Markov decision processes with restricted observations: Finite horizon case

In this article we consider a Markov decision process subject to the constraints that result from some observability restrictions. We assume that the state of the Markov process under consideration is unobservable. The states are grouped so that the group that a state belongs to is observable. So, we want to find an optimal decision rule depending on the observable groups instead of the states. This means that the same decision applies to all the states in the same group. We prove that a deterministic optimal policy exists for the finite horizon. An algorithm is developed to compute policies minimizing the total expected discounted cost over a finite horizon. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44 : 439–456, 1997     

An interactive branch-and-bound algorithm for bicriterion nonconvex/mixed integer programming

Although there has been extensive research on interactive multiple objective decision making in the last two decades, there is still a need for specialized interactive algorithms that exploit the relatively simple structure of bicriterion programming problems. This article develops an interactive branch-and-bound algorithm for bicriterion nonconvex programming problems. The algorithm searches among only the set of nondominated solutions since one of them is a most preferred solution that maximizes the overall value function of the decision maker over the set of achievable solutions. The interactive branch-and-bound algorithm requires only pairwise preference comparisons from the decision maker. Based on the decision maker's responses, the algorithm reduces the set of nondominated solutions and terminates with his most preferred nondominated solution. Branching corresponds to dividing the subset of nondominated solutions considered at a node into two subsets. The incumbent solution is updated based on the preference of the decision maker between two nondominated solutions. Fathoming decisions are based on the decision maker's preference between the incumbent solution and the ideal solution of the node in consideration.     

Integrated capacity,demand, and production planning with subcontracting and overtime options

Models for integrated production and demand planning decisions can serve to improve a producer's ability to effectively match demand requirements with production capabilities. In contexts with price‐sensitive demands, economies of scale in production, and multiple capacity options, such integrated planning problems can quickly become complex. To address these complexities, this paper provides profit‐maximizing production planning models for determining optimal demand and internal production capacity levels under price‐sensitive deterministic demands, with subcontracting and overtime options. The models determine a producer's optimal price, production, inventory, subcontracting, overtime, and internal capacity levels, while accounting for production economies of scale and capacity costs through concave cost functions. We use polyhedral properties and dynamic programming techniques to provide polynomial‐time solution approaches for obtaining an optimal solution for this class of problems when the internal capacity level is time‐invariant. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007