Simulation of multi-echelon macro-inventory policies

Alternative repair part inventory policies are examined for a multi-echelon logistics system. The policies assessed pertain to the design of multi-echelon systems rather than the evaluation of stock level decisions for individual repair parts. Although the context is one of a military inventory system, the policies examined are of importance in nonmilitary systems where item failure rates are low, and only periodic access to resupply is possible.     

A backward recursive technique for optimal sequential sampling plans

This paper presents a procedure akin to dynamic programming for designing optimal acceptance sampling plans for item-by-item inspection. Using a Bayesian procedure, a prior distribution is specified, and a suitable cost model is employed depicting the cost of sampling, accepting or rejecting the lot. An algorithm is supplied which is digital computer oriented.     

Stock control in a many depot system

The chief problems considered are: (1) In a parallel set of warehouses, how should stocks be allocated? (2) In a system consisting of a central warehouse and several subsidiary warehouses, how much stock should be carried in each? The demands may have known, or unknown, distribution functions. For problem (1), the i-th stock n_i should usually be allocated in proportion to the i-th demand m_i; in special cases, a significant improvement is embodied in the formula (N = total allocable stock)

     

The discrete max-min problem

The historic max-min problem is examined as a discrete process rather than in its more usual continuous mode. Since the practical application of the max-min model usually involves discrete objects such as ballistic missiles, the discrete formulation of the problem seems quite appropriate. This paper uses an illegal modification to the dynamic programming process to obtain an upper bound to the max-min value. Then a second but legal application of dynamic programming to the minimization part of the problem for a fixed maximizing vector will give a lower bound to the max-min value. Concepts of optimal stopping rules may be applied to indicate when sufficiently near optimal solutions have been obtained.     

Suboptimal algorithms for the quadratic assignment problem

The idea of combining relatively simple continuous methods with discrete procedures is used for the construction of suboptimal algorithms for quadratic assignment problems. Depending on the nature of the special problem these steps may vary in complexity. The simplest procedures require minimum storage space and result in tolerable computation times. Different choices of parameters and random variations may be used in order to obtain statistical distributions of suboptimal solutions. Computational results for sample problems indicate improvements on results of Steinberg, Gilmore, and Hillier and Connors.     

Probabilistic priorities in the M/G/1 queue

A simple method is presented for deriving the mean and variance of the queueing time distribution in an M/G/1 queue when the priorities assigned to customers have an assignment probability distribution. Several examples illustrate the results. The mean and variance of the queueing time distribution for the longest service time discipline are derived, and its disadvantages are discussed.     

A finiteness proof for modified dantzig cuts in integer programming

Let be a basic solution to the linear programming problem subject to: where R is the index set associated with the nonbasic variables. If all of the variables are constrained to be nonnegative integers and x_u is not an integer in the basic solution, the linear constraint is implied. We prove that including these “cuts” in a specified way yields a finite dual simplex algorithm for the pure integer programming problem. The relation of these modified Dantzig cuts to Gomory cuts is discussed.     

Computing equilibria via nonconvex programming

The problem of determining a vector that places a system in a state of equilibrium is studied with the aid of mathematical programming. The approach derives from the logical equivalence between the general equilibrium problem and the complementarity problem, the latter being explicitly concerned with finding a point in the set S = {x: < x, g(x)> = 0, g(x) ≦ 0, x ≧ 0}. An associated nonconvex program, min{? < x, g(x) > : g(x) ≦ 0, x ≧ 0}, is proposed whose solution set coincides with S. When the excess demand function g(x) meets certain separability conditions, equilibrium solutions are obtained by using an established branch and bound algorithm. Because the best upper bound is known at the outset, an independent check for convergence can be made at each iteration of the algorithm, thereby greatly increasing its efficiency. A number of examples drawn from economic and network theory are presented in order to demonstrate the computational aspects of the approach. The results appear promising for a wide range of problem sizes and types, with solutions occurring in a relatively small number of iterations.