Operations policy for a supply chain system with fixed-interval delivery and linear demand

This research addresses a production-supply problem for a supply-chain system with fixed-interval delivery. A strategy that determines the optimal batch sizes, cycle times, numbers of orders of raw materials, and production start times is prescribed to minimize the total costs for a given finite planning horizon. The external demands are time-dependent following a life-cycle pattern and the shipment quantities follow the demand pattern. The shipment quantities to buyers follow various phases of the demand pattern in the planning horizon where demand is represented by piecewise linear model. The problem is formulated as an integer, non-linear programming problem. The model also incorporates the constraint of inventory capacity. The problem is represented using the network model where an optimal characteristic has been analysed. To obtain an optimal solution with N shipments in a planning horizon, an algorithm is proposed that runs with the complexity of Θ(N²) for problems with a single-phase demand and O(N³) for problems with multi-phase demand.     

Solitary Potential in a Space Plasma Containing Dynamical Heavy Ions and Bi-Kappa Distributed Electrons of Two Distinct Temperatures

The heavy ion-acoustic solitary waves(HIASWs) in a magnetized, collisionless, space plasma system(containing dynamical heavy ions and bi-kappa distributed electrons of two distinct temperatures) have been theoretically investigated. The Korteweg-de Vries(K-dV), modified K-dV(MK-dV), and higher-order MK-dV(HMK-dV) equations are derived by employing the reductive perturbation method. The basic features of HIASWs(viz. speed, polarity,amplitude, width, etc.) are found to be significantly modified by the effects of number density and temperature of different plasma species, and external magnetic field(obliqueness). The K-dV and HM-Kd V equations give rise to both compressive and rarefactive solitary structures, whereas the MK-dV equation supports only the compressive solitary structures. The implication of our results in some space and laboratory plasma situations are briefly discussed.     

Stability of soap films: hysteresis and nucleation of black films

We study the stability of soap films of a nonionic surfactant under different applied capillary pressures on the film. Depending on the pressure, either a thick common black film (CBF), or a micro-scopically thin Newton black film (NBF) is formed as a (metastable) equilibrium state, with a first-order (discontinuous) transition between the two. Studying the dynamics of the CBF-NBF transition, it is found that under certain conditions a hysteresis for the transition is observed: for a given range of pressures, either of the two states may be observed. We quantify the nucleation process that is at the basis of these observations both experimentally and theoretically.     

Performance analysis of an all-optical wavelength converter based on XPM in semiconductor optical amplifiers

Performance analysis is carried out for an all-optical wavelength converter based on cross-phase modulation in two semiconductor optical amplifiers (SOAs) arranged in a Mach–Zehnder interferometer configuration to evaluate the efficiency of conversion and the signal-to-crosstalk ratio (SCR) at the output of the converter. The results evaluated analytically for input non-return to zero signal at a bit rate of 10 Gb/s show that conversion is possible over a wavelength separation of 2 nm between the pump and the input wavelengths. It is further noticed that SCR of the order of 50 dB or more can be achieved at a bit rate of 10 Gb/s, optical amplifier bandwidth of 10 times bit rate and driving current of 600 mA when the input pump is 60% of saturation intensity. The range of wavelength conversion can further be increased by increasing the driving current.     

Job routing and operations scheduling: a network-based virtual cell formation approach

Virtual cellular manufacturing inherits the benefits of traditional cellular manufacturing and maintains the responsiveness to the changing market and routing flexibility of a job shop by integrating machine-grouping, shop layout design and intercellular flow handling. The primary goal of virtual cell formation is to minimize the throughput time of a given job. This paper proposes a method for virtual cell formation by adopting the double-sweep algorithm for the k-shortest path problem, and a heuristic is devised to schedule the virtual cells for the multiple job orders. Results generated from this method include not only the optimal candidates of the virtual cell with the shortest throughput time with sub-optimal alternative route(s) and throughput time(s) as the alternative candidates in case some resources are restricted or are not available. The procedure of virtual cell creation and scheduling is illustrated explicitly with examples. Since most of the scheduling problems are NP-hard and virtual cell scheduling is even more complex due to the bottleneck machines that are demanded by jobs at other cells. For multiplicity of possible virtual cell candidates, in addition to the precedence and resource constraints, heuristic solutions are found to be reasonable.     

A disruption recovery model for a single stage production-inventory system

This paper presents a newly developed disruption recovery model for a single stage production and inventory system, where the production is disrupted for a given period of time during the production up time. The model is categorized as a constrained non-linear optimization program which we have solved using an efficient heuristic developed in this paper. The model was also solved using an evolutionary algorithm and a comparison of the results from both methods was performed. The heuristic was able to accurately solve the model with significantly less time compared to the evolutionary algorithm. It can be shown that the optimal recovery schedule is dependent on the shortage cost parameters, as well as the extent of the disruption. The proposed model offers a potentially useful tool to help manufacturers decide on the optimal recovery plan in real time whenever the production system experiences a sudden disruption.     

A just-in-time three-level integrated manufacturing system for linearly time-varying demand process

This paper considers a just-in-time (JIT) manufacturing system in which a single manufacturer procures raw materials from a single supplier, process them to produce finished products, and then deliver the products to a single-buyer. The customer demand rate is assumed to be linearly decreasing time-varying. In the JIT system, in order to minimize the suppliers as well as the buyers holding costs, the supply of raw materials and the delivery of finished products are made in small quantities. In this case, both the supply and the delivery may require multiple installments for a single production lot. We develop a mathematical model for this problem, propose a simple methodology for solving the model, and illustrate the effectiveness of the method with numerical examples.     

On the Anistropy of the Speed of Light on a Rotating Platform

The paper discusses a recently posed paradox in relativity concerning the speed of light as measured by an observer on board a rotating turn-table. The counter-intuitive problem put forward by F. Selleri concerns the theoretical prediction of an anisotropy in the speed of light in a reference frame comoving with the edge of a rotatiing disc even in the limit of zero acceleration. The paradox not only challenges the internal consistency of the special relativity theory but also undermines the basic tenet of the conventionality of simultaneity thesis of relativity. The present paper resolves the issue in a novel way by recasting the original paradox in the Galilean world and thereby revealing, in a subtle way, the weak points of the reasonings leading to the fallacy. As a background the standard and the non-standard synchronies in the relativistic as well as in the Galilean world are discussed. In passing, this novel approach also clarifies (contrary to often made assertions in the literature) that the so-called desynchronization of clocks cannot be regarded as the root cause of the Sagnac effect. Finally in spite of the flaw in the reasonings leading to the paradox Selleri's observation regarding the superiority of the absolute synchrony over the standard one for a rotation observer has been upheld.     

From approximate balls to approximate ellipses

A ball spans a set of n points when none of the points lie outside it. In Zarrabi-Zadeh and Chan (Proceedings of the 18th Canadian conference on computational geometry (CCCG’06), pp 139–142, 2006) proposed an algorithm to compute an approximate spanning ball in the streaming model of computation, and showed that the radius of the approximate ball is within 3/2 of the minimum. Spurred by this, in this paper we consider the 2-dimensional extension of this result: computation of spanning ellipses. The ball algorithm is simple to the point of being trivial, but the extension of the algorithm to ellipses is non-trivial. Surprisingly, the area of the approximate ellipse computed by this approach is not within a constant factor of the minimum and we provide an elegant proof of this. We have implemented this algorithm, and experiments with a variety of inputs, except for a very pathological one, show that it can nevertheless serve as a good heuristic for computing an approximate ellipse.