Decision Making & Negotiations

Consider a central depot that supplies several locations experiencing random demands. Periodically, the depot may place an order for exogenous supply. Orders arrive after a fixed leadtime, and are then allocated among the several locations. Each allocation reaches its destination after a further delay. We consider the special case where the penalty-cost/holding-cost ratio is constant over the locations. Several approaches are given to approximate the dynamic program describing the problem.

We address the combined problem of allocating a scarce resource among several locations, and planning deliveries using a fleet of vehicles. Demands are random, and holding and shortage costs must be considered in the decision along with transportation costs. We show how to extend some of the available methods for the deterministic vehicle routing problem to this case. Computational results using one such adaptation show that the algorithm is fast enough for practical work, and that substantial cost savings can be achieved with this approach.

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.

In this paper we study the determination of forward foreign exchange rates. An exchange rate is the price of one currency in terms of another currency, and a forward rate is a contractual exchange rate established at a point in time for a transaction that will take place at the maturity date on the contract in the future. Well-organized forward markets exist for all major currencies of the world for various maturities, with the most active contract lengths being one, three, six, and twelve months.

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.