Operations & Supply Chain Management

We examine a multi-server queueing system with Poisson arrivals in which customers require simultaneous service from a random number of servers. Servers assigned to the same customer begin and end service concurrently. Service times are, in general, assumed to be exponentially distributed. A system point approach is presented as a framework for obtaining the waiting time distribution for each customer type. Explicit solutions are derived for the two-server system.

This paper establishes the existence of a solution to the optimality equations in undiscounted semi-Markov decision models with countable state space, under conditions generalizing the hitherto obtained results. In particular, we merely require the existence of a finite set of states in which every pair of states can reach each other via some stationary policy, instead of the traditional and restrictive assumption that ever stationary policy has a single irreducible set of states.

This paper presents methods for solving allocation problems that can be stated as convex knapsack problems with generalized upper bounds. Such bounds may express upper limits on the total amount allocated to each of several subsets of activities. In addition our model arises as a subproblem in more complex mathematical programs. We therefore emphasize efficient procedures to recover optimality when minor changes in the parameters occur from one problem instance to the next. These considerations lead us to propose novel data structures for such problems.

In continuous review models with a fixed delivery lag T, the state of the system is conveniently described by the net inventory position = (inventory on hand) plus (outstanding orders), in spite of most cost components depending on the actual inventory on hand. To relate these two inventory concepts one observes that the distribution of the inventory on hand at time t + T is determined by the inventory position at time t.

Consider a renewal process {Xn, n ≥ 1} for which there is defined an associated sequence of independent and identically distributed random variables {Bn, n ≥ 1} such that Bn is the length of a subinterval of Xn. We show that when attention is restricted only to B-intervals, the asymptotic joint distribution of the residual life and total life of a B-interval is that of a renewal process generated by {Bn, n ≥ 1}.

This paper considers the solution of Markov decision problems whose parameters can be obtained only via approximating schemes, or where it is computationally preferable to approximate the parameters, rather than employing exact algorithms for their computation. Various models are presented in which this situation occurs. Furthermore, it is shown that a modified value-iteration method may be employed, both for the discounted version and for the undiscounted version of the model, in order to solve the optimality equation and to find optimal policies.

Recent papers have shown that Π∞k = 1 P(k) = limm→∞ (P(m) ... P(1)) exists whenever the sequence of stochastic matrices {P(k)}∞k = 1 exhibits convergence to an aperiodic matrix P with a single subchain (closed, irreducible set of states). We show how the limit matrix depends upon P(1).