An analysis of degeneracy

Degeneracy in linear programming models has been analyzed for its impacts on algorithmic properties. A complementary analysis here is on what the solutions mean. The framework presented is couched in marginal sensitivity analysis, introducing concepts of “compatible bases” and “transition graphs”.     

Decentralized stockage policies in a multiechelon environment

Characteristics of supply performance at the top echelon of an optimally managed multiechelon supply system are investigated; insights are developed which are useful in devising coordinated single-echelon policies which can approximate the benefits derived from multiechelon management.     

A class of inventory models with customer impatience

Classical inventory models generally assume either no backlogging of demands or unlimited backlogging. This paper treats the case wherein backlogged customers are willing to wait for a random period of time for service. A broad class of such models is discussed, with a more complete analysis performed on a simple subclass. Steady state equations are derived and solved assuming exponentially distributed interarrival times of customers, order delivery lead times, and customer patience.     

A note on a paper by houston and huffman

This paper calls attention to an experimental design which enhances the efficiency of the technique described by B. F. Houston and R. A. Huffman [3]. This alternative design is a modification of the simplex lattice design developed by Scheffé [6] for the mixture problem. While not possessing the optimal statistical properties of the central composite design proposed in [3], such as minimum bias and minimum variance, this modified design is optimum with respect to the number of design points employed; hence, it is the minimum cost design. Further, the design proposed in this note is excellent for use in multiple-block experimentation, which is very often required with constrained systems.     

Bayes adaptive control of two-echelon inventory systems i: development for a special case of one-station lower echelon and monte carlo evaluation

Bayes adaptive control policies are developed in the present paper for the special case of a one-station lower echelon: a Poisson distribution of demand, whose mean is assumed to have a prior gamma distribution. The cost structure is of a common type. The ordering policy for the upper echelon, which minimizes expected cost, is replaced by a new type of policy, called Bayes prediction policy. This policy does not require tedious computations, of the sort required by dynamic programming solutions. The characteristics of the policies are studied by Monte Carlo simulation, and supplemented by further theoretical development.     

The relationship between decision variables and penalty cost parameter in (Q,R) inventory models

This paper is concerned with the optimum decision variables found using order quantity, reorder point (Q, R) inventory models. It examines whether the optimum variables (Q* and R*) are necessarily monotonic functions of the backorder cost parameter (or equivalently of the performance objective). For a general class of models it is proved that R* must increase as the performance objective is raised, and an inequality condition is derived which governs how Q* will change. Probability distributions of lead time demand are cited or found for which Q* increases, Q* decreases, and Q* is independent of increases in performance objectives or backorder cost parameter.     

Values for optimum reject allowances

Industrial situations exist where it is necessary to estimate the optimum number of parts to start through a manufacturing process in order to obtain a given number of completed good items. The solution to this problem is not straightforward when the expected number of rejects from the process is a random variable and when there are alternative penalties associated with producing too many or too few items. This paper discusses various aspects of this problem as well as some of the proposed solutions to it. In addition, tables of optimum reject allowances based on a comprehensive model are presented.