This paper is concerned with the linear programming solutions to sequential decision (or control) problems in which the stochastic element is Markovian and in which the objective is to minimize the discounted sum of expected costs when a discount factor \lambda, 0 \leqq \lambda < 1, is used. In praticular, it deals with a class of "separable" problems for which it is possible to define a "reduced" linear programming problem which will yield the optimal policy and the shadow prices for this problem. The reduced problem involves a substantially smaller number (e.g., 3N vs. N²) of variables...</1,>

This paper considers an N period production planning problem in which a sequence of known demands d₁, d₂,..., d_N must be satisfied. The cost of production in period t consists of a setup cost K_t plus a marginal cost per unit c_t. The cost of carrying a unit of inventory into period t is h_{t - 1}....

We consider the problem of setting safety stock when both the demand in a period and the lead time are random variables. There are two cases to consider. In the first case the parameters of the demand and lead time distributions are known; in the second case they are unknown and must be...

This paper considers a model for the maintenance of a deteriorating system with a discrete state space. At discrete points in time a sequence of maintenance decisions is to be made. These decisions are either to leave the system in its present state, or by performing maintenance to place it in a...

This paper describes the form of the optimal operating policy for a three asset cash balance problem in which (1) holding and penalty costs are proportional to the level of the cash balance, (2) the costs incurred in transferring funds between cash and earning assets are proportional to the...

We focus on backup agreements between a catalog company and manufacturers---a scheme to provide upstream sourcing flexibility for fashion merchandise. A backup agreement states that if the catalog company commits to a number of units for the season, the manufacturer holds back a constant...

A method for determining where to locate the inspection stations in a multistage production process with imperfect inspection is presented. Dynamic programming is used to establish that the optimal expected total cost function at every stage is piecewise linear and concave. While the optimal...