate composites in a Lagrangian setting. One of the major challenges in using SPH method for modelling composite materials depends on accurate and efficient way to treat interface and boundary conditions. In this paper, a master-slave method based multi-freedom constraints is proposed to impose essential boundary conditions and interfacial displacement constraints in modelling mechanical behaviour of composite materials using SPH method. The proposed methodology enforces the above constraints more accurately and requires only smaller condition number for system stiffness matrix than the procedures based on typical penalty function approach. A minimum cut-off value-based error criteria is employed to improve the compu-tational efficiency of the proposed methodology. In addition, the proposed method is further enhanced by adopting a modified numerical interpolation scheme along the boundary to increase the accuracy and computational efficiency. The numerical examples demonstrate that the proposed master-slave approach yields better accuracy in enforcing displacement constraints and requires approximately the same computational time as that of penalty method.     

Influence of a liquid-filled compartment structure on the incoming shaped charge jet stability

Liquid-filled compartment structure consists of a bulk steel plate with matrix blind holes which are filled with liquid and a steel front plate to seal up the liquid with rings and bolts.The liquid-filled compart-ment structure can resist the shaped charge warhead effectively.This paper presents experimental and theoretical investigations of the penetration ability of the residual shaped charge jet emerging from the liquid-filled compartment structure after the penetration process at different impact angles.On the basis of shock wave propagation theory,the influence of the liquid-filled compartment structure on jet sta-bility is analysed.The interferences of the liquid backflow caused by a reflected shock wave and a back plate on jet stability under different impact angles are also examined.In addition,the range of the disturbed velocity segments of the jet at different impact angles and the penetration ability of the re-sidual jet are obtained.A theoretical model is validated against the experimental penetration depths.     

A note on circular error probabilities

An approximation for P(X² + Y² ≤ K²σ²₁) based on an unpublished result of Kleinecke is derived, where X and Y are independent normal variables having zero means and variances σ²₁ and σ²₂ and σ₁ ≥ σ₂. Also, we provide asymptotic expressions for the probabilities for large values of β = K²(1 - c²)/4c² where c = σ₂/σ₁. These are illustrated by comparing with values tabulated by Harter [6]. Solution of K for specified P and c is also considered. The main point of this note is that simple and easily calculable approximations for P and K can be developed and there is no need for numerical evaluation of integrals.     

Single-lane bridge serving two-lane traffic

This paper presents a mathematical model of a single-lane bridge serving two-way traffic in alternating directions (with an FIFO rule observed within each directional queue). While the bridge serves cars moving in one direction, cars approaching from the opposite direction wait in a queue at its foot. When cars in the current direction finish crossing the bridge, it begins serving cars from the other direction, if any are present. A newly-arrived car finding an empty bridge mounts it immediately. Several cars moving in the same direction may occupy the bridge simultaneously. The crossing speed is assumed to be constant, and the arrival processes in both directions are assumed to be independent, homogeneous Poisson processes. A generalization of the alternating-priority models [1, 2] is developed to arrive at the Laplace-Stieltjes transform and the expected value of the flow time (the time interval between the moments of arrival at the bridge and departure from it) for steady state conditions. The results are discussed and some examples are presented graphically.     

Maintenance policies when failure distribution of equipment is only partially known

An optimal schedule for checking an equipment subject to failure which can be detected by inspection only, is derived. Increasing failure rate and one percentile specify the otherwise unknown life distribution. Dynamic programming methodology yields the solution which minimizes the maximum expected cost. Numerical examples are presented and compared with models employing differing amounts of knowledge.     

Queueing processes and trade-offs during ship-to-shore transfer of cargo

This article examines the ship-to-shore transfer of cargo from ships that are located offshore. In these situations, cargo is transferred from the ships to smaller craft, which in turn transport the cargo the remaining distance to shore. These craft cycle back and forth from the ship to the shore until the transfer is complete. Queueing of these craft often occurs, as they must wait at either the ship or the shore for a loading or unloading position to become free. Two different methods of modeling this ship-to-shore transfer of cargo are developed and applied. One is an analytic queueing model and the other is a more traditional simulation model. The analytic model is found to produce results quite similar to the simulation model. Examples are shown that use these models to analyze trade-offs between variables affecting the ship-to-shore transfer of cargo and the total time to transfer a given amount of cargo ashore. © 1994 John Wiley & Sons, Inc.     

Optimal redesign decisions through failure rate estimates

To reduce the time-to-market of newly developed systems, manufacturers increasingly adopt strategies where systems are brought to market while system field reliability is still uncertain. These systems are typically sold under performance-based contracts, which incentivizes potential customers to invest in them despite reliability uncertainty. Such contracts make the manufacturer (partly) responsible for the availability of the system. Subsequently, when field reliability is lower than anticipated, the manufacturer may choose to redesign the system to avoid high contract penalties. Redesign is a costly effort which may substantially increase field reliability. Deciding when to redesign is challenging, especially because the initial failure rate estimate by the system's engineers is refined over time as failure data accrues. We propose a model that endogenizes the failure rate updating to analyze this tactical redesign decision. We study additive and multiplicative redesigns and show that the optimal policy has a control limit structure. We benchmark our optimal policy against a static counterpart numerically, and conclude that basing redesign decisions on the updated estimate of the failure rate can substantially reduce costs.