An improved branch and bound procedure for n × m flow shop problems

This paper considers the classical nXm flow shop sequencing problem. An improved branch and bound procedure is proposed. Computational experience shows that the proposed procedure is more efficient compared to the existing optimizing procedures.     

A new bivariate negative binomial distribution

A new bivariate negative binomial distribution is derived by convoluting an existing bivariate geometric distribution; the probability function has six parameters and admits of positive or negative correlations and linear or nonlinear regressions. Given are the moments to order two and, for special cases, the regression function and a recursive formula for the probabilities. Purely numerical procedures are utilized in obtaining maximum likelihood estimates of the parameters. A data set with a nonlinear empirical regression function and another with negative sample correlation coefficient are discussed.     

A note on integer solutions to linear fractional interval programming problems by a branch & bound technique

This paper provides a method for solving linear fractional interval programming problems in integers with the help of a branch and bound technique.     

Parametric analysis of linear programs with upper bounded variables

Linear programming problems with upper bounded variables can be solved by regular simplex method by considering upper bounding constraints as explicit constraints of the problem. However, more efficient methods exist which consider these upper bound constraints implicitly. When parametric analysis for problems with upper bounds is to be carried out, one can use the regular parameter analysis by considering the upper bound constraints explicitly. This paper develops formulas for parametric analysis where upper bound constraints are used implicitly, thus reducing the size of the basic matrix.     

An algorithm for a class of loading problems

The loading problem we consinder is to assign a set of discrete objects, each having a weight, to a set of boxes, each of which has a capacity limit, in such a way that every object is assigned to a box and the number of boxes used is minimized. A characterization of the assignments is offered and used to develop a set of rules for generating nonredundant assignments. The rules are incorporated into an implicit enumeration algorithm. The algorithm is tested against a very good heuristic. Computational experience shows that the algorithm is highly efficient, solving problems of up to 3600 0-1 variables in a CPU second.     

An algorithm for 0-1 multiple-knapsack problems

The 0-1 multiple-knapsack problem is an extension of the well-known 0-1 knapsack problem. It is a problem of assigning m objects, each having a value and a weight, to n knapsacks in such a way that the total weight in each knapsack is less than its capacity limit and the total value in the knapsacks is maximized. A branch-and-bound algorithm for solving the problem is developed and tested. Branching rules that avoid the search of redundant partial solutions are used in the algorithm. Various bounding techniques, including Lagrangean and surrogate relaxations, are investigated and compared.     

Optimal maintenance-repair policies for the machine repair problem

We consider a model with M + N identical machines. As many as N of these can be working at any given time and the others act as standby spares. Working machines fail at exponential rate λ, spares fail at exponential rale γ, and failed machines are repaired at exponential rate μ. The control variables are λ. μ, and the number of removable repairman, S, to be operated at any given time. Using the criterion of total expected discounted cost, we show that λ, S, and μ are monotonic functions of the number of failed machines M, N, the discount factor, and for the finite time horizon model, the amount of time remaining.     

Discounted production scheduling and employment smoothing

We consider the problem of minimizing the sum of production, employment smoothing, and inventory costs over a finite number of time periods where demands are known. The fundamental difference between our model and that treated in [1] is that here we permit the smoothing cost to be nonstationary, thereby admitting a model with discounting. We show that the values of the instrumental variables are nondecreasing in time when demands are nondecreasing. We also derive some asymptotic properties of optimal policies.     

Bayes sequential design of stock levels

Bayesian determination of optimal stock levels is studied for the case of Poisson distribution of the demand variable, and prior gamma distribution of the expected demand. Bayes sequential procedure is derived, assuming that stock level can be adjusted at the beginning of each period so that a shortage can be immediately replenished and an overstock can be corrected. The Bayes sequential procedure is more difficult to obtain if this assumption is removed. A dynamic programming method for obtaining the general Bayes sequential procedure is outlined. Finally, an empiric Bayes estimation procedure of the optimal Bayesian stock level is presented.     

State and society in Asia

India and China are the 2 most populous countries of the world; in the 1950s, both countries initiated a centrally planned program for rapid development within vastly differing political systems. China embarked India's policy encouraged only voluntary acceptance of family planning. In both cases, however, government involvement in population forms a part of comprehensive national planning. Both countries rely on a limited resource base and technological sophistication in order to alleviate mass poverty and misery. The political implications of population growth cannot be neatly isolated from those that are generated by social and economic forces of change in a society that is in a transitional stage of modernization and development. Development has not been an unmixed bleesing; population growth is one of its counterproductive outcomes. The development process has begun to draw increasing attention to hitherto neglected correlates of fertility decline, such as a reduction in infant mortality, universal education, improvement in women's status, and women's participation in economic activity outside the home, all of which eventually result in greater demand for family planning services. Both the Indian and Chinese models highlight the importance of taking the people into one's confidence; the response of the common people to official initiatives is critical in securing a reduction in fertility levels. China has adopted a 1 child family policy, yet it is unreasonable to expect that the Indian people would agree to a nationally prescribed family size norm below 2 children. The principal determinant of future population trends in both these countries is the course of their politics. The success of developing countries will be assured if the developed nations support their progress without being worried about their population growth, which is the result of their unavoidable failure to modernize their social and economic structures.