A study on an inventory model for non-instantaneous deteriorating items with permissible delay in payments

In this study, an appropriate inventory model for non-instantaneous deteriorating items with permissible delay in payments is considered. The purpose of this study is to find an optimal replenishment policy for minimizing the total relevant inventory cost. This mathematical model is a general framework that comprises numerous previous models such as in Ghare and Schrader [Ghare, P. M., & Schrader, G. H. (1963). A model for exponentially decaying inventory system. International Journal of Production Research, 21, 449–460], Goyal [Goyal, S. K. (1985). Economic order quantity under conditions of permissible delay in payments. Journal of the Operational Research Society, 36, 335–338], and Teng [Teng, J. T. (2002). On the economic order quantity under conditions of permissible delay in payments. Journal of the Operational Research Society, 53, 915–918] as special cases. We have developed some useful theorems to characterize the optimal solutions and provide an easy-to-use method to find the optimal replenishment cycle time and order quantity under various circumstances. Several numerical examples are given to test and verify the theoretical results. Finally, a sensitivity analysis of the optimal solution with respect to major parameters is also included. According to the results of numerical analysis, we provided several ways for the retailer to effectively reduce total annual relevant inventory cost.     

An EOQ model for deteriorating items with time-varying demand and shortages

The study explores the inventory replenishment policies for the cases with time-varying demand, linearly increasing deterioration rate, partial back-ordering, constant service level and equal replenishment intervals over a fixed planning horizon. Since it is difficult to solve the problem directly, we derive the upper bound of replenishment number for a specific planning horizon and find the solution of service level under a given number of replenishment. The optimal solutions of replenishment number and service level are then determined. Numerical examples and sensitivity analyses are also provided to illustrate the solution procedure.     

Uniform and optimal schemes for stiff initial-value problems

We formulate a class of difference schemes for stiff initial-value problems, with a small parameter ε multiplying the first derivative. We derive necessary conditions for uniform convergence with respect to the small parameter ε, that is the solution of the difference scheme u_i^h satisfies |u_i^h−u(x_i)| Ch, where C is independent of h and ε. We also derive sufficient conditions for uniform convergence and show that a subclass of schemes is also optimal in the sense that |u_i^h−u(x_i)| C min (h, ε). Finally, we show that this class contains higher-order schemes.     

A parallel algorithm for approximate regularity

Spatial regularity amidst a seemingly chaotic image is often meaningful. Many papers in computational geometry are concerned with detecting some type of regularity via exact solutions to problems in geometric pattern recognition. However, real-world applications often have data that is approximate, and may rely on calculations that are approximate. Thus, it is useful to develop solutions that have an error tolerance.

A solution has recently been presented by Robins et al. [Inform. Process. Lett. 69 (1999) 189–195] to the problem of finding all maximal subsets of an input set in the Euclidean plane that are approximately equally-spaced and approximately collinear. This is a problem that arises in computer vision, military applications, and other areas. The algorithm of Robins et al. is different in several important respects from the optimal algorithm given by Kahng and Robins [Patter Recognition Lett. 12 (1991) 757–764] for the exact version of the problem. The algorithm of Robins et al. seems inherently sequential and runs in O(n^5/2) time, where n is the size of the input set. In this paper, we give parallel solutions to this problem.     

A robustness measure for hypercube networks

Hypercube networks offer a feasible cost-effective solution to parallel computing. Here, a large number of low-cost processors with their own local memories are connected to form an n-cube (B_n) or one of its variants; and the inter-processor communication takes place by message passing instead of shared variables. This paper addresses a constrained two-terminal reliability measure referred to as distance reliability (DR) as it considers the probability that a message can be delivered in optimal time from a given node s to a node t. The problem is equivalent to that of having an operational optimal path (not just any path) between the two nodes. In B_n, the Hamming distance between labels of s and t or H(s, t) determines the length of the optimal path between the two nodes. The shortest distance restriction guarantees optimal communication delay between processors and high link/node utilization across the network. Moreover, it provides a measure for the robustness of symmetric networks. In particular, when H(s, t) = n in B_n, DR will yield the probability of degradation in the diameter, a concept which directly relates to fault-diameter. The paper proposes two schemes to evaluate DR in B_n. The first scheme uses a combinatorial approach by limiting the number of faulty components to (2H(s, t) − 2), while the second outlines paths of length H(s, t) and, then generates a recursive closed-form solution to compute DR. The theoretical results have been verified by simulation. The discrepancy between the theoretical and simulation results is in most cases below 1% and in the worst case 4.6%.     

Optimal signal design strategy with improper Gaussian signaling in the Z-interference channel

We propose a thoroughly optimal signal design strategy to achieve the Pareto boundary (boundary of the achievable rate region) with improper Gaussian signaling (IGS) on the Z-interference channel (Z-IC) under the assumption that the interference is treated as additive Gaussian noise. Specifically, we show that the Pareto boundary has two different schemes determined by the two paths manifesting the characteristic of improperly transmitted signals. In each scheme, we derive several concise closed-form expressions to calculate each user’s optimally transmitted power, covariance, and pseudo-covariance of improperly transmitted signals. The effectiveness of the proposed optimal signal design strategy is supported by simulations, and the results clearly show the superiority of IGS. The proposed optimal signal design strategy also provides a simple way to achieve the required rate region, with which we also derive a closed-form solution to quickly find the circularity coefficient that maximizes the sum rate. Finally, we provide an in-depth discussion of the structure of the Pareto boundary, characterized by the channel coefficient, the degree of impropriety measured by the covariance, and the pseudo-covariance of signals transmitted by two users.     

Fast, long-lived renaming improved and simplified

In the long-lived M-renaming problem, N processes repeatedly acquire and release names ranging over {0, …, M − 1}, where M < N. It is assumed that at most k M processes concurrently request or hold names. Efficient solutions to the long-lived renaming problem can be used to improve the performance of applications in which processes repeatedly perform computations whose time complexity depends on the size of the name space containing the processes that participate concurrently. In this paper, we consider wait-free solutions to the long-lived M -renaming problem that use only read and write instructions in an asynchronous, shared-memory multiprocessor. A solution to long-lived renaming is fast if the time complexity of acquiring and releasing a name once is independent of N. We present a new fast, long-lived (k(k + 1)/2)renaming algorithm that significantly improves upon the time and space complexity of similar previous algorithms, while providing a much simpler solution. We also show that fast, long-lived (2k − 1)-renaming can be implemented with reads and writes. This result is optimal with respect to the size of the name space.     

A complete proof on the solution procedure for non-instantaneous deteriorating items with permissible delay in payment

Ouyang et al. [Ouyang, L. Y., Wu, K. S., & Yang C. T. (2006). A study on an inventory model for non-instantaneous deteriorating items with permissible delay in payments. Computers & Industrial Engineering, 51, 637–651] present an inventory model for non-instantaneous deteriorating items with permissible delay in payments. They develop some theorems to characterize the optimal solutions and provide an easy-to-use method to find the optimal replenishment cycle time. Although, their inventory models are correct and interesting, processes of arguments to derive those theorems and the easy-to-use method to search for the optimal replenishment cycle time are not complete. So, the main purpose of this paper is to overcome those shortcomings and present complete proofs for Ouyang et al. (2006).     

CIPP — a versatile analytical model for VBR traffic

Correlated interarrival time Poisson process (CIPP) has been proposed in Proceedings of the Fifth Biennial Conference on Signal Processing and Communications (SPCOM’99), IISc, Bangalore, July 1999, pp. 43–50; J. Indian Inst. Sci. 79 (3) (1999) 233–249] for modeling both the composite arrival process of packets in broadband networks and the individual video source modeling. The CIPP — a generalization of the Poisson process — is a stationary counting process and is parameterized by correlation parameter ‘ρ’, the degree of correlation in adjacent interarrivals and ‘λ’, the intensity of the process. In this paper, we develop the theory for CIPP/M/1 queue and undertake the performance modeling of statistical multiplexer with VBR video traffic in broadband networks using the CIPP/M/1 queue. We first derive the expressions for stationary distributions for queue length and waiting time in a CIPP/M/1 queue. Then, we derive the queuing performance measures of interest. For reasons of feasibility of theoretical performance modeling and realistic compulsions, we propose a deterministic smoothing with random (geometrically distributed) packet sizes. We simulate a queue with (thus smoothed) VBR video trace data as input to compare with the theoretical performance measures derived above. Experimental results show that the CIPP/M/1 queue models well the statistical multiplexer performance with the real-world MPEG-1 VBR video traffic input.     

Two ant-colony algorithms for minimizing total flowtime in permutation flowshops

The problem of scheduling in flowshops with the objective of minimizing total flowtime is studied. For solving the problem two ant-colony algorithms are proposed and analyzed. The first algorithm refers to some extent to ideas by Stuetzle [Stuetzle, T. (1998). An ant approach for the flow shop problem. In: Proceedings of the sixth European Congress on intelligent techniques and soft computing (EUFIT '98) (Vol. 3) (pp. 1560–1564). Aachen: Verlag Mainz] and Merkle and Middendorf [Merkle, D., & Middendorf, M. (2000). An ant algorithm with a new pheromone evaluation rule for total tardiness problems. In: Proceedings of the EvoWorkshops 2000, lecture notes in computer science 1803 (pp. 287–296). Berlin: Springer]. The second algorithm is newly developed. The proposed ant-colony algorithms have been applied to 90 benchmark problems taken from Taillard [Taillard, E. (1993). Benchmarks for basic scheduling problems. European Journal of Operational Research, 64, 278–285]. A comparison of the solutions yielded by the ant-colony algorithms with the best heuristic solutions known for the benchmark problems up to now, as published in extensive studies by Liu and Reeves [Liu, J., & Reeves, C.R. (2001). Constructive and composite heuristic solutions to the P//ΣC_i scheduling problem. European Journal of Operational Research, 132, 439–452, and Rajendran and Ziegler [Rajendran, C., & Ziegler, H. (2004). Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs. European Journal of Operational Research, 155, 426–438], shows that the presented ant-colony algorithms are better, on an average, than the heuristics analyzed by Liu and Reeves and Rajendran and Ziegler.     

The production size and inventory policy for a manufacturer in a two-echelon inventory model

This paper proposes a two-echelon inventory model for a periodical commodity, in which the market and manufacturing channels are combined. This model can be used to solve the production policy, the order policies of the raw materials for the manufacturer, and order size for the retailer. By assuming that the retailers’ demand obeys normal distribution and that the retailer makes orders according to the Newsboy Rule, we derive the necessary and sufficient conditions for the optimal solution of production size, wholesale price, and replenishment cycle of raw materials for the manufacturer. Also, the necessary condition is explored in order to gain managerial insights and economic implications based on numerical examples and sensitivity analysis.     

Optimal Admission Control of Discrete Event Systems with Real-Time Constraints

The problem of optimally controlling the processing rate of tasks in Discrete Event Systems with hard real-time constraints has been addressed in prior work under the assumption that a feasible solution exists. Since this cannot generally be the case, we introduce in this paper an admission control scheme in which some tasks are removed with the objective of maximizing the number of remaining tasks which are all guaranteed feasibility. We derive several optimality properties based on which we develop a computationally efficient algorithm for solving this admission control problem under certain conditions. Moreover, when no future task information is available, we derive necessary and sufficient conditions under which idling is optimal and define a metric for evaluating when and how long it is optimal to idle. Numerical examples are included to illustrate our results.     

New spectral lower bounds on the bisection width of graphs

The communication overhead is a major bottleneck for the execution of a process graph on a parallel computer system. In the case of two processors, the minimization of the communication can be modeled using the graph bisection problem. The spectral lower bound of λ₂|V|/4 for the bisection width of a graph is widely known. The bisection width is equal to λ₂|V|/4 iff all vertices are incident to λ₂/2 cut edges in every optimal bisection.

We present a new method of obtaining tighter lower bounds on the bisection width. This method makes use of the level structure defined by the bisection. We define some global expansion properties and we show that the spectral lower bound increases with this global expansion. Under certain conditions we obtain a lower bound depending on λ₂^β|V| with . We also present examples of graphs for which our new bounds are tight up to a constant factor. As a by-product, we derive new lower bounds for the bisection widths of 3- and 4-regular Ramanujan graphs.     

Existence of multiple positive solutions for functional differential equations

In this paper, the existence of at least three positive solutions for the boundary value problem (BVP) of second-order functional differential equation with the form y″(t) + f(t, y^t) = 0, for t ε [0,1], y(t) -βy′(t) =η(t), for t ε [−τ,0], −γy(t) + Δy′(t) = ζ(t), for t ε [1, 1 + a], is studied. Moreover, we investigate the existence of at least three partially symmetric positive solutions for the above BVP with Δ = βγ.     

Shaking a forced string to rest

In [1] Parks showed that there exists a minimum time T within which a free, taut, vibrating string of finite length can be brought to rest. The string is fastened at the end χ = 0, and the position of the string at the end χ = 1 is assumed to be controlled as a given continuously differentiable function of time.

In this paper we show that if, in addition, the string is under an external force F(χ, t), a similar result can be obtained provided that F satisfies a certain condition.     

Optimal and nearly optimal algorithms for approximating polynomial zeros

We substantially improve the known algorithms for approximating all the complex zeros of an n^th degree polynomial p(x). Our new algorithms save both Boolean and arithmetic sequential time, versus the previous best algorithms of Schönhage [1], Pan [2], and Neff and Reif [3]. In parallel (NC) implementation, we dramatically decrease the number of processors, versus the parallel algorithm of Neff [4], which was the only NC algorithm known for this problem so far. Specifically, under the simple normalization assumption that the variable x has been scaled so as to confine the zeros of p(x) to the unit disc x : |x| ≤ 1, our algorithms (which promise to be practically effective) approximate all the zeros of p(x) within the absolute error bound 2^−b, by using order of n arithmetic operations and order of (b + n)n² Boolean (bitwise) operations (in both cases up to within polylogarithmic factors). The algorithms allow their optimal (work preserving) NC parallelization, so that they can be implemented by using polylogarithmic time and the orders of n arithmetic processors or (b + n)n² Boolean processors. All the cited bounds on the computational complexity are within polylogarithmic factors from the optimum (in terms of n and b) under both arithmetic and Boolean models of computation (in the Boolean case, under the additional (realistic) assumption that n = O(b)).     

Matching sets of 3D line segments with application to polygonal arcmatching

In this paper, we consider two sets of corresponding 3D line segments of equal length. We derive a closed-form solution for the coordinate transform (rotation and translation) that gives the best match between the two sets; best in the sense of a least-squares distance measure between the sets. We use these results as the basis to construct efficient algorithms for solving other problems in computer vision. Specifically, we address the problem of matching polygonal arcs, that is, the problem of finding a match between a short arc and a piece of long arc     

Comment on “Nonlinear optimal tracking control with application to super-tankers for autopilot design” by T. Çimen and S.P. Banks

A recent paper by Çimen and Banks [2004. Nonlinear optimal tracking control with application to super-tankers for autopilot design. Automatica, 40(11), 1845–1863] on optimal control system design for oil tanker propulsion and heading highlighted the importance of accurately representing the dynamics of such a vessel. Results presented in that paper are based on a simulation model that provides unrealistic results for an oil tanker of the size considered. Therefore, the results obtained from the simulated ship control problem are not representative of the physical system being considered. In this communication an alternative, more realistic model is presented and discussed with reference to the original publications that define the ship model dynamics.     

A general and optimal approach for three inventory models with a linear trend in demand

This study provides a general and simple algorithm to obtain an optimal solution for three inventory models with a replenishment batching policy, production batching policy, and an integrated replenishment/production batching policy in a manufacturing system, under a finite time horizon and linear trend in demand. This study determines the replenishment or production schedule with one general equation for these three problems and provides fully theoretical proofs for relaxing some of the conjectures in previous studies. A general and explicit procedure to derive the optimal solution for these three inventory models is presented, while considering both linearly increasing and decreasing demands. In addition, demonstrations of applicability are performed.     

Supply chain models for deteriorating products with ramp type demand rate under permissible delay in payments

In this paper an order level inventory model for deteriorating items with general ramp type demand rate under conditions of permissible delay in payments is proposed. In this model shortages are allowed and partially backlogged. The backlogging rate is variable and dependent on the waiting time for the next replenishment. Its study requires exploring the feasible ordering relations between the time parameters appeared, which leads to three models. For each model the optimal replenishment policy is determined. The sufficient conditions of the existence and uniqueness of the optimal solutions are also provided. Suitably selected numerical examples highlight the obtained results. Sensitivity analysis of the optimal solution with respect to major parameters of the system has been carried out and the implications are discussed.