Showing papers in "ORiON in 2007"

Threat evaluation and weapon assignment decision support: A review of the state of the art

Abstract: In a military environment an operator is typically required to evaluate the tactical situation in real-time and protect defended assets against enemy threats by assigning available weapon systems to engage enemy craft. This environment requires rapid operational planning and decision making under severe stress conditions, and the associated responsibilities are usually divided between a number of operators and computerized decision support systems that aid these operators during the decision making processes. The aim in this paper is to review the state of the art of this kind of threat evaluation and weapon assignment decision support process as it stands within the context of a ground based air defence system (GBADS) at the turn of the twenty first century. However, much of the contents of the paper may be generalized to military environments other than a GBADS one.

Combining morphological analysis and Bayesian Networks for strategic decision support

Abstract: Morphological analysis (MA) and Bayesian networks (BN) are two closely related modelling methods, each of which has its advantages and disadvantages for strategic decision support modelling. MA is a method for defining, linking and evaluating problem spaces. BNs are graphical models which consist of a qualitative and quantitative part. The qualitative part is a cause-and-effect, or causal graph. The quantitative part depicts the strength of the causal relationships between variables. Combining MA and BN, as two phases in a modelling process, allows us to gain the benefits of both of these methods. The strength of MA lies in defining, linking and internally evaluating the parameters of problem spaces and BN modelling allows for the definition and quantification of causal relationships between variables. Short summaries of MA and BN are provided in this paper, followed by discussions how these two computer aided methods may be combined to better facilitate modelling procedures. A simple example is presented, concerning a recent application in the field of environmental decision support.

The essential multiobjectivity of linear programming

Abstract: It is argued that any non-trivial real world problems involve multiple objectives. The simplistic approach of combining objectives in linear form can generate highly misleading and biased results, and is poor operational research practice. Such biases are illustrated by means of a simple example, and it is demonstrated that two simple approaches based on goal programming and piecewise linear value functions can largely resolve these problems. These methods require careful attention to problem structuring but are easily implemented by use of standard linear programming (LP) packages.

Stochastic inventory management at a service facility with a set of reorder levels

Abstract: We consider a continuous review perishable inventory system at a service facility with a finite waiting capacity. The maximum inventory level is fixed and the customers arrive according to a Markov arrival process. The life time of each item and the service time are assumed to have independent exponential distributions. Unlike the conventional method of placing an order at a prefixed level, we consider a set of reorder levels with a specified probability for placing an order at a particular reorder level. This allows the modelling of a situation in which the decision maker may advance or postpone the placement of reorder as a result of his/her memory on the past supply behaviour. The reordering quantity depends upon the reorder level at which an order was triggered and the lead time is distributed as negative exponential. The joint probability distribution of the number of customers in the system and the inventory level is obtained in the steady state. We also derive some stationary system performance measures and compute the total expected cost rate under a cost structure. We also present a numerical illustration.

Variable selection in multiple linear regression : the influence of individual cases

Abstract: The influence of individual cases in a data set is studied when variable selection is applied in multiple linear regression. Two different influence measures, based on the C_p criterion and Akaike's information criterion, are introduced. The relative change in the selection criterion when an individual case is omitted is proposed as the selection influence of the specific omitted case. Four standard examples from the literature are considered and the selection influence of the cases is calculated. It is argued that the selection procedure may be improved by taking the selection influence of individual data cases into account.

Operations research at CSIR: A brief history through cases

Abstract: Apart from work in the mining industry during the 1950s, the first real Operations Research (OR) group in South Africa was established at CSIR in the early 1960s. Those initially involved in this group played a significant role in establishing OR at various universities in South Africa. The OR group at CSIR did, however, continue and today the group still exists. This paper presents a brief history of this group and endeavours to provide a glimpse of some of the projects conducted over the many years since its establishment.

A procurement decision model for a video rental store — A case study

Abstract: A procurement decision model for a video rental store is presented in this paper. The model is based on inventory management, but many classical inventory management principles are inappropriate since the commodities (movie titles) are removed from, and after a certain time period, returned to inventory. The commodities also have a decaying demand in general; hence the video rental store owner (the decision maker) is required to procure new titles periodically. The question addressed in this paper is how to determine which movie titles to acquire, and how many copies of each in order to best maximise profit. An approximated demand function is presented, and attributes of movie titles in inventory are used to classify candidate movie titles and predict their future demand. This allows the decision maker to select the most profitable candidate items from a list, whilst remaining within a predetermined budget. The procurement decision model is evaluated by means of predicting the expected turnover using the procurement decision model solution, and then comparing it to the turnover achieved using the procurement strategy followed by the store owner. The model is not prescriptive - the decision maker may still utilise his/her experience to acquire new movie titles. The procurement decision model, however, does assist the decision making process by presenting a point of departure from which procurement decisions may be made.

Selection and scheduling of jobs with time-dependent duration

Abstract: In this paper two mathematical programming models, both with multiple objective functions, are proposed to solve four related categories of job scheduling problems. All four of these categories have the property that the duration of the jobs is dependent on the time of implementation and in some cases the preceding job. Furthermore, some jobs (restricted to subsets of the total pool of jobs) can, to different extents, run in parallel. In addition, not all the jobs need necessarily be implemented during the given time period.

Operations research and development

Abstract: The paper begins with a discussion of the concepts "operations research" and "development." An overview is next given of the RDP (Reconstruction and Development Programme), which still embodies the vision of development in South Africa associated with the political transition in 1994. The efforts of ORSSA (the Operations Research Society of South Africa) to help with the implementation of the RDP are described. The international OR (Operations Research) community has been involved in various ways with the promotion of development, especially through IFORS (the International Federation of Operational Research Societies), and these are reviewed. Sustainable development, which deals specifically with a long-term view of development, is mentioned briefly. Lastly some suggestions are made as to how ORSSA and its members could help to promote development in South Africa. In the Appendix a summary is given of a paper by Gerhard Geldenhuys in which he analyzes the needs identified by the RDP as well as relevant OR methods.

On the ?(d) - chromatic number of a complete balanced multipartite graph

Abstract: In this paper we solve (approximately) the problem of finding the minimum number of colours with which the vertices of a complete, balanced, multipartite graph G may be coloured such that the maximum degrees of all colour class induced subgraphs are at most some specified integer d 2 N. The minimum number of colours in such a colouring is referred to as the Δ(d)–chromatic number of G. The problem of finding the Δ(d)–chromatic number of a complete, balanced, multipartite graph has its roots in an open graph theoretic characterisation problem and has applications conforming to the generic scenario where users of a system are in conflict if they require access to some shared resource. These conflicts are represented by edges in a so–called resource access graph, where vertices represent the users. An efficient resource access schedule is an assignment of the users to a minimum number of groups (modelled by means of colour classes) where some threshold d of conflict may be tolerated in each group. If different colours are associated with different time periods in the schedule, then the minimum number of groupings in an optimal resource access schedule for the above set of users is given by the Δ(d)–chromatic number of the resource access graph. A complete balanced multipartite resource access graph represents a situation of maximum conflict between members of different user groups of the system, but where no conflict occurs between members of the same user group (perhaps due to an allocation of diverse duties to the group members). Keywords : Graph/vertex colouring, chromatic number, maximum degree. ORiON Vol. 23 (1) 2007: pp. 29-49

An algorithm for the ‹ r , s › - domination number of a tree

Abstract: Suppose that at most r units of some commodity may be positioned at any vertex of a graph G = (V,E) while at least s (>= r) units must be present in the vicinity (i.e. closed neighbourhood) of each vertex. Suppose that the function f : V -> {0,...,r}, whose values are the numbers of units stationed at vertices, satisfies the above requirement. Then f is called an s-dominating r-function. We present an algorithm which finds the minimum number of units required in such a function and a function which attains this minimum, for any tree.