Control aspects in proportionality Markov manpower systems

In this paper, the control aspects of a hierarchical organization under the influence of “proportionality” policies are analyzed. Proportionality policies are those that restrict the recruitment to every level of the hierarchy (except the bottom most level or base level) to be in strict proportion to the promotions into that level. Both long term and short term control analysis have been discussed. In long term control the specific roles of the parameters of the system with regard to control of the shape and size of the system have been analyzed and yield suitable control strategies. In short term control, the attainability of a target or goal structure within a specific time from a given initial structure has been analyzed and yields the required recruitment strategies. The theoretical analyses have been illustrated with computational examples and also with real world data.The control of such proportionality systems is then compared with that of the general systems (which do not follow such policies) with some significant conclusions. The control relations of such proportionality systems are found to be simpler and more practically feasible than those of general Markov systems, which do not have such restrictions. Such proportionality systems thus not only retain and match the flexibility of general Markov systems but also have the added advantage of simpler and more practically feasible controls. The proportionality policies hence act as an alternative and more practicably feasible means of control.     

On the development of manpower number and recruitment in the civil service

We present a model for manpower planning which describes the dependence between stocks, flows and age distributions. An unbalanced age distribution results in the following conflict: either a recruitment is chosen which produces minimal deviations from a given stock. Then the unbalanced age distribution will be reproduced. Or a recruitment is selected which produces a balanced age distribution, but then oscillations of the stock will occur until a stationary age distribution will be reached. A mixture of these two recruitment policies is possible.

---

Zusammenfassung Das vorliegende Personalplanungsmodell beschreibt den Zusammenhang zwischen Beständen, Personalflüssen und Altersstrukturen. Eine unausgewogene Altersverteilung des Personalbestandes führt zu einem Zielkonflikt: Entweder werden Einstellungen so vorgenommen, daß Abweichungen von einem stabilen Soll-Bestand minimal werden, dann aber bleibt die Altersverteilung unausgewogen. Oder Einstellungen werden so gewählt, daß eine stabile Altersstruktur erreicht wird, dann aber schwankt der Gesamtbestand, bis eine stabile Altersverteilung erreicht wird. Mischungen zwischen diesen Einstellungsstrategien sind möglich.

     

Control of manpower systems by recruitment

This paper examines the attainable and maintainable states of a graded manpower system, where control is imposed through recruitment. Whilst certain constraints are imposed on the recruitment vector it is not assumed that the total size of the system is fixed nor that it grows at a fixed rate.

---

Zusammenfassung Diese Arbeit untersucht die erreichbaren und erhaltbaren Zustände eines gestuften Systems von Arbeitskräten, wobei mit Hilfe gezielter Einstellung gesteuert wird. Während dem Einstellungssteuerungsvektor gewisse Bedingungen auferlegt werden, werden weder ein fixierter Gesamtumfang noch ein Anwachsen des Systems in festen Raten angenommen.

     

Manpower planning procedures for hierarchical manpower systems

In this paper, a model which describes manpower planning procedures for a hierarchical system having certain desired properties to be achieved is presented. These properties will act as constraints on the system. It will be assumed that eventual, desired properties are achieved gradually over a period of time. Promotion policies will be wastagelinked and designed to satisfy vacancy-expansion demands. The model will be applied to data from a group of English County Police Constabularies.     

A model for promotion rate control in hierarchical manpower systems

In optimization models of hierarchical manpower systems, thenumbers promoted from each of the grades in a time period arenormally considered as decision variables. As a result, promotionrates, defined in terms of the proportions of staff promoted,can vary substantially from period to period in these models.Policies of this type may be unacceptable in practice becauseof their adverse impact on staff morale. In this paper, a mixedinteger programming (MIP) manpower planning model is developedfor determining minimum-cost manpower policies in which promotionrates remain stable while satisfying specified manpower requirementsover the planning period. In this MIP model, promotion ratesare considered as decision variables by using binary variables,and the model is solved by using an iterative procedure. Theuse of the approach is illustrated with representative datafor a military system.     

Hidden heterogeneity in manpower systems: A Markov-switching model approach

In modeling manpower systems, it is of crucial importance to deal with heterogeneity. Until recently, manpower models are dealing with heterogeneity due to observable sources, neglecting heterogeneity due to latent sources. In this paper a two-step procedure is introduced. In the first step personnel groups homogeneous with respect to the transition probabilities are determined in a classical way by taking into account the observable sources of heterogeneity. In the second step heterogeneity caused by latent sources is handled. A multinomial Markov-switching manpower model is introduced that deals with heterogeneity due to latent sources for the internal flows as well as for the wastage flows. The model incorporates the mover-stayer principle. A re-estimation algorithm is presented to estimate the parameters of the Markov-switching manpower model. The switching approach offers a methodology to build a Markov model with personnel groups as states that are more homogeneous, and therefore can contribute to a better validity of the manpower model.     

A continuous time markov-renewal replacement model for manpower systems

A continuous time Markov-renewal model is presented that generalizes the classical Young and Almond model for manpower systems with given size. The construction is based on the associated Markov-renewal replacement process and exploits the properties of the embedded replacement chain. The joint cumulant generating function of the grade sizes is derived and an asymptotic analysis provides conditions for these to converge in distribution to a multinominal random vector exponentially fast independently of the initial distribution, both for aperiodic and periodic embedded replacement chains. A regenerative approach to the wastage process is outlined and two numerical examples from the literature on manpower planning illustrate the theory.     

Balancing attainability,desirability and promotion steadiness in manpower planning systems

A Markov manpower planning model with fixed internal transition probabilities, enables assessing the feasibility to attain the most desirable personnel structure. In case the desirable personnel structure is not attainable under control by recruitment, the internal personnel flows can be modified while not disrupting the career progression expectations. This paper introduces the promotion steadiness degree to quantify the personnel policy deviation from the career progression expectations. As a result, this paper focuses on a model that balances three criteria, that is, the desirability degree, the attainability degree and the promotion steadiness degree, formulated by fuzzy membership functions. A new set of instances is introduced, and the algorithms are evidenced in a set of experiments.     

Stable pricing policies in service systems

Summary Customers arriving for service at a service system are allowed to purchase their priorities. A pricing policy is said to be stable if no one customer can reduce his expected cost by deviating from it, provided that all other customers follow it. The policy considered specifies prices to be paid by arrivals based on the number in the system at the epoch of the arrival and a parameter, which is the number of customers in a group paying the same price. The necessary and sufficient conditions for this policy to be stable are derived. The optimal value of the parameter and the prices that will maximize the expected return to the service center operator while maintaining stability are discussed. The basic queueing model assumesPoisson arrivals, exponential service times and single server.

---

Zusammenfassung Für die zur Abfertigung an einem Bedienungssystem eintreffenden Kunden besteht die Möglichkeit, ihre gewünschte Abfertigungspriorität gegen einen entsprechenden Preis zu kaufen. Eine vom Betreiber des Bedienungssystems verfolgte Preispolitik wird als stabil bezeichnet, falls kein Kunde seine erwarteten Kosten durch Abweichungen von dieser Preispolitik senken kann, vorausgesetzt daß alle anderen Kunden gemäß dieser Preispolitik behandelt werden. Bei der hier untersuchten Politik werden die von den eintreffenden Kunden zu zahlenden Preise nach der zum Ankunftszeitpunkt im System vorhandenen Kundenzahl festgesetzt. Außerdem wird zusätzlich als Parameter die Anzahl der Kunden in derselben Preisgruppe berücksichtigt. Es werden dann die notwendigen und hinreichenden Bedingungen für die Stabilität der Preispolitik abgeleitet. Anschließend werden diejenigen Werte für den Parameter und die Preise diskutiert, durch die der erwartete Gewinn für den Betreiber des Bedienungssystems bei stabiler Preispolitik maximiert wird. Der Untersuchung wurde ein Warteschlangenmodell mitPoisson-verteilten Ankünften, exponentialverteilten Abfertigungszeiten und einer Bedienungsstation zugrunde gelegt.

     

The combined manpower planning and preventive maintenance strategies by aggregate planning for the service division of vending machines

This paper presents a mathematical model of aggregate planning for the service division of vending machines, which determines its workforce size and the preventive maintenance level that may affect the failure rate. The unique aspect of this problem is that it exhibits two types of failures requiring different repair and preventive maintenance. The practice is to divide the service division into two groups, within which there are hierarchies according to these types of failures, and in each group, there are full-time workers with annual contracts and temporary workers hired only during the peak season. A case study based on actual operational data demonstrates how effective the introduced model and the policy are in reducing the total cost and improving the quality of service, and thus enhancing the overall system performance of the service division. We perform sensitivity analysis on key parameters, which helps us change maintenance strategies under diverse operating situations.     

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.     

Reducing disparities in large-scale emergency medical service systems

Emergency Medical Service (EMS) systems operate under the pressure of knowing that human lives might be directly at stake. In the public eye there is a natural expectation of efficient response. There is abundant literature on the topic of efficient planning of EMS systems (maximizing expected coverage or minimizing response time). Other objectives have been considered but the literature available is very sparse compared to efficiency-based works. Furthermore, while real size EMS systems have been studied, the use of exact models is usually hindered by the amount of computational time required to obtain solutions. We approach the planning of large-scale EMS systems including fairness considerations using a Tabu Search-based heuristic with an embedded approximation procedure for the queuing submodel. This allows for the analysis of large-scale real systems, extending the approach in which strategic decisions (location) and operative decisions (dispatching) are combined to balance efficiency and fairness.     

Optimal scheduling policies in time sharing service systems

We consider optimal scheduling problems in a TSSS (Time Sharing Service System), i.e., a tandem queueing network consisting of multiple service stations, all of which are served by a single server. In each station, a customer can receive service time up to the prescribed station dependent upper bound, but he must proceed to the next station in order to receive further service. After the total amount of the received services reaches his service requirement, he departs from the network. The optimal policy for this system minimizes the long-run average expected waiting cost per unit of time over the infinite planning horizon. It is first shown that, if the distribution of customer's service requirement is DMRL (Decreasing Mean Residual Life), the policy of giving the highest priority to the customer with the most attained service time is optimal under a set of some appropriate conditions. This implies that any policy without interruptions and preemptions of services is optimal. If the service requirement is DFR (Decreasing Failure Rate), on the other hand, it is shown that the policy of giving the highest priority to the customer with the least attained service time, i.e., the so-called LAST (Least Attained Service Time first) is optimal under another set of some appropriate conditions. These results can be generalized to the case in which there exist multiple classes of customers, but each class satisfies one of the above sets of conditions.     

Batch service systems with heterogeneous servers

Bulk-service multi-server queues with heterogeneous server capacity and thresholds are commonly seen in several situations such as passenger transport or package delivery services. In this paper, we develop a novel decomposition-based solution approach for such queues using arguments from renewal theory. We then obtain the distribution of the waiting time measure for multi-type server systems. We also obtain other useful performance measures such as utilization, expected throughput time, and expected queue lengths.

     

Wigner distribution transformations in high-order systems

By combining the definition of the Wigner distribution function (WDF) and the matrix method of optical system modeling, we can evaluate the transformation of the former in centered systems with great complexity. The effect of stops and lens diameter are also considered and are shown to be responsible for nonlinear clipping of the resulting WDF in the case of coherent illumination and nonlinear modulation of the WDF when the illumination is incoherent. As an example, the study of a single lens imaging system illustrates the applicability of the method.     

Predicting high-codimension critical transitions in dynamical systems using active learning

Complex dynamical systems, from those appearing in physiology and ecology to Earth system modelling, often experience critical transitions in their behaviour due to potentially minute changes in their parameters. While the focus of much recent work, predicting such bifurcations is still notoriously difficult. We propose an active learning approach to the classification of parameter space of dynamical systems for which the codimension of bifurcations is high. Using elementary notions regarding the dynamics, in combination with the nearest-neighbour algorithm and Conley index theory to classify the dynamics at a predefined scale, we are able to predict with high accuracy the boundaries between regions in parameter space that produce critical transitions.