Multi-Skilled Workforce Optimisation

This paper describes a problem faced by CS Energy's Swanbank Power Station in the Australian state of Queensland. It involved the personnel scheduling (rostering) of staff with multiple skill levels at the power station. Such a problem can be classified using the six stage construction process proposed by Ernst et al. We assume that the three processes of ‘demand modelling,’ ‘shift starting times’ and ‘task scheduling’ are specified. We are concerned with the essential processes of ‘day off scheduling,’ ‘line of work construction’ and ‘shift assignment to staff’ with requirements to maintain multiple skills. Several other authors have reported results for staff with hierarchical skills while the methods proposed in this paper are for non-hierarchical skill sets. The paper describes a set covering approach to the multi-skilled rostering problem. We propose a number of solution strategies for the set covering approach and give a comparison of the results.     

Inequity aversion in a joint economic lot sizing environment with asymmetric holding cost information

Screening contracts (or ‘menu of contracts’) are frequently used for aligning the incentives in supply chains with private information. In this context, it is assumed that all supply chain parties are strictly (expected) profit-maximizing. However, previous empirical work shows that this is a critical assumption. In fact, it seems that inequity adverse subjects are willing to invest money for achieving higher relative payoffs. Interestingly, the classical approach to design incentive compatible mechanisms gives the agent cheap leeway to increase relative pecuniary payoffs and thereby achieving more equitable profit allocations, because the agent is left (almost) indifferent between two contract alternatives. In other words, we argue (and actually observe in laboratory experiments) that this classical approach of contract design allows the agent to achieve more equitable outcomes at low cost. Since the agent’s better relative performance solely stems from reducing the principal’s payoffs, we observe a substantial negative impact on the overall supply chain performance. The present work relaxes the assumption of the profit-maximizing buyer (agent) in a serial supply chain for a lot sizing framework with asymmetrically distributed holding cost information and deterministic end-customer demand. The study provides researchers and managers an approach on how to account for disadvantageous inequity aversion (ie, the agent suffers from profits being lower than the principals profits) by designing a contract that anticipates such behaviour while providing a solution method for the resulting non-linear mathematical program. We denote the resulting contract as ‘behavioural robust’, since it limits the inefficiency losses that result if agents exhibit disadvantageous inequity aversion instead of being strictly profit-maximizing. A numerical study compares the advantages of the ‘behavioural robust’ contract against the classical screening contract. The results highlight that supply chain performance losses can be substantially reduced under the behavioural robust contract.     

Evaluating models for classifying customers in retail banking collections

When seeking to establish a repayment strategy with delinquent borrowers, it is useful to determine how they are likely to behave, so that an optimal use of resources can be made. We examine two behavioural classifications (‘settle immediately’ versus ‘not settle immediately’, and ‘make some repayment’ versus ‘make no repayment’) and apply a variety of rules for predicting into which class each customer is likely to belong. Since no such rule will yield perfect predictions, the way in which performance is evaluated is crucial in choosing a good rule, and hence subsequently in obtaining accurate predictions of likely future behaviour. We examine some popular standard performance evaluation criteria, showing that they have major weaknesses. We describe and illustrate the use of an alternative measure that overcomes these weaknesses.     

A signal-recovery system: asymptotic properties,and construction of an infinite-volume process

We consider a linear sequence of ‘nodes’, each of which can be in state 0 (‘off’) or 1 (‘on’). Signals from outside are sent to the rightmost node and travel instantaneously as far as possible to the left along nodes which are ‘on’. These nodes are immediately switched off, and become on again after a recovery time. The recovery times are independent exponentially distributed random variables. We present results for finite systems and use some of these results to construct an infinite-volume process (with signals ‘coming from infinity’), which has some peculiar properties. This construction is related to a question by Aldous and we hope that it sheds some light on, and stimulates further investigation of, that question.     

A unified theory for coherent systems in reliability II. A unified viewpoint on multinary coherent systems through monotone coherence and relevance

Binary coherent system theory has played an important part in reliability. Its extension to (‘degradable’ or ‘multistate’ or) multinary systems has recently been considered in various papers, through various definitions. This paper studies the most general model for multinary systems, proposes a unified viewpoint on multinary coherent systems and gives unified arguments to apply and to investigate further the binary and multinary cases. In a more detailed way, the ‘helpful bridge’ lately proposed by Block and Savits¹ between the binary and multinary cases is completed and multinary systems then can be studied in terms of monotone binary coherent systems, introduced in a companion paper.² Through various results, multinary systems are examined in terms of structure functions and of life functions; fundamental relations for their analysis are obtained with their set characterizations; the main axis that can be retained among the numerous types of coherence is emphasized, in a unified way, through relevance; reliability models are examined through performance processes, life lengths and performance functions; and Birnbaum's factors of importance are thoroughly extended to the multinary case. Fundamental results proposed in previous studies are thus completed with a shorter unified approach.     

Emergent learning behaviour in a simulated organization faced with tasks requiring team effort

We conceptualize organizational learning as a result of the collective learning behaviour of knowledge agents in an organization. Each agent provides a range of attributes that may be required to perform organizational tasks. We devised a computational model consisting of three processes to simulate an organization's response to performing repeated tasks: (1) Expert Selection Process for selecting the winner knowledge agent or lead agent; (2) Plan Formation Process for deciding what additional attributes are needed, but not possessed by the winner expert agent, and iteratively selecting further agents with the needed attributes until the task can be accomplished by the combined attributes of the ‘coalition of agents’ so formed; and (3) Capital Modification Process for rewarding participating agents according to the success of their combined organizational performance. We observed the simulated results for different combinations of three levels of task difficulty (requiring, respectively, 5, 10 and, 15 different attributes, each at a sufficient level in the coalition or team to complete the task), and three levels of selection, during plan formation, for knowledge agent performance (the extent to which selection favours knowledge agents with much capital or large strength versus knowledge agents without much capital or large strength). The simulated organization exhibited aspects of both single loop and double loop learning, in repeatedly performing the same task, and ‘learning to perform the task’ with the smallest possible team.     

Semi‐Markov processes and mobility†

A stochastic model of migration, occupational and vertical mobility, based on the theory of Semi‐Markov processes, is presented and important features of these processes derived. The model is a generalization of the Markov process in which the probability of leaving a state can depend in any arbitrary way on the length of time the state has been occupied (duration‐of‐stay) and on the next state entered (pushes and pulls). For mobility processes it thus captures McGinnis’ ‘axiom of cumulative inertia.’ Several distributions with cumulative inertia are presented and the relationship between the Semi‐Markov model and the Mover‐Stayer model explored. A method of including age effects is described. The model is shown to have applications to many other social processes, in addition to mobility, which have duration‐of‐stay effects.     

A stylized model of ‘Momentum’ processes: a research note

Several phenomena of interest like stock price movements, online auction bidprices or inventory levels, can be stylized as ‘momentum processes’,whereby the very start of activity (‘up’ or ‘down’) cantrigger subsequent activity in that direction. We calculate the transientprobabilities of being in a particular state (eg, stock price or current auctionbid level) in such activities. The calculations can be used to estimate theexpected time to reach a certain price, inventory level or bid. The processescan be modified to show the phenomenon where the lack of activity can have an‘inertia of rest’.     

On the nature of OR: taking stock

This paper argues that OR, having reached its maturity, must now play to its strengths. In strategic terms this means competing in those areas where OR's core competences can be brought to bear. Using a competence model it is suggested that OR's core products are (i) the development and implementation of the quantitative, algorithmic ‘smart bits’ and (ii) the ‘helpful ways’ of managing intervention processes. These core products are supported and sustained by three core competences labelled process, analytic, and context. Individuals and small groups of practitioners develop ‘strands of practice’ and larger groups ‘webs of practice’ on the basis of their core competences. It is argued that this is giving rise to the emergence of three archetypes of OR service, namely the OR technical consultancy, the OR process consultancy, and the full service OR consultancy. Both the technical and process consulting are built around ‘strands of practice’ of individuals and find their natural home in small service providers. The full service OR consulting practice, in the past located in internal OR groups, will in the future be located within the large management consultancies, which are capable of managing ‘webs of practice’. The implications for the worlds of OR practice and academia are examined.     

Modelling of Marginally Regular Bivariate Counting Process and its Application to Shock Model

In this paper, we develop a new class of bivariate counting processes that have ‘marginal regularity’ property. But, the ‘pooled processes’ in the developed class of bivariate counting processes are not regular. Therefore, the proposed class of processes allows simultaneous occurrences of two types of events, which can be applicable in practical modeling of counting events. Initially, some basic properties of the new class of bivariate counting processes will be discussed. Based on the obtained properties, the joint distributions of the numbers of events in time intervals will be derived and the dependence structure of the bivariate process will be discussed. Furthermore, the marginal and conditional processes will be studied. The application of the proposed bivariate counting process to a shock model will also be considered. In addition, the generalization to the multivariate counting processes will be discussed briefly.     

Setting Job-Shop Due-Dates with Service-Level Constraints

The job-shop due-date assignment problem arises when a manager needs to ‘promise’ a delivery date to a customer. Previous methods yield due-dates which are either optimistic (unlikely to be achieved) or conservative (the promise will be met, but too easily, because the date given was very pessimistic). This paper investigates the due-date assignment problem with a customer ‘service-level’ constraint, the percentage of time that promised delivery dates are honoured. We formulate a rule to attain this service level, yet maintain as short a due-date lead time as possible. Unlike previous attempts, this due-date rule considers not only the job content and instantaneous shop congestion information, but also implicitly incorporates information on how the jobs will be scheduled (or ‘loaded’) once they are in the shop. We simulate a single-machine shop for various measures of performance under several dispatching priorities, comparing our due-date rule with one reported to yield satisfactory performance. Our rule meets all requirements and is found to be superior for most measures of performance.     

Helping Managers Manage

Do conventional management accounts help managers manage? This paper argues that the answer to this question is ‘No’, primarily because conventionally prepared budgets are not accepted by managers as valid measures of performance as a result of either forecasting errors in the data used in the original budget or weaknesses in the simulation algorithms inherent in the budget. The paper then suggests that management accounts can be made more meaningful by incorporating within the management accounting system a ‘resource management system’, the basis of which is a powerful simulation model.     

Incorporating human fatigue and recovery into the learning–forgetting process

The available learning and forgetting models do not consider the physical loading that performing a task requires. In some situations, physical loading results in workers’ fatigue on the job that is followed by rest breaks to alleviate it. The aim of this paper is to present the “learning–forgetting–fatigue–recovery model” (LFFRM) that addresses possible issues relating to workers’ capabilities and restrictions in manufacturing environments. Numerical examples are solved to address some research questions regarding the model optimization and its constraints. The main results show that incorporating learning into a production process decreases fatigue and improves the performance of the system. Worker fatigue, on the other hand, increases production time and decreases production output. A recovery break must be of enough length to alleviate some of the accumulated fatigue. However, longer recovery times extend the lead time and deteriorate the production performance due to forgetting.     

On Dynamic Generalized Linear Models with Applications

In this paper we combine the idea of ‘power steady model’, ‘discount factor’ and ‘power prior’, for a general class of filter model, more specifically within a class of dynamic generalized linear models (DGLM). We show an optimality property for our proposed method and present the particle filter algorithm for DGLM as an alternative to Markov chain Monte Carlo method. We also present two applications; one on dynamic Poisson models for hurricane count data in Atlantic ocean and the another on the dynamic Poisson regression model for longitudinal count data.     

Structural Electricity Models and Asymptotically Normal Estimators to Quantify Parameter Risk

ABSTRACT

We estimate a structural electricity (multi-commodity) model based on historical spot and futures data (fuels and power prices, respectively) and quantify the inherent parameter risk using an average value at risk approach (‘expected shortfall’). The mathematical proofs use the theory of asymptotic statistics to derive a parameter risk measure. We use far in-the-money options to derive a confidence level and use it as a prudent present value adjustment when pricing a virtual power plant. Finally, we conduct a present value benchmarking to compare the approach of temperature-driven demand (based on load data) to an ‘implied demand approach’ (demand implied from observable power futures prices). We observe that the implied demand approach can easily capture observed electricity price volatility whereas the estimation against observable load data will lead to a gap, because – amongst others – the interplay of demand and supply is not captured in the data (i.e., unexpected mismatches).     

CHILDREN'S PROPORTIONAL REASONING AND TENDENCY FOR AN ADDITIVE STRATEGY: THE ROLE OF MODELS

In this paper we report on 10 –14 year old children's strategies while solving two versions of ratio and proportion tasks: one ‘with models’ thought to facilitate proportional reasoning and one ‘without’. Rasch methodology was used to develop ‘with’ and ‘without models’ test versions which were given to a linked sample involving 673 children. We examine the pupils’ additive errors, their effect on ratio reasoning and how contingent on ‘model’ presentation this is. First, we provide a single scale on which pupils, item-difficulty and additive errors can be located. We then provide a new scale constructed from the error prone items, which we name the ‘tendency for additive strategy’. The measurement data is supported by qualitative data showing that the presence of ‘models’ can sometimes affect children's strategies, both positively and negatively but rarely makes a significant measurement difference on this, untutored, sample.     

On efficient stopping times

This paper is devoted to efficient sequential estimation in stochastic processes whose corresponding sufficient statistics are processes with stationary independent increments. It is proved that a stopping time is efficient if and only if it represents a time of the first attaining of a hyperplane., which cannot ‘be passed’, in the sense which is made precise below. The problem of determining the explicit form of the hyperplanes which cannot ‘be passed’ is also discussed.     

Information in the operations research process

The article deals with information in the OR process. The value of an ‘optimal’ model solution which is not implemented is not very high. Many errors are due to a too narrow formulation of the problem, often a formulation which has focused on purely technical and economic aspects, or a formulation which has been adapted for a standard model. The concepts and models treated in the article take their point of departure in the actual problem. The models can be used as a frame of reference by various individuals and groups which are involved in OR work.     

Managing performance and power consumption in a server farm

We examine the problem of managing a server farm in a way that attempts to satisfy the conflicting objectives of high performance and low power consumption. A subset of servers is designated as ‘reserve’. The reserves are powered up when the number of jobs in the system is sufficiently high, and are powered down when that number is sufficiently low. Powering up takes an interval of time during which the reserves consume power but do not serve jobs. The question of how to choose the number of reserves, and the up and down thresholds, is answered by analyzing a suitable queueing model and minimizing an appropriate cost function. Heuristics and numerical results are also presented.