Multicriteria variable selection for classification of production batches

In many industrial processes hundreds of noisy and correlated process variables are collected for monitoring and control purposes. The goal is often to correctly classify production batches into classes, such as good or failed, based on the process variables. We propose a method for selecting the best process variables for classification of process batches using multiple criteria including classification performance measures (i.e., sensitivity and specificity) and the measurement cost. The method applies Partial Least Squares (PLS) regression on the training set to derive an importance index for each variable. Then an iterative classification/elimination procedure using k-Nearest Neighbor is carried out. Finally, Pareto analysis is used to select the best set of variables and avoid excessive retention of variables. The method proposed here consistently selects process variables important for classification, regardless of the batches included in the training data. Further, we demonstrate the advantages of the proposed method using six industrial datasets.     

Augmenting the lot sizing order quantity when demand is probabilistic

In this paper we consider a single item, discrete time, lot sizing situation where demand is random and its parameters (e.g., mean and standard deviation) can change with time. For the appealing criterion of minimizing expected total relevant costs per unit time until the moment of the next replenishment we develop two heuristic ways of selecting an appropriate augmentation quantity beyond the expected total demand through to the planned (deterministic) time of the next replenishment. The results of a set of numerical experiments show that augmentation is important, particularly when orders occur frequently (i.e., the fixed cost of a replenishment is low relative to the costs of carrying one period of demand in stock) and the coefficient of variability of demand is relatively low, but also under other specified circumstances. The heuristic procedures are also shown to perform very favourably against a hindsight, baseline (s, S) policy, especially for larger levels of non-stationarity.     

Numerical simulation of oblique and multidirectional wave propagation and breaking on steep slope based on FEM model of Boussinesq equations

Creating a representative numerical simulation of the propagation and breaking of waves along slopes is an important problem in engineering design. Most studies on wave breaking have focused on the propagation of normal incident waves on gentle slopes. In practice, however, waves on steep slopes are obliquely incident or multidirectional irregular waves. In this paper, the eddy viscosity term is introduced to the momentum equation of the improved Boussinesq equations to model wave dissipation caused by breaking and friction, and a numerical model based on an unstructured finite element method (FEM) is established based on the governing equations. It is applied to simulate wave propagation on a steep slope of 1:5. Parallel physical experiments are conducted for comparative analysis that considered a large number of cases, including those featuring of normal and oblique incident regular and irregular waves, and multidirectional waves. The heights of the incident wave increase for different periods to represent different kinds of waves breaking. Based on examination, the effectiveness and accuracy of the numerical model is verified through a comprehensive comparison between the numerical and the experimental results, including in terms of variation in wave height, wave spectrum, and nonlinear parameters. Satisfactory agreement between the numerical and experimental values shows that the proposed model is effective in representing the breaking of oblique incident regular waves, irregular waves, and multidirectional incident irregular waves. However, the initial threshold of the breaking parameter η_t^(I) takes different values for oblique and multidirectional waves. This needs to be paid attention when the breaking of waves is simulated using the Boussinesq equations.     

A critical condition for the cost density in the circular city model

In regard to the problem of determining minimal-cost routes in a region with variable cost density, it has been shown elsewhere that, for a radially symmetric cost density which is inversely proportional to the distance from a central point O, the minimal cost between two pointsP ₁ andP ₂ which are equidistant from O is attained along a circular arc. This is not true in general for an arbitrary, radially symmetric cost density. In the present paper, critical conditions for determining when a circular arc will be a relative minimal-cost path are derived. These criteria are then employed to examine a class of special cases in which the cost density is constant outside the city limits.The author would like to express his appreciation to Professor J. B. Keller for calling his attention to the work of R. K. Luneberg and to Professor K. A. Brakke for some helpful advice.     

A recursive method for the F-policy G/M/1/K queueing system with an exponential startup time

This paper deals with the optimal control of a finite capacity G/M/1 queueing system combined the F-policy and an exponential startup time before start allowing customers in the system. The F-policy queueing problem investigates the most common issue of controlling arrival to a queueing system. We provide a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining interarrival time, to develop the steady-state probability distribution of the number of customers in the system. We illustrate a recursive method by presenting three simple examples for exponential, 3-stage Erlang, and deterministic interarrival time distributions, respectively. A cost model is developed to determine the optimal management F-policy at minimum cost. We use an efficient Maple computer program to determine the optimal operating F-policy and some system performance measures. Sensitivity analysis is also studied.     

Value iteration in countable state average cost Markov decision processes with unbounded costs

We deal with countable state Markov decision processes with finite action sets and (possibly) unbounded costs. Assuming the existence of an expected average cost optimal stationary policyf, with expected average costg, when canf andg be found using undiscounted value iteration? We give assumptions guaranteeing the convergence of a quantity related tong?Ν _n (i), whereΝ _n (i) is the minimum expectedn-stage cost when the process starts in statei. The theory is applied to a queueing system with variable service rates and to a queueing system with variable arrival parameter.     

Mean width inequalities for isotropic measures

In this paper, we establish Barthe’s mean width inequalities for continuous isotropic measures by a direct approach rather than using the Brascamp–Lieb inequality. The following results are obtained: among the convex hulls of the support of isotropic measures on S ^n–1, the regular simplex inscribed in the Euclidean unit ball has maximal ?-norm; in the dual situation, there is a reverse result for their polar bodies. Moreover, the case of even isotropic measures is also investigated.     

Optimal paths in bi-attribute networks with fractional cost functions

An important routing problem is to determine an optimal path through a multi-attribute network which minimizes a cost function of path attributes. In this paper, we study an optimal path problem in a bi-attribute network where the cost function for path evaluation is fractional. The problem can be equivalently formulated as the “bi-attribute rational path problem” which is known to be NP-complete. We develop an exact approach to find an optimal simple path through the network when arc attributes are non-negative. The approach uses some path preference structures and elimination techniques to discard, from further consideration, those (partial) paths that cannot be parts of an optimal path. Our extensive computational results demonstrate that the proposed method can find optimal paths for large networks in very attractive times.     

On the flow cost lowering problem

This paper presents the flow cost lowering problem (FCLP), which is an extension to the integral version of the well-known minimum cost flow problem (MCFP). While in the MCFP the flow costs are fixed, the FCLP admits lowering the flow cost on each arc by upgrading the arc. Given a flow value and a bound on the total budget which can be used for upgrading the arcs, the goal is to find an upgrade strategy and a flow of minimum cost. The FCLP is shown to be NP-hard even on series–parallel graphs. On the other hand the paper provides a polynomial time approximation algorithm on series–parallel graphs.     

关于逐步回归分析的一个注记

逐步回归是多元回归分析筛选自变量的一种重要思想方法。利用矩阵消去变换的知识,证明了逐步回归第一步引入变量,第二步引入变量,第三步不可能剔除变量。最后对经典Hald数据利用SAS统计软件,编程实现逐步回归分析.     

A remark on split least-squares mixed element procedures for pseudo-parabolic equations

In this paper, we introduce two novel split least-squares mixed element procedures for pseudo-parabolic equations. By selecting the least-squares functional properly, each procedure can be split into two independent symmetric positive definite sub-procedures. One of sub-procedures is for the primitive unknown variable u, which is the same as the standard Galerkin finite element procedure and the other is for the introduced flux variable σ. Optimal order error estimates are developed. A numerical example is given to show the efficiency of the introduced schemes.     

A parametric algorithm for convex cost network flow and related problems

The convex cost network flow problem is to determine the minimum cost flow in a network when cost of flow over each arc is given by a piecewise linear convex function. In this paper, we develop a parametric algorithm for the convex cost network flow problem. We define the concept of optimum basis structure for the convex cost network flow problem. The optimum basis structure is then used to parametrize v, the flow to be transsshipped from source to sink. The resulting algorithm successively augments the flow on the shortest paths from source to sink which are implicitly enumerated by the algorithm. The algorithm is shown to be polynomially bounded. Computational results are presented to demonstrate the efficiency of the algorithm in solving large size problems. We also show how this algorithm can be used to (i) obtain the project cost curve of a CPM network with convex time-cost tradeoff functions; (ii) determine maximum flow in a network with concave gain functions; (iii) determine optimum capacity expansion of a network having convex arc capacity expansion costs.     

A strong characterization on the ΩEP-property

In this paper a result of A. Illanes and J.J. Charatonik obtained in [J.J. Charatonik, A. Illanes, Mappings on dendrites, Topology Appl. 144 (2004) 109-132, Corollary 5.14] is extended, by showing that a locally connected continuum X has the nonwandering-eventually-periodic property. (ΩEP-property) iff X is a dendrite that does not contain a homeomorphic copy of the null-comb. Also using “An engine breaking the ΩEP-property” constructed by P. Pyrih et al. in [P. Pyrih, J. Hladký, J. Novák, M. Sterzik, M. Tancer, An engine breaking the ΩEP-property, Topology Appl. 153 (2006) 3621-3626] the results obtained in [J.J. Charatonik, A. Illanes, Mappings on dendrites, Topology Appl. 144 (2004) 109-132; H. Méndez-Lango, On the ΩEP-property, Topology Appl. 154 (2007) 2561-2568] and [P. Pyrih, J. Hladký, J. Novák, M. Sterzik, M. Tancer, An engine breaking the ΩEP-property, Topology Appl. 153 (2006) 3621-3626] are extended, by proving that every nonlocally connected continuum X that contains a nondegenerate arc A and a point p∈A such that X is not connected in kleinen at p does not have the ΩEP-property. Answering Question 1 of [P. Pyrih, J. Hladký, J. Novák, M. Sterzik, M. Tancer, An engine breaking the ΩEP-property, Topology Appl. 153 (2006) 3621-3626]. Finally an uncountable family of non-locally connected continua containing arcs with the ΩEP-property is shown.     

Inventory of damagable items with variable replenishment rate,stock-dependent demand and some units in hand

Items made of glass, ceramics, etc., break/get damaged during the storage due to the accumulated stress of heaped stock. For the first time, a deterministic inventory model of such a damagable item is developed with variable replenishment when both demand and damage rates are stock-dependent in polynomial form. Here replenishment rate for the first cycle is partly instantaneous and partly varies with demand. For the next cycle, the variable replenishment is augmented when the inventory level falls to Q₀, the instantaneous replenishment amount for the first cycle. After this, the cycle repeats itself. The amount, Q₀ is also here varied and the optimum Q₀ and Q (inventory level) are evaluated following the profit maximization principle in integral form. The model is illustrated numerically and sensitivity analyses are presented.     

Economic design of an adaptive <Emphasis Type="Italic">T</Emphasis><Superscript>2</Superscript> control chart

Varying three parameters of the Hotelling's T² control chart, namely, the sample size, the sampling interval length, and the action limit, results in a great improvement over the traditional T² control chart particularly for the small process shift. This paper presents the economic model for designing the variable parameters T² chart. In the economic design, a cost function is constructed, involving the cost of sampling and testing, the cost of false alarm, the cost to detect and remove the assignable cause, and the cost when the process is operating out-of-control. Also, a heuristic method of finding optimal values of adaptive design parameters for minimizing the cost function is presented. Variable and fixed parameters T² control charts are compared with respect to the expected loss per unit time. Furthermore, the effects of the initial sample number (used for estimating the parameters of F-distribution) upon the operating cost and adaptive design parameters are examined.     

Consistent variable selection in large panels when factors are observable

In this paper we develop an econometric method for consistent variable selection in the context of a linear factor model with observable factors for panels of large dimensions. The subset of factors that best fit the data is sequentially determined. Firstly, a partial R² rule is used to show the existence of an optimal ordering of the candidate variables. Secondly, We show that for a given order of the regressors, the number of factors can be consistently estimated using the Bayes information criterion. The Akaike will asymptotically lead to overfitting of the model. The theory is established under approximate factor structure which allows for limited cross-section and serial dependence in the idiosyncratic term. Simulations show that the proposed two-step selection technique has good finite sample properties. The likelihood of selecting the correct specification increases with the number of cross-sections both asymptotically and in small samples. Moreover, the proposed variable selection method is computationally attractive. For K potential candidate factors, the search requires only 2K regressions compared to 2^K for an exhaustive search.     

Single item lot-sizing problem for a warm/cold process with immediate lost sales

We consider the dynamic lot-sizing problem with finite capacity and possible lost sales for a process that could be kept warm at a unit variable cost for the next period t + 1 only if more than a threshold value Q_t has been produced and would be cold, otherwise. Production with a cold process incurs a fixed positive setup cost, K_t and setup time, S_t, which may be positive. Setup costs and times for a warm process are negligible. We develop a dynamic programming formulation of the problem, establish theoretical results on the structure of the optimal production plan in the presence of zero and positive setup times with Wagner–Whitin-type cost structures. We also show that the solution to the dynamic lot-sizing problem with lost sales are generated from the full commitment production series improved via lost sales decisions in the presence of a warm/cold process.     

A multicriteria approach to the location of public facilities

We argue that practical problems involving the location of public facilities are really multicriteria problems, and ought to be modeled as much. The general criteria are those of cost and service, but there exist several distinct criteria in each of those two categories. For the first category, fixed investment cost, fixed operating cost, variable operating cost, total operating cost, and total discounted cost are all reasonable criteria to consider. In terms of service, both demand served and response time (or distance traveled) are appropriate criteria, either agglomerated or considered on the basis of the individual clients. In this paper we treat such multicriteria questions in the framework of a model for selecting a subset of M sites at which to establish public facilities in order to serve client groups located at N distinct points. We show that for some combinations of specific criteria, parametric solutions of a generalized assignment problem (GAP) will yield all efficient solution. In most other cases the efficient solutions can be found through parametric solution of a GAP with additional constraints of a type which can be incorporated into an existing algorithm for the GAP. Rather than attempting to find all efficient solutions, however, we advocate an interactive approach to the resolution of multicriteria location problems and elaborate on a specific interactive algorithm for multicriteria optimization which for the present model solves a finite sequence of GAP's or GAP-type problems. Finally, some similar aspects of private sector location problems are discussed.     

On the discrete-time Geo/G/1 queue with randomized vacations and at most J vacations

This paper examines a discrete-time Geo/G/1 queue, where the server may take at most J − 1 vacations after the essential vacation. In this system, messages arrive according to Bernoulli process and receive corresponding service immediately if the server is available upon arrival. When the server is busy or on vacation, arriving messages have to wait in the queue. After the messages in the queue are served exhaustively, the server leaves for the essential vacation. At the end of essential vacation, the server activates immediately to serve if there are messages waiting in the queue. Alternatively, the server may take another vacation with probability p or go into idle state with probability (1 − p) until the next message arrives. Such pattern continues until the number of vacations taken reaches J. This queueing system has potential applications in the packet-switched networks. By applying the generating function technique, some important performance measures are derived, which may be useful for network and software system engineers. A cost model, developed to determine the optimum values of p and J at a minimum cost, is also studied.