Yasemin Serin

Competitive newsvendor problems with the same Nash and Stackelberg solutions

Consider two newsvendors: (i) they compete satisfying substitutable demands searching Nash equilibrium or (ii) one is the leader deciding first, the other responds optimally playing a Stackelberg game. The leader profits more than she does in (i). We present conditions under which the leaders profit does not improve from (i) to (ii).

Markov decision processes under observability constraints

We develop an algorithm to compute optimal policies for Markov decision processes subject to constraints that result from some observability restrictions on the process. We assume that the state of the Markov process is unobservable. There is an observable process related to the unobservable state. So, we want to find a decision rule depending only on this observable process. The objective is to minimize the expected average cost over an infinite horizon. We also analyze the possibility of performing observations in more detail to obtain improved policies.

Pooling through lateral transshipments in service parts systems

We study the inventory management problem of a service center operating in a decentralized service parts network. The service centers collaborate through inventory and service pooling, and through sharing information on the inventory status. Upon demand arrival, a service center may request a part from the other center, in which case a payment is made. Under this competitive and collaborative environment, we first characterize the optimal operating policy of an individual service center. Through computational analysis we identify the conditions under which pooling is most beneficial to the service center, and make an assessment of different pooling strategies which are commonly adopted in practice and in the literature. Finally, we analyze the effect of interaction between the centers on the benefit of pooling.

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.

An interactive probabilistic approach to multi-criteria sorting

This article addresses the problem of sorting alternatives evaluated by multiple criteria among preference-ordered classes. An interactive probabilistic sorting approach is developed in which the probability of an alternative being in each class is calculated and alternatives are assigned to classes keeping the probability of incorrect assignments below a specified small threshold value. The decision maker is occasionally required to place alternatives to classes. The probabilities for unassigned alternatives are updated in light of the new information and the procedure is repeated until all alternatives are classified. This is the first sorting approach reported in the literature to use an explicit probability of classifying alternatives that is consistent with the underlying preference structure of the decision maker. The proposed approach is demonstrated in a problem concerning the sorting MBA programs.

Lot Splitting Under Learning Effects with Minimal Revenue Requirements and Multiple Lot Types

The lot splitting problem in the presence of learning is addressed. This work is an extension of an approach proposed for splitting in the case of a single item. We address the issue of a minimal revenue requirement from partial deliveries until a predetermined time. This is achieved by imposing a constraint on what is originally an unconstrained optimization problem. When sublots of different items are involved, the optimal splitting decisions have to be combined with the sequencing of the deliveries. Numerical examples are presented to demonstrate the proposed approach.

A nonlinear programming model for partially observable Markov decision processes: Finite horizon case

The concept of partially observable Markov decision processes was born to handle the problem of lack of information about the state of a Markov decision process. If the state of the system is unknown to the decision maker then an obvious approach is to gather information that is helpful in selecting an action. This problem was already solved using the theory of Markov processes. We construct a nonlinear programming model for the same problem and develop a solution algorithm that turns out to be a policy iteration algorithm. The policies found this way are easier to use than the policies found by the existing method, although they have the same optimal objective value.

Implementable Policies: Discounted Cost Case

We consider a Markov decision process (MDP) with finite state space S and finite action set A. The state space is partitioned into K sets S 1, S 2, …, S K. A stationary randomized policy is described by the parameters {α ia i ∈, S, a ∈ A}, where αia = the parobability that action a is taken when the system is in state i. A policy is called implementable if α ia = α ja for all α ∈ A whenever states i and j belong to a common subset S τ for some r = 1, 2,…, K In this paper we discuss the importance of implementable policies and present an algorithm to find implementable policies that (locally) minimize the expected total discounted cost over infinite horizon.

Comments on: A policy improvement method for constrained average Markov decision processes [Oper. Res. Lett. 35 (2007) 434-438]

Markov decision processes (MDP) under constraints were analyzed in a number of studies other than those given in the references of [1]. Ross and Varadarajan [2] consider MDP under linear constraints while Smith [4], Serin and Kulkarni [3] have nonlinear constraints in terms of the steady state probabilities. In general, the optimal policy for a constrained MDP can be randomized. In [3], such an optimal policy is obtained by applying a feasible descent method to the resulting nonlinear programming problem, where there is more than one nonlinear constraint. The algorithm turns out to be a policy iteration algorithm. Smith [4] solves the same problem under deterministic policies. In [1], a single constraint is considered, and the policies are restricted to be deterministic, which is sub-optimal in general. The constrained quantity is an expectation that gives rise to a