On the equilibrium personnel structure in the presence of vertical and horizontal mobility via multivariate Markov chains

The present paper employs the Multivariate Homogeneous Markov System (MHMS) in the context of Markov manpower planning modelling. The system is regulated by an embedded multivariate Markov process that allows us to distinguish employees’ mobility patterns that take place either within or among the existing divisions (departments) of an organization. The motivation behind this step arises from the generalization of univariate Markov manpower planning models in which the organization is considered a single (probably hierarchical) group and from the fact that departmental mobility is actually common in most realistic establishments. The first part of the paper presents the functional relations of the MHMS governing intra/inter-departmental transitions. Using these functional forms, we proceed by studying the system’s equilibrium behaviour. This asymptotic analysis reveals the inherent tendencies of the system to reach the limiting structures of specific forms and properties under conditions imposed in the long run.     

Optimal dynamic investment with learning by doing in the adjustment cost function

In an optimal control model of a firm's dynamic investment policy, we analyze the effects of including learning by doing in the adjustment cost function (the larger the existing capital stock, the smaller the cost of installing an additional unit of capital stock).The authors wish to thank two anonymous reviewers for valuable comments. The research of the second author was sponsored by a fellowship of the Royal Netherlands Academy of Arts and Sciences.     

The impact of multi-skilling on personnel scheduling in the service sector: a retail industry case

Using personnel scheduling to reduce overstaffing and understaffing in a service industry across multiple periods is often undermined by lack of flexibility due to the exclusive use of specialized personnel. This study analyses the impacts of assigning multi-skilled personnel to different activities and its potential for improving schedule efficiency. A proposed mixed integer linear programming model determines which employees are trained to work in which activities and their assignments over a one-week planning horizon. The model results show that the lowest total-cost multi-skilled configurations are obtained in scenarios where personnel supply and demand are in equilibrium. Half of employees would continue to be specialized for just one activity while the half slated for multi-skilling would be trained in most cases for just one additional activity, even though training cost is assumed to be minimal. It is also shown that multi-skilling is best applied to employees whose contracts are highly flexible.     

Markov链在人力资源供给预测中的应用

本文利用Ｍａｒｋｏｖ链建立模型,对组织各类人员的供给作出定量预测,为组织的人事部门或人力资源管理部门根据职位人员需求安排合适的人选提供决策的依据。文中介绍的模型不仅可以预测组织中各类人员的供给人数,而且可以预测组织中各类人员的分布。对于人力资源管理部门如何用人和用好人有一定的指导意义和应用价值     

Economic design of integrated model of control chart and maintenance management

There are two key tools for the control of production processes — Statistical Process Control (SPC) and Maintenance Management (MM), which are traditionally separated (both in science and in business practice), even though their goals overlap a great deal. Their common goal is to achieve optimal product quality, little downtime and cost reduction by controlling variances in the process. Since single or separated parallel applications may not be fully effective, this paper discusses the integration of statistical process control and maintenance, and provides an integrated model of Control Chart (CC) and MM. A mathematical model is given to analyze the cost of the integrated model and the grid-search approach is used to find the optimal values of policy variables (n,h,L,k) that minimize hourly cost. Finally, a numerical experiment is conducted to investigate the effects of cost parameters on the solution of the design.     

An extended and tractable approach on the convergence problem of the mixed push-pull manpower model

In this paper, the asymptotic behavior of the time-homogeneous mixed push-pull manpower model is studied under the assumption that the desired stock vector and the recruitment policy are fixed over time. In the mixed push-pull manpower model, the internal mobility of a personnel system can be regulated by both pull and push transitions. Based on those characteristics, we express and examine the dynamics of the personnel system by formulating the mixed push-pull manpower model by means of particular transition matrices, which we demonstrate to have interesting properties. We show that under certain conditions the stock vector converges. An explicit analytical form for this limiting personnel stock vector is found.     

Optimal recruitment strategies in a multi-level manpower planning model

Markov manpower planning models have extensively been analysed in the past in order to find an optimal personnel strategy for which the stocks of the manpower system evolve towards desirable ones. So far, those models do not take into account interactions among different organizational decision levels. In this paper, a multi-level manpower planning model is presented that considers, besides the desirable stock vector at overall level, proposals for the departmental stocks from lower organizational levels. Attainability of the stock vectors at departmental level is examined under control by recruitment and interdepartmental transitions. A multi-level optimization algorithm is presented to determine an optimal recruitment strategy resulting in attainable and acceptable stocks that are a compromise between the proposal from the top and the proposals from the departments.     

Network flow models for intraday personnel scheduling problems

Personnel scheduling problems can be decomposed into two stages. In the first stage for each employee the working days have to be fixed. In the second stage for each day of the planning period an intraday scheduling problem has to be solved. It consists of the assignment of shifts to the employees who have to work on the day and for each working period of an employee a task assignment such that the demand of all tasks for personnel is covered. In Robinson et al. (Burke and Trick (Eds.), Proceedings of the 5th International Conference on the Practice and Theory of Automated Timetabling, 18th August–20th August 2004, Pittsburgh, PA, USA, pp. 561–566, 2005), the intraday problem has been formulated as a maximum flow problem. The assumptions are that, employees are qualified for all tasks, their shifts are given, and they are allowed to change tasks during the day. In this work, we extend the network flow model to cover the case where not all employees are qualified to perform all tasks. The model is further extended to be able to calculate shifts of employees for the given day, assuming that an earliest starting time, a latest finishing time, and a minimal working time are given. Labour cost can be also taken into account by solving a minimum cost network flow problem.     

A successive convex approximation method for multistage workforce capacity planning problem with turnover

Workforce capacity planning in human resource management is a critical and essential component of the services supply chain management. In this paper, we consider the planning problem of transferring, hiring, or firing employees among different departments or branches of an organization under an environment of uncertain workforce demands and turnover, with the objective of minimizing the expected cost over a finite planning horizon. We model the problem as a multistage stochastic program and propose a successive convex approximation method which solves the problem in stages and iteratively. An advantage of the method is that it can handle problems of large size where normally solving the problems by equivalent deterministic linear programs is considered to be computationally infeasible. Numerical experiments indicate that solutions obtained by the proposed method have expected costs near optimal.     

基于灰色预测模型的山西省批发零售业人员需求分析

以灰色预测模型GM(1,1)的原理与方法为基础,以山西省2010-2014年批发零售业从业人员数为依据.对山西省未来五年的批发零售业人员需求量进行预测,预测结果为山西省未来的产业政策与就业政策的制定提供参考.     

Performance appraisal based on distance function methods

Performance appraisal is a process used by some firms to evaluate their employees’ efficiency and productivity in order to plan their promotion policy, salary policy, layoffs policy, etc. Initially this process was just carried out by the executive staff, but recently it has evolved into an evaluation process based on the opinion of different reviewers, supervisors, collaborators, customers and the employees themselves (360-degree method). In such an evaluation process the reviewers evaluate some indicators related to employees performance appraisal. In this paper we propose an evaluation framework where there are different sets of reviewers taking part in the evaluation process. Since reviewers have a different knowledge about the evaluated employee, it seems suitable to offer a flexible framework in which different reviewers can express their assessments in different finite scales according to their knowledge. The final aim is to compute a global evaluation for each employee, that can be used by the management team to make their decisions regarding their human resources policy. In this way, to obtain a global evaluation for each employee, we propose a methodology able to aggregate individual valuation in a metric L_p framework. In this context, the associated optimization problems can be reduced to an Extended Goal Programming formulation that is very easy to compute.     

Optimal strategy policy in batch arrival queue with server breakdowns and multiple vacations

This paper considers a like-queue production system in which server vacations and breakdowns are possible. The decision-maker can turn a single server on at any arrival epoch or off at any service completion. We model the system by an M^[x]/M/1 queueing system with N policy. The server can be turned off and takes a vacation with exponential random length whenever the system is empty. If the number of units waiting in the system at any vacation completion is less than N, the server will take another vacation. If the server returns from a vacation and finds at least N units in the system, he immediately starts to serve the waiting units. It is assumed that the server breaks down according to a Poisson process and the repair time has an exponential distribution. We derive the distribution of the system size through the probability generating function. We further study the steady-state behavior of the system size distribution at random (stationary) point of time as well as the queue size distribution at departure point of time. Other system characteristics are obtained by means of the grand process and the renewal process. Finally, the expected cost per unit time is considered to determine the optimal operating policy at a minimum cost. The sensitivity analysis is also presented through numerical experiments.     

Optimal Sequential Sampling Policy of Partitioned Random Search and Its Approximation

The paper studies the optimal sequential sampling policy of the partitioned random search (PRS) and its approximation. The PRS is a recently proposed approach for function optimization. It takes explicitly into consideration computation time or cost, assuming that there exist both a cost for each function evaluation and a finite total computation time constraint. It is also motivated at improving efficiency of the widely used crude random search. In particular, the PRS considers partitioning the search region of an objective function into K subregions and employing an independent and identically distributed random sampling scheme for each of K subregions. A sampling policy decides when to terminate the sampling process or which subregion to be sampled next.     

Joint employee weekly timetabling and daily rostering: A decision-support tool for a logistics platform

To deal with their highly variable workload, logistics companies make their task force flexible using multi-skilled employees, flexible working hours or short-term contracts. Together with the legal constraints and the handling equipments’ capacities, these possibilities make personnel scheduling a complex task. This paper describes a model to support their chain of decisions from the weekly timetabling to the daily rostering (detailed task allocation).     

Inventory models with minimal service level constraints

This paper investigates inventory models in which the stockout cost is replaced by a minimal service level constraint (SLC) that requires a certain level of service to be met in every period. The minimal service level approach has the virtue of simplifying the computation of an optimal ordering policy, because the optimal reorder level is solely determined by the minimal SLC and demand distributions. It is found that above a certain “critical” service level, the optimal (s,S) policy “collapses” to a simple base-stock or order-up-to level policy, which is independent on the cost parameters. This shows the minimal SLC models to be qualitatively different from their shortage cost counterparts. We also demonstrate that the “imputed shortage cost” transforming a minimal SLC model to a shortage cost model does not generally exist. The minimal SLC approach is extended to models with negligible set-up costs. The optimality of myopic base-stock policies is established under mild conditions.     

税企非零和博弈分析

本以献[1]和献[2]为基础，将税收检查成本及偷税成本量化后，对防止偷骗税行为进行非零和博弈分析。具体指出罚款系数的确定方法，为税务决策部门针对偷骗税行为制定合理的罚款系数提供了可操作的理论依据。     

A geometric process maintenance model with preventive repair

In this paper, a geometric process maintenance model with preventive repair is studied. A maintenance policy (T, N) is applied by which the system will be repaired whenever it fails or its operating time reaches T whichever occurs first, and the system will be replaced by a new and identical one following the Nth failure. The long-run average cost per unit time is determined. An optimal policy (T^∗, N^∗) could be determined numerically or analytically for minimizing the average cost. A new class of lifetime distribution which takes into account the effect of preventive repair is studied that is applied to determine the optimal policy (T^∗, N^∗).     

Average optimality inequality for continuous-time Markov decision processes in Polish spaces

In this paper, we study the average optimality for continuous-time controlled jump Markov processes in general state and action spaces. The criterion to be minimized is the average expected costs. Both the transition rates and the cost rates are allowed to be unbounded. We propose another set of conditions under which we first establish one average optimality inequality by using the well-known “vanishing discounting factor approach”. Then, when the cost (or reward) rates are nonnegative (or nonpositive), from the average optimality inequality we prove the existence of an average optimal stationary policy in all randomized history dependent policies by using the Dynkin formula and the Tauberian theorem. Finally, when the cost (or reward) rates have neither upper nor lower bounds, we also prove the existence of an average optimal policy in all (deterministic) stationary policies by constructing a “new” cost (or reward) rate. Research partially supported by the Natural Science Foundation of China (Grant No: 10626021) and the Natural Science Foundation of Guangdong Province (Grant No: 06300957).     

Algorithms for large scale Shift Minimisation Personnel Task Scheduling Problems

In this paper we introduce the Personnel Task Scheduling Problem (PTSP) and provide solution algorithms for a variant of this problem known as the Shift Minimisation Personnel Task Scheduling Problem (SMPTSP). The PTSP is a problem in which a set of tasks with fixed start and finish times have to be allocated to a heterogenous workforce. Personnel work in shifts with fixed start and end times and have skills that enable them to perform some, but not all tasks. In other words, some personnel are qualified to only perform a subset of all tasks. The objective is to minimise the overall cost of personnel required to perform the given set of tasks. In this paper we introduce a special case in which the only cost incurred is due to the number of personnel (shifts) that are used. This variant of the PTSP is referred to as the Shift Minimisation Personnel Task Scheduling Problem (SMPTSP). While our motivation is a real-life Personnel Task Scheduling Problem, the formulation may also be applied to machine shop scheduling. We review the existing literature, provide mathematical formulations, and develop a heuristic approach for the SMPTSP.     

Control Policies for Inventory with Service Time

Abstract

This article introduces an additional control policy—the N-policy–into (s, S) inventory system with positive service time. Under specified interarrival and service time distributions, which are independent of each other, we obtain the necessary and sufficient condition for the system to be stable. We also obtain the optimal values of the control variables s, S, and N; it is seen that the cost function attains the minimum value at s = 0. It is also shown that the cost function is separately convex in the variables S and N. Numerical illustrations are provided. Several measures of performance of the system are evaluated.