A two-stage tandem queue attended by a moving server with holding and switching costs

We consider a two-stage tandem queue attended by a moving server, with homogeneous Poisson arrivals and general service times. Two different holding costs for stages 1 and 2 and different switching costs from one stage to the other are considered. We show that the optimal policy in the second stage is greedy; and if the holding cost rate in the second stage is greater or equal to the rate in the first stage, then the optimal policy in the second stage is also exhaustive. Then, the optimality condition for sequential service policy in systems with zero switchover times is introduced. Considering some properties of the optimal policy, we then define a Triple-Threshold (TT) policy to approximate the optimal policy in the first stage. Finally, a model is introduced to find the optimal TT policy, and using numerical results, it is shown that the TT policy accurately approximates the optimal policy. This revised version was published online in June 2006 with corrections to the Cover Date.     

Using composite moving averages to forecast sales

Combining moving averages has been suggested as a simple and practical means to improve sales forecasting. Here we present a natural extension whereby combinations of all possible moving averages up to a given number of periods are employed. We evaluate the method's performance relative to other methods, such as simple moving averages and exponentially-weighted moving averages, on two industrial data sets. Particular attention is placed on methods for selecting the number of periods employed, and on handling noisy data.     

Simple random order methods to share costs

A simple random order method (SROM) is an extension of Webers random order values (ROVs), which allows the convex weights on orderings of agents to depend on the set of agents with strictly positive demands. Thus, a SROM permits different coalitions of agents adopting exogenously different ROVs to take into account the differences in, for example, bargaining abilities, rights or status of the agents in a cost sharing problem. Within the family of additive methods satisfying the dummy axiom, we characterize SROMs by Measurement Invariance in the discrete cost sharing model where demands are indivisible, and Ordinality in the continuous model where demands are divisible, respectively.I am indebted to Yves Sprumont for initiating and providing the starting point of this paper, and for his great help in this work. I thank Hervé Moulin, Ahmet Alkan, Anirban Kar, an associate editor, and a referee whose comments greatly improved the paper. I gratefully acknowledge the support from Sabanci University Research Fund.     

Designing routes to minimize fleet operating costs

A route-planner must try to schedule the delivaries by a fleet of vehicles such that customer requirements are met and management objectives are satisfied. In most cases, the number of feasible arrangements is legion, and calculations relating to individual vehicle loads, mileages, delivery times, etc. are tedious, allowing only a small fraction of possible route plans to be established and compared. The problem presents an ideal opportunity for computer application, not least to ensure that solutions are timely and error free.Several algorithms have been developed to improve the quality of vehicle routes, but in practice only those that rely on simple selection rules have found widespread acceptance, due to the innate complexity of the calculations that follow from a more rigorous approach and to the great variety of customer, vehicle, and operational characteristics that distinguish transport systems and which must be accomodated.The method presented here is based upon the well-known ‘savings’ criterion, but avoids many of its deficiencies by employing a random selection mode and producing (efficiently) a large sample of schedules from which to choose the most suitable. In particular, this allows greater flexibility in defining management objectives, and has led to substantial reductions in both fleet sizes and distances travelled, compared to published results, for a set of nine test cases each involving more than 200 customer locations.     

Dynamic scheduling to minimize lost sales subject to set-up costs

We consider scheduling a shared server in a two-class, make-to-stock, closed queueing network. We include server switching costs and lost sales costs (equivalently, server starvation penalties) for lost jobs. If the switching costs are zero, the optimal policy has a monotonic threshold type of switching curve provided that the service times are identical. For completely symmetric systems without set-ups, it is optimal to serve the longer queue. Using simple analytical models as approximations, we derive a heuristic scheduling policy. Numerical results demonstrate the effectiveness of our heuristic, which is typically within 10% of optimal. We also develop and test a heuristic policy for a model in which the shared resource is part of a series network under a CONWIP release policy. This revised version was published online in June 2006 with corrections to the Cover Date.     

Vibration of submerged floating tunnels due to moving loads

The concept of submerged floating tunnel (SFT) has become an increasingly attractive idea to cross the straits. The structural solution in this scheme includes buoyancy force on tunnel body plus tension in mooring tethers. This paper investigates the effect of submergence on the dynamic response of SFT due to moving load. The inertial effect of the fluid is accounted for by evaluating the added mass of tunnel using two and three dimensional models. It is found that fluid–structure interaction increases dynamic amplification of the tunnel deflection (in some cases very significantly). The results show that although the 3D model predicts lesser inertial contribution for surrounding fluid, it is not always possible to associate the larger response with the 2D or 3D models. The discrepancy between the results of the two models decreases as the tether stiffness increases. This indicates that the adoption of Morison’s equation for evaluating the fluid loading on the tunnel is a reasonable assumption when the tether stiffness is high. It is also found that by increasing the tether stiffness, it is possible to introduce a major reduction in the dynamic amplification of the response and by this way control the dynamic response of the SFT.     

How to collect balls moving in the Euclidean plane

In this paper, we study how to collect n balls moving with a fixed constant velocity in the Euclidean plane by k robots moving on straight track-lines through the origin. Since all the balls might not be caught by robots, differently from Moving-target TSP, we consider the following 3 problems in various situations: (i) deciding if k robots can collect all n balls; (ii) maximizing the number of the balls collected by k robots; (iii) minimizing the number of the robots to collect all n balls. The situations considered in this paper contain the cases in which track-lines are given (or not), and track-lines are identical (or not). For all problems and situations, we provide polynomial time algorithms or proofs of intractability, which clarify the tractability-intractability frontier in the ball collecting problems in the Euclidean plane.     

Algorithms to control the moving ship during harbour entry

Automation is being accepted for control systems onboard ships in view of the shortage of skilled manpower in marine sector. Control theory has long been applied to maneuvering problems and at present this trend is continuing at an increased rate. This is for speed control, course control and path keeping. Heading control and course keeping are very important for surface ships while they enter shallow water regions. A typical situation is the entry of a large commercial ship into the harbour basin. The ship faces a sudden change of forces and moments around it due to the change in the hydrodynamics. The Master of the ship regulates the speed while entering the basin. Forces and moments, due to the hydrodynamic flow around the moving hull, are balanced by the rudder behind it. The feed back from the heading angle is taken and the gain in the control system prompts the steering gear to turn the rudder. The conventional control algorithm based on PID is attempted in the first part of the paper and case studies are shown for a Mariner class ship whose hydrodynamic derivatives are known. Displacement, velocities and accelerations are determined for short duration from the simulation of a voyage in calm water. The proposed system can be implemented into autopilot systems. The codes developed in MATLAB can accommodate wind and wave forces as well. The simulation is of a general type and can be used for other vessels with a change in the constants of P (Proportional), I (Integral) and D (Derivative) which can be arrived at by trial and error. The design of the control system depends on the choice of the three control constants K_p, K_i and K_d. These will change as per sea state and extra loads. The control of motions in shallow water and deep water cases are discussed in the paper.     

How to correctly calculate discounted healthcare costs and benefits

A feature of a healthcare policy (such as screening) with interventions at specific ages is that when it is introduced, part of the population is too old to participate in the full programme. This fact changes the formulae to be used for cost and benefit discounting in a non-intuitive way. General formulae are derived for the expected discounted costs and benefits of such health promotion policies, for a stationary population. Correct ways to calculate discounted costs and benefits via simulation are also described. The formulae have some surprising properties, for example the relative cost of two health policies does not depend on the discounting rate. They are also relevant to the ongoing debate over the correct discounting rate for benefits. It is shown that when health benefits follow quickly on treatments, varying the discounting rate for health benefits is merely equivalent to rescaling the cash value of a benefit. It is only when benefit follows long after treatment that the problem of choosing an appropriate discount rate for benefits cannot be simplified.     

The effect of viscosity on the waves due to a moving oscillatory surface pressure

Summary It is known that when a pressure distributionp ₀(x) exp (i t moves with a constant velocityu ₀ parallel to on the surface (y=0) of an inviscid liquid, (i) the steady-state wave amplitude does not die out at large distances from the source for (u ₀/g1/4, and(ii) the solution becomes singular for u ₀/g=1/4.Here is shown that the consideration of even a slight viscosity of the liquid leads to a wave decay with distance for all (u ₀/g), the solution remaining non-singular for (u ₀/g=1/4. Furthermore, for a finitely distributedp ₀(x), the wave amplitude is always non-zero, unlike in the case of an inviscid fluid, where no energy is transmitted for an infinite number of values of a parameter involving ,u ₀ and the length of the pressure strip.

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Zusammenfassung Es ist bekannt, daß, wenn eine periodische Druckverteilungp ₀(x) exp (i t) sich mit einer konstanten Geschwindigkeitu ₀ inx-Richtung über die Oberflächey=0 einer reibungslosen Flüssigkeit bewegt, daß dann (1) die Amplitude des stationären Zustandes in großen Entfernungen von der Quelle nicht abklingt für (u ₀/g)1/4, und (2) die Lösung wird singulär für (u ₀/g)=1/4.Hier wird gezeigt, daß die Berücksichtigung einer geringen Zähigkeit in der Flüssigkeit zu einem Abklingen der Wellen führt für alle (u ₀/g)=1/4. Zudem ist für eine Verteilung vonp ₀(x) über eine endliche Länge die Wellenamplitude immer endlich, im Gegensatz zum reibungsfreien Fall, in dem keine Energie übertragen wird für gewisse Werte eines Parameters, der ,u ₀ und die Länge des Druckstreifens enthält.

     

On optimal search plans to detect a target moving randomly on the real line

A target, whose initial position is unknown, is performing a random walk on the integers. A searcher, starting at the origin, wants to follow a search plan for which E[τ^k] is finite, where k ≥ 1 and τ is the time to capture. The searcher, who has a prior distribution over the target's initial position, can move only to adjacent positions, and cannot travel faster than the target. Necessary and sufficient conditions are given for the existence of search plans for which E[τ^k] is finite and a minimum.     

Supply chain scheduling to minimize holding costs with outsourcing

This paper addresses a scheduling problem in a flexible supply chain, in which the jobs can be either processed in house, or outsourced to a third-party supplier. The goal is to minimize the sum of holding and delivery costs. This problem is proved to be strongly \(\mathcal{NP}\) -hard. Consider two special cases, in which the jobs have identical processing times. For the problem with limited outsourcing budgets, a \(\mathcal{NP}\) -hardness proof, a pseudo-polynomial algorithm and a fully polynomial time approximation scheme are presented. For the problem with unlimited outsourcing budgets, the problem is shown to be equivalent to the shortest path problem, and therefore it is in class  \(\mathcal{P}\) . This shortest-path-problem solution approach is further shown to be applicable to a similar but more applicable problem, in which the number of deliveries is upper bounded.