On using discrete random models within decision support systems

In this paper we review how models for discrete random systems may be used to support practical decision making. It will be demonstrated how organizational requirements determine to a large extent the type of model to be applied as well as the way in which the model should be applied. This demonstration is given via several practical examples of Markov chain models, cohort models, and Markov decision models. The examples are drawn from various areas ranging from the purely technical to social applications. It is demonstrated that the models that are needed for supporting the decision making process may vary from purely descriptive models to optimization models. Similarly, the obvious way of application of a model may vary from straightforward numerical analysis to interactive modelling procedures based upon managerial evaluation. It will also be demonstrated how the numerical methods to be used depend on the structure of the model as well as on applicational aspects. The numerical aspect is strongly related to the aforementioned aspects, since the model choiche heavily determines the computational possibilities

FORMASY : forecasting and recruitment in manpower systems

In this paper the tools are developed for forecasting and recruitment planning in a graded manpower system. Basic features of the presented approach are: - the system contains several grades or job categories in which the employees stay for a certain time before being promoted or leaving the system, - promotability and leaving rate for any employee depend on time spent in the job category and personal qualifications (like education, experience, age), - recruitment is not necessarily restricted to the lowest level ln the system, - several planning aims and restrictions are allowed. The approach is based on a generalized Markov model for the dynamic behaviour of an individual employee. On this Markov model a forecasting procedure and a recruitment-scheduling procedure are based

A note on dynamic programming with unbounded rewards

In a recent paper, Lippman presents sufficient conditions for Denardo's N-stage contraction in discounted semi-Markov decision processes with unbounded rewards. In this note it is demonstrated that Lippman's conditions may be replaced by weaker conditions which even imply 1-stage contraction. The verification of the conditions of this note is somewhat easier

Solving linear systems by methods based on a probabilistic interpretation

In this paper it is demonstrated how the probabilistic concept of a stopping time in a random process may be used to generate an iterative method for solving a system of linear equations. Actually all known iterative approximation methods for solving linear equations are generated by various choices of a stopping time e.g. the point and block Jacobi methods, the point and block Gauss-Seidel Methods and overrelaxation methods are covered. The probabilistic approach offers -in a natural way- the possibility of adapting the solution technique to the special structure of the problem. Moreover, posterior bounds for the solution are constructed, which lead to faster convergence of the approximations than with usual prior bounds

Successive approximations for Markov decision processes and Markov games with unbounded rewards

The aim of this paper is to give an overview of recent developments in the area of successive approximations for Markov decision processes and Markov games. We will emphasize two aspects, viz. the conditions under which successive approximations converge in some strong sense and variations of these methods which diminish the amount of computational work to be executed. With respect to the first aspect it will be shown how much unboundedness of the rewards may be allowed without violation of the convergence. With respect to the second aspect we will present four ideas, that can be applied in conjunction, which may diminish the amount of work to be done. These ideas are: I. the use of the actual convergence of the iterates for the construction of upper and lower bounds (McQueen bounds), 2. the use of alternative policy improvement procedures (based on stopping times), 3. a better evaluation of the values of actual policies in each iteration step by a value oriented approach, 4. the elimination of suboptimal actions not only permanently, but also temporarily. The general presentation ~s given for Markov decision processes with a final section devoted to the possibilities of extension to Markov games

FORMASY : forecasting and recruitment in manpower systems

In this paper the tools are developed for forecasting and recruitment planning in a graded manpower system. Basic features of the presented approach are: - the system contains several grades or job categories in which the employees stay for a certain time before being promoted or leaving the system, - promotability and leaving rate for any employee depend on time spent in the job category and personal qualifications (like education, experience, age), - recruitment is not necessarily restricted to the lowest level ln the system, - several planning aims and restrictions are allowed. The approach is based on a generalized Markov model for the dynamic behaviour of an individual employee. On this Markov model a forecasting procedure and a recruitment-scheduling procedure are based

The generation of successive approximation methods for Markov decision processes by using stopping times

In this paper we will consider several variants of the standard successive approximation technique for Markov decision processes. It will be shown how these variants can be generated by stopping times. Furthermore it will be demonstrated how this class of techniques can be extended to a class of value oriented techniques. This latter class contains as extreme elements several variants of Howard's policy iteration method. For all methods presented extrapolations are given in the form of MacQueen's upper and lower bounds

A principle for generating optimization procedures for discounted Markov decision processes

No abstract

One and Two Way Packaging in the Dairy Sector

Choosing packaging material for dairy products and soft drinks is an interesting issue at the moment. Discussions arise on the costs impacts and environmental impacts of both one way packaging and reusable packaging. The aim of this article is to develop an evaluation tool providing costs and environmental impacts of the PC-bottle and the GT-packs in the dairy sector, considering forward and return flows. The evaluation tool enables the user to analyse the costs and environmental impacts of a supply chain with and without return flows using scenario analyses with respect to the use of various carrier types and the number of return loops. It appears that costs differences between PC-bottles and GT-pack are quite small. The PC bottle has a better environmental profile than the GT-pack. Scenario analysis on the carriers results in the advice to use preferably roll-in-containers with direct delivery, secondly roll-in-containers with delivery via distribution centers, thirdly in case of direct delivery either cartons or crates and cartons in case of delivery via distribution centers.pricing;supply chain management;reverse logistics;environment;life cycle assessment