Minimal forecast horizons in equipment replacement models with multiple technologies and general switching costs

This article considers the problem of equipment replacement in which the replacement decision at a particular time must take into account (i) the state of the existing machine in use, (ii) the available replacement alternatives at the time, (iii) the future advances in the relevant technologies with regard to the equipment under consideration, and (iv) costs of switching between different technologies. A methodology that attains minimal forecast horizons for the problem is developed. A numerical example illustrates the methodology.     

A note on the influence of missing operations on scheduling problems

This paper attempts to resolve the existing confusion concerning missing operations. Scheduling problems are classified in two groups: (i) null-continuous (NC)—comprising the problems where an optimal schedule remains optimal on replacement of arbitrarily small processing times (existing operations) with zeros (missing operations); (ii) null-discontinuous (NDC)—comprising those problems which are not null-continuous.     

Application of level crossing analysis to discrete state processes in queueing systems

In this paper we introduce a discrete state level crossing analysis and present some basic results and a key theorem of level crossings. We illustrate the fertility of the discrete state level crossing analysis by applying it to queueing systems with (i) bulk arrival, (ii) instantaneous feedback, (iii) limited waiting space, and (iv) to machine interference problems.     

Planning horizon procedures for machine replacement models with several possible replacement alternatives

This paper develops a forward algorithm and planning horizon procedures for an important machine replacement model where it is assumed that the technological environment is improving over time and that the machine-in-use can be replaced by any of the several different kinds of machines available at that time. The set of replacement alternatives may include (i) new machines with different types of technologies such as labor- and capital- intensive, (ii) used machines, (iii) repairs and/or improvements which affect the performance characteristics of the existing machine, and so forth. The forward dynamic programming algorithm in the paper can be used to solve a finite horizon problem. The planning horizon results give a procedure to identify the forecast horizon T such that the optimal replacement decision for the first machine based on the forecast of machine technology until period T remains optimal for any problem with horizon longer than T and, for that matter, for the infinite horizon problem. A flow chart and a numerical example have been included to illustrate the algorithm.     

A note on two IFR systems

We present probabilistic proofs for the following two facts: (i) A k out of n system of i.i.d (independent identically distributed). IFR (increasing failure rate) components has an IFR life distribution. (ii) A compound Poisson process with nonnegative i.i.d jumps with PF₂ distribution is IFR.     

On parallel machine replacement problems with general replacement cost functions and stochastic deterioration

The parallel machine replacement problem consists of finding a minimum cost replacement policy for a finite population of economically interdependent machines. In this paper, we formulate a stochastic version of the problem and analyze the structure of optimal policies under general classes of replacement cost functions. We prove that for problems with arbitrary cost functions, there can be optimal policies where a machine is replaced only if all machines in worse states are replaced (Worse Cluster Replacement Rule). We then show that, for problems with replacement cost functions exhibiting nonincreasing marginal costs, there are optimal policies such that, in any stage, machines in the same state are either all kept or all replaced (No‐Splitting Rule). We also present an example that shows that economies of scale in replacement costs do not guarantee optimal policies that satisfy the No‐Splitting Rule. These results lead to the fundamental insight that replacement decisions are driven by marginal costs, and not by economies of scale as suggested in the literature. Finally, we describe how the optimal policy structure, i.e., the No‐Splitting and Worse Cluster Replacement Rules, can be used to reduce the computational effort required to obtain optimal replacement policies. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Optimal production growth for the machine loading problem

This paper investigates a production growth logistics system for the machine loading problem (generalized transportation model), with a linear cost structure and minimum levels on total machine hours (resources) and product types (demands). An algorithm is provided for tracing the production growth path of this system, viz. in determining the optimal machine loading schedule of machines for product types, when the volumes of (i) total machine hours, and (ii) the total amount of product types are increased either individually for each total or simultaneously for both. Extensions of this methodology, when (i) the costs of production are convex and piecewise linear, and (ii) when the costs are nonconvex due to quantity discounts, and (iii) when there are upper bounds for productions are also discussed. Finally, a “goal-programming” production growth model where the specified demands are treated as just goals and not as absolute quantities to be satisfied is also considered.     

一种采用应力分离法的杂交/混合板壳单元

本文利用一种采用应力分离法的杂交/混合板壳有限元模型分析板壳结构静力学问题。分析表明,该元素在总体水平上没有多余零能模式。而且,该元素通过了薄板的闭锁试验,对薄壳算例也没有观察到闭锁现象。与参考解相比,该元素对各种壳结构均能适用,且收敛性较好,精度也较高。     

General trigger-off replacement procedures for two-unit systems

A trigger-off replacement policy, suggested and analyzed in [1], for two-unit systems composed of identical units, is generalized and extended in this work in several ways. In the first part of the paper we obtain the appropriate integral equations for nonidentical units and then use them for a complete solution of the case of two units, whose lifetimes are distributed according to general Erlang distributions. In the second part of the paper we extend the trigger-off policy itself by allowing preventive replacements of units which reach a certain critical age. The system stops working if either one of the two units fails or reaches its critical age. Both cases present natural replacement possibilities for the remaining unit, provided that its age exceeds a predetermined critical age. Finally, we consider the question of which policy parameters, i.e. control limits and critical ages, to choose when facing a real-life situation. Using the criterion of expected costs per unit time in the long run, we show how to find the optimal parameters which minimize this objective function. The fact that a restricted optimization, within the class of trigger-off replacement policies, leads to the global optimal policy has been proved in [2] by a different approach.     

Two‐machine flow shop no‐wait scheduling with a nonavailability interval

We study a two‐machine flow shop scheduling problem with no‐wait in process, in which one of the machines is not available during a specified time interval. We consider three scenarios of handing the operation affected by the nonavailability interval. Its processing may (i) start from scratch after the interval, or (ii) be resumed from the point of interruption, or (iii) be partially restarted after the interval. The objective is to minimize the makespan. We present an approximation algorithm that for all these scenarios delivers a worst‐case ratio of 3/2. For the second scenario, we offer a 4/3‐approximation algorithm. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Closure properties of the relevation transform*

Sufficient conditions under which the relevation of two probability distributions is (i) NBU, (ii) IFRA, (iii) IFR are derived. The result for case (iii) corrects an error in a previous article by Baxter.     

A note on “resource flexibility with responsive pricing”

We revisit the capacity investment decision problem studied in the article “Resource Flexibility with Responsive Pricing” by Chod and Rudi [Operations Research 53, (2005) 532–548]. A monopolist firm producing two dependent (substitutable or complementary) products needs to determine the capacity of one flexible resource under demand risk so as to maximize its expected profit. Product demands are linear functions of the prices of both products, and the market potentials are random and correlated. We perform a comparative statics analysis on how demand variability and correlation impact the optimal capacity and the resulting expected profit. In particular, C&R study this problem under the following assumptions/approximations: (i) demand intercepts follow a bivariate Normal distribution; (ii) demand uncertainty is of an additive form; (iii) and under approximate expressions for the optimal capacity and optimal expected profit. We revisit Propositions 2, 3, 4, 5, and 10 of C&R without these assumptions and approximations, and show that these results continue to hold (i) for the exact expressions for the optimal expected profit and optimal capacity, and (ii) under any arbitrary continuous distribution of demand intercepts. However, we also show that the additive demand uncertainty is a critical assumption for the C&R results to hold. In particular, we provide a case of multiplicative uncertainty under which the C&R results (Propositions 2 and 3) fail. © 2010 Wiley Periodicals, Inc. Naval Research Logistics 2010     

A note on a paper by W. Szwarc

In this note the authors call for a change of the optimality criteria given by Theorem 3 in section 5 of the paper of W. Szwarc “On Some Sequencing Problems” in NRLQ Vol. 15, No. 2 [2]. Further, two cases of the three machine problem, namely, (i) ≦ and (ii) ≦ are considered, and procedures for obtaining optimal sequences in these cases are given. In these cases the three-machine problem is solved by solving n (the number of jobs) two-machine problems.     

On the bivariate negative binomial distribution of mitchell and paulson

The bivariate negative binomial distribution of Mitchell and Paulson [17] for the case b = c = 0 is shown to be equivalent to the accident proneness model of Edwards and Gurland [4] and Subrahmaniam [19,20]. The diagonal series expansion of its joint probability function is then derived. Two other formulations of this distribution are also considered: (i) as a mixture model, which showed how it arises as the discrete analogue to the Wicksell-Kibble bivariate gamma distribution, and (ii) as a consequence of the linear birth-and-death process with immigration.     

由新比旧好元件组成的指数寿命系统的特性研究

文中研究了由独立的新比旧好元件组成的指数寿命系统,证明了:(i)对单调系统,它本质上是由指数寿命的元件串联而成;(ii)对系统的寿命是元件寿命的情形,除了一个元件是指数的外,其余元件的寿命分布均在零处退化。     

THE PEACE DIVIDEND EFFECT OF TURKISH CONVERGENCE TO THE EU: A MULTI‐REGION DYNAMIC CGE MODEL ANALYSIS FOR GREECE AND TURKEY

This paper examines the peace dividend effect of Turkish convergence to EU membership. By employing a multi‐region dynamic CGE model, we examine the prospect for conflict resolution if Turkey becomes an EU member. The model allows us to analyse several scenarios that imply varying amounts of reduction of the military expenditure/GDP ratios. On the one hand, this change will cause a decrease in sectoral demand for military expenditures, while on the other hand, reallocation of the reduced expenditure on (i) education, (ii) tax decrease, and (iii) infrastructure, should have a huge growth impact. Our dynamic CGE simulation experiments emphasize the economic gain for all parties involved.     

Scheduling on a single machine with a single breakdown to minimize stochastically the number of tardy jobs

Jobs with known processing times and due dates have to be processed on a machine which is subject to a single breakdown. The moment of breakdown and the repair time are independent random variables. Two cases are distinguished with reference to the processing time preempted by the breakdown (no other preemptions are allowed): (i) resumption without time losses and (ii) restart from the beginning. Under certain compatible conditions, we find the policies which minimize stochastically the number of tardy jobs.     

Estimating defence budget saving from disarmament: the United States’ case

Probing the technology in the production of US national defence by using a dynamic cost‐function model with adjustment costs, this paper evaluates the effect of reducing the level of national defence on the defence budget saving. Our inquiry involves estimating the defence production structure without output data for non‐market goods that are normally unavailable. Our findings include: (i) the United States behaves rationally to minimize cost in the production of national defence; (ii) the adjustment costs are larger in disarmament than in military build‐up; (iii) due to the adjustment costs peculiar to disarmament, the defence budget saving from disarmament appears small, but cutbacks allow great savings on the defence budget.     

Military spending and budget deficits: the impact of US military spending on public debt in Europe (1988–2013)

The aim of this paper is to study the relationship between military spending and sovereign debt in a panel of 13 European countries. In particular, under the assumption of the interdependence of military spending between US and European countries, we analyse whether US military spending affected European sovereign debt in the period 1988–2013. The empirical estimation is based on different steps: (i) a unit root test; (ii) an Arellano–Bond panel estimation and a linear fixed effect model; and (iii) a FMOLS estimation to highlight the long run relationship between debt and relevant variables. General results highlight that debt burden of European countries is: (1) positively associated with US military burden and (2) negatively associated with average military burden of other European countries.     

Group testing procedures with quantitative features and incomplete identification

We present a group testing model for items characterized by marker random variables. An item is defined to be good (defective) if its marker is below (above) a given threshold. The items can be tested in groups; the goal is to obtain a prespecified number of good items by testing them in optimally sized groups. Besides this group size, the controller has to select a threshold value for the group marker sums, and the target number of groups which by the tests are classified to consist only of good items. These decision variables have to be chosen so as to minimize a cost function, which is a linear combination of the expected number of group tests and an expected penalty for missing the desired number of good items, subject to constraints on the probabilities of misclassifications. We treat two models of this kind: the first one is based on an infinite population size, whereas the second one deals with the case of a finite number of available items. All performance measures are derived in closed form; approximations are also given. Furthermore, we prove monotonicity properties of the components of the objective function and of the constraints. In several examples, we study (i) the dependence of the cost function on the decision variables and (ii) the dependence of the optimal values of the decision variables (group size, group marker threshold, and stopping rule for groups classified as clean) and of the target functionals (optimal expected number of tests, optimal expected penalty, and minimal expected cost) on the system parameters.© 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011