Een indelingsprobleem

Summary A branch and bound algorithm is given to solve the following problem: To each pair of elements (i,j) from a set X={l,…, n} a number r_ij with r_ij≥ 0, r_ij=r_ij and r_ij= 0 has been assigned. Find a prescribed number of disjoint subsets P₁…,P_m from X, such that Experiments indicate that an optimal solution is usually found in a small number of iterations, but the verification may be rather time consuming. The algorithm may be used to find the minimum value of m for which a partitioning of X with z= 0 exists. The algorithm appears to be efficient for finding this ‘chromatic number of a graph’.     

Een smaak-onderzoek

A comparison has been made between three designs for flavor testing. In the test-situation even a flavor-difference which might be noticed by only a few people was of practical importance. In addition not only the unjustified rejection of the null hypothesis (no flavor-difference), but also the unjustifed rejection of the alternative hypothesis might have important practical consequences.     

Een lading van kraaltjes

Summary An urn containing 200 red beads and 1000 yellow ones is frequently used for demonstration of the hypergeometric or binomial distribution. Experiments show that the practical frequency distribution differs slightly but definitely from the theoretical one. This deviation turned out to be caused by electro-static forces.     

Een systeem van kostenbeheersende productieplanning

In this paper a system of cost-controlled production planning is described. This system considers all kinds of costs associated with a production in phases (e.g. production of units, production of subassemblies, assembly) which may be affected by the planning, such as set-up costs, costs of transport, control, inventories, capacity and changes in capacity.
The mathematical model leads to a linear or mixed discrete-linear programming problem whose solution gives for each time period considered the size of the capacities which should be used and of the series of different products which should be produced. Practical recommendations are given for obtaining a sufficiently satisfying solution.     

Een meer-loketten probleem met overwerk

In an office a number of employees do the same kind of work. The jobs arrive at random and the holding time is exponential; the queuediscipline is first in, first served. The mean queuelength is shortened by work done in overtime according to the rule that on every day on which the total number of jobs exceeds a certain number N, one or more extra hours of work will be done. The distribution of the number of jobs in the office, the mean value of this number and the probability of overtime are given. The model is illustrated with a numerical example.     

Een algemene methode tot leemtevulling

An exposition of the missing plot technique often applied in analysis of variance is given in very general terms.
Non-orthogonality mostly implies heavy computations. If the scheme of observations is almost orthogonal this technique, however, supplies in a simple way unbiassed and efficient estimates of the expectation values which occur in a linear hypothesis underlying an analysis of variance. Moreover the correct residual sum of squares required for a test or a confidence interval estimation is obtained without difficulty.
A correct test of an effect or an interaction will be provided by two estimates, the first under the null-hypothesis, the second under the alternative hypothesis. In the case of non-orthogonality this may imply two separate applications of the discussed technique. The difference between the two residual sums of squares will be used for the numerator of a valid F-criterion.
The technique is illustrated by an example.     

Een berekeningsmethode voor de logistische curve

Summary “Simple estimation of the parameters of the logistic curve.” By means of an appropriate transformation of the dependent variable Y_t into a simple function of Y_t, which depends only linearly on time, one of the parameters can be estimated in the usual way. A second transformation leads to the estimation of the two remaining parameters. As a numerical illustration two examples are presented.     

Een berekeningsmethode voor de logistische curve

Summary  " Simple estimation of the parameters of the logistic curve ."
By means of an appropriate transformation of the dependent variable Y _t into a simple function of Y _t, which depends only linearly on time, one of the parameters can be estimated in the usual way. A second transformation leads to the estimation of the two remaining parameters. As a numerical illustration two examples are presented.     

Een mathematisch model voor een reserveringsprobleem

A mathematical model for a booking problem
Air companies have several problems in connection with booking. Clients may book for a certain flight some time in advance and are also allowed to cancel their bookings.
As a result of this it is possible that an airplane leaves with some places empty or that the company, expecting some clients to cancel their booking, has sold to many places.
In both cases losses are the result. In this paper a booking policy that minimizes the expected losses is developed.     

Een toepassing van "importance sampling"

Summary  This paper describes an experiment with "importance sampling", to show how much reduction of the computation time and sample size can be achieved in comparison with the usual Monte Carlo method. A comparison is made between each of the three methods of "importance sampling" and the usual Monte Carlo method by the determination of the expression

Of the three methods A, B and C the first one uses the shifted exponential distribution, the second one uses the gamma distribution, and the third one uses the exponential distribution with modified parameter. These three methods have all smaller variances, ranges and sample sizes than the usual Monte Carlo method. Their order of preference is A, B, C. With respect to computing time only the method A is significantly better. So only the method A is an improvement in respect of both the sample size and the computing time.     

Een criterium voor het kiezen van een proefopzet

A characterization of D-optimality is given together with several examples where D-optimal designs are computed.     

Een model voor discreet verdeelde grootheden met negatieve correlatie

Summary
A model for negatively correlated variables.
A mathematical model is described with which a bivariate distribution of two negatively correlated binomially distributed variables can be constructed. Let be given a vase with W white, Z black and R red balls; N = W + Z + R; P1= W: N;P2 = Z: N.
Let be drawn a random sample with replacement of n balls. Let be w = number of white en z = number of black balls; w + z < n. Then and are binomially distributed variates, correlated according to (1).
At the end of the paper the author formulates the following statistical problem: let be drawn a finite number of times () such random samples of n balls. The pairs w, z furnish a correlation coefficient r, which itself is a stochastical variable. How is the distribution of? In particular what are the expectation (, N) and the standard deviation (k, n, N)     

Een steekproef ter vaststelling van de verdeling van de hoenderstapel

A sample estimate of the poultry distribution
In 1954 a sample survey was carried out of the returns of the agricultural census, May 1954, in order to establish the distribution of the number of holdings and the number of poultry, by size-group of arable land and by size-group of number of poultry. A simple 10 per cent, sample was planned and the expected variances of the numbers of poultry in each size-group were estimated beforehand. The method of estimation is indicated in this paper. This resulted in comparatively high relative errors in the size-groups above 500 hens and also in the size-groups of arable land. Therefore holdings with 500 hens and over were enumerated completely. Some tests were performed with the sample results and finally the efficiency of the stratification is discussed.