A. P. Muhlemann

A variable holding cost rate EOQ model

Abstract This paper presents a modification to the classical EOQ formula, which takes into account the disproportionate change in cost that may be incurred in holding stocks, as the average value of the stock held increases. A revised formula is derived, and this is illustrated with an example. The implications of this modification on the total cost are discussed.

The dynamic aspects of a production scheduling problem

This paper presents a single machine scheduling problem with sequence dependent changeover times. An optimizing solution procedure and various appropriate heuristics are reviewed. We then go on to consider the performance of these and other heuristics in the dynamic situation, as new jobs arrive to be processed and have to be added into the existing schedule at some time. Clearly an ideal solution would be to reschedule as each new job arrived, but as this is not generally practical from a computational viewpoint, it has to be carried out less frequently. The actual frequency of this rescheduling is clearly of importance, and some of the heuristics are more adaptable to this than others. Some results are presented which attempt to quantify this adaptability for the heuristics in question, and it is demonstrated that the best heuristic for the static problem is not necessarily the best heuristic in the dynamic situation.

A problem of aggregate scheduling An application of goal programming

The paper introduces mi overall scheduling problem. One crucial aspect is identified; this is the production of an aggregate schedule which is to be fed into the detailed scheduling package currently employed. The problem is seen to be that of achieving a balance between a smooth work-load on the factory floor and matching production with promised delivery dates. A goal programming model for this coordination is developed and discussed. Numerical examples illustrating the approach are presented, and computational experience is discussed.

A unified approach to the acquisition of subjective data in R&D

Many quantitative models have been developed and tried in the R&D management environment. Although very successful in providing an insight framework, their actual everyday use appears to have been limited. Although there could be many reasons for this, one of the main ones is the general problem of data collection. The subjective nature of the topic makes this inherently difficult. A new approach to this problem is presented which is based on a method of prioritized hierarchies, backed up by a simple procedure of pairwise comparisons. A case study is presented of a group decision-making activity based in a research environment. Numerical results are given which show how the participants behaved in practice.

Group Decision Making and Multiple Criteria — A Documented Application

Most models of decision making processes have assumed the existence of a single rational decision maker. In practice many experiments have been reported which negate some of these assumptions. This paper adopts an approach initiated by Saaty as a method of allowing for apparent inconsistency of the decision maker. It is extended to cover the group situation where the point of decision is diffuse. A real life problem is presented, based in the R & D/ Marketing interface, in which a group analyse and make choices amongst a series of alternatives each having multiple attributes. The main purpose of the paper is to gain better understanding of ill-structured group decision making which will lead to the development of better methodology.

A stochastic programming model for aggregate production planning

Abstract This paper looks at a problem of production planning at the level of the work centre, rather than of the individual machine. The approach is based on methodology which combines aspects of decision analysis with mathematical programming procedures. A model is developed which can take into account various real life factors in the planning phase, including delaying production, and the probability of production being scrapped, or of extra work being required. An extension to the multiple objective situation is outlined, and some computational results are reported.

A scheduling problem with machine flexibility

A problem of scheduling the production of pharmaceuticals in a limited number of vessels is presented. It has the characteristics of sequence dependent changeover times, multi-stage production, parallel usage of vessels and flexibility in the choice of vessels. An optimizing procedure is discussed, but dismissed as computationally infeasible. Consequently, a heuristic is developed, and its performance evaluated. Typical results are also reported.

A general reorder quantity-reorder level (>Q, r) inventory model with complex shortage cost structure

This paper develops a general [>Q, r) single item model, based on the usual assumptions of stationary, normally distributed probabilistic demand, but covering simultaneously all three types of shortage costs commonly dealt with in the literature; namely shortage costs proportional to the number of units short and to the duration of the shortage, or proportional to the number of units short, or proportional to the number of stockout occasions. The model considers that the item stocked is subject to throe different uses, each being linked with the different type of shortage cost. A methodology for the graphical solution of the model is proposed, an illustrative nomograph for such a solution presented, and the results of some sensitivity analyses for some of the assumptions are discussed.

Developments in undergraduate education for operational research in the U.K. since 1965

Abstract Until quite recently most courses in Operational Research at Universities in the U.K. have been at postgraduate or post experience level. Entrance requirements have frequently been a degree or equivalent professional qualification, and for some of the more well established and popular courses, industrial experience in addition. An often used argument is that the inter-disciplinary origins and nature of Operational Reseach require those entering the profession to have basic training in some discipline, most commonly reflected in the possession of a degree or professional qualification. Frequently this is a scientific or quantitative subject. Engineering, Mathematics, Economics are common examples. In recent years, however, there has been an increasing trend within Universities to mount undergraduate courses involving substantial portions of material which is taught under the title of Operational Research. This paper looks at this trend in more detail, and the courses themselves are analysed. Some of the reasons for these developments are discussed, their effects on the OR Profession and the Education Sector outlined, and future trends suggested.