# The manpower planning

### LITRETURE REVIEWS

This chapter represents general view of the manpower planning, followed by MACL, In addition, manpower planning using the bee's algorithm. Some previous related work in manpower planning and GA will be proposed.

### Manpower Planning

The basic factors of a manpower system are people, jobs, time and money (Grinold, 1977). When determining on a manpower plan it is important to be attentive to how these factors interact together. Ideally the intention of manpower planning is "to provide the right (required) number of the right (qualified) employee at the right (specified) time at the minimum cost" (Wang, 2005), but often the restrict of the system do not allow the needs to be harmonized perfectly (Grinold, 1977).

There are many definitions and descriptions of manpower planning but a common definition is that manpower planning is a process involving of three fundamentals:

- Analyzing, reviewing and looking for predicting the number of workers needed to achieve the objectives of the organization.
- Predicting the future supply of workers in the organization by examining current workers stocks, future staffing, wastage etc.
- Considering policies to resolve any difference between the result of 1 and 2.

It is important to understand that the fundamentals of manpower Planning is not executed serially but relatively in parallel, initial at an aggregated level and succeeding to a more comprehensive level as the function day comes closer. Choosing how to aggregate employee on various levels are one of the first important decisions that manpower planners have to make (Purkiss,1981). The groups should be represent features important for the institute; examples of features that might be one of interest are entry points, increasing grades, important job steps and streams, and the limitations of the system (Purkiss, 1981).

### Predicting Demand

Predicting the number of workers needed in the future is the main goal of demand predicting. This predicting is usually the most difficult part of manpower planning. A reason for this is that demand predicting requires customized models, since the factors in need of consideration differ considerably between companies. Output level of the company is a factor that all companies need to consider. But since this level is needed by the company anyway, it is usually predicted by another department and serves as an input to manpower planners. Some other factors that usually need to be considered are productivity changes, technological changes, organizational changes, market forces and trends, corporate strategy, etc. (Bartholomew et al. 1991, Edwards, 1983)

Some methods for prediction are extrapolation of time-series data, work study techniques, regression or factor analysis, and product life cycles (Edwards, 1983). Most of these methods have frequently been used in other areas than manpower planning.

### Predicting Supply

When studying workers supply within an organization, manpower models are often used as an aid. The foundation of the majority of manpower models is the representation of the organization as a dynamic system of stocks and flows. The members of an organization are classified into disjunction groups based on attributes relevant for the area of study, and the number in such a group at a specific time is called the stock. Changes of the system are represented by flows which are the number of movements between groups during an interval of time. A flow can be either a "push" or a "pull" flow; the size of a "push" flow is determined only by the origin of the flow while the size of "pull" flows are determined by the destination of the flow.

The manpower models of the system are used to understand how factors such as e.g. recruitment policies, wastage, promotion policies and age distribution affect the supply of workers (Purkiss, 1981). Another area of application for manpower models are to compute optimal personnel decisions (such as recruitment, promotion, training, etc.) when the situation can be clearly defined (Purkiss, 1981). Literature often distinguishes between two types of models: descriptive models constructed to reproduce the behavior of the manpower system and normative models which can prescribe a course of action, typically by various optimization techniques (Price et al. 1980).

The main types of descriptive models are Markov chain models, renewal models and simulation models (Price et al. 1980). Markov chain models assume that all flows are "push" flows while renewal models assume "pull" flows. In many organizations there are flows of both types and therefore models including combinations of "push" and "pull" flows have been constructed.

### Strategies for Closing the Gap

There are almost as many strategies for closing the gap between supply and demand as there are companies, although the factors that are possible to affect are similar. Each of these factors has been investigated thoroughly and many are separate fields of studies. It would therefore be possible to write an essay on each of them, but only a short overview will be given here.

Work flow an obvious way to equalize the gap between supply and demand is of course to fire, hire or move workers. It is important when using these means to consider what effects there will be on the gap in the future, for example hiring when the need is only temporary might be more expensive than being short on supply for a short while. The process of recruiting can be extensive and an overview of the process and what to consider when recruiting personnel is provided by Bratton and Gold (2007). Another part of managing the work flow is career and succession planning whose aim is to designing career paths and to make sure that positions have suitable occupants. Since most position requires a "learning period" a long-term view is needed.

Training can be considered as the activities intended to enhance the skill, knowledge and capabilities of the personnel. The processes and procedures that try to provide the learning activities are often referred to as human resource development (HRD) and have been a major field of study during recent years. (Bratton and Gold, 2007)

Reward management defined as "all the monetary, non-monetary and psychological payments that an organization provides for its employees in exchange for the work they perform" (Bratton and Gold, 2007). The way employees and managers are rewarded has undergone a significant change during the past decade, from being based on hours worked and seniority to individual effort and performance. There are many objectives that a reward system must meet: support the organization's strategy, recruit qualified employees, retain capable employees, ensure internal and external equity, be sustainable within the financial means of the organization, motivate employees to perform to the maximum of their extent, and so on (Bratton and Gold, 2007).

Demand factors, some of the factors that affecting demand are : corporate strategy, productivity changes, technological changes, organizational changes, market forces and trends etc. When trying to find strategies to close the gap these factors are still important but from another perspective.

### 2.2 Manpower Allocation on Cell Loading (MACL)

Although MACL is an important subject, it is difficult to find enough literature and research related on this problem. It is especially difficult to find relevant literature that is related with how genetic algorithms and bees algorithm are applied to solve MACL problems. However, attempts to solve this problem with optimizing and heuristics methods are more common in the literature.

In 1968, Moore suggested an optimizing algorithm to minimize the amount of tardy jobs in single machine scheduling. Maxwell (1970) developed an integer programming formulation for the same problem. Ho and Chang (1995) and later Süer, Baez, and Czajkiewicz (1993) proposed heuristics for minimizing the number of tardy jobs in parallel machine scheduling.

Ho and Chang (1995) propose two approaches named job-focused and machine-focused to minimize the number of tardy jobs. Three of the proposed heuristics perform well and the best heuristic is about 1.2% of the optimum. Later, Süer (1995) extended this problem to loading in a multi-period cellular environment. He analyzes different approaches with advantages and disadvantages. He gives the mathematical formulations for the different approaches. Süer (1996) introduced a two-phase hierarchical methodology to find the optimal manpower allocation and cell loads simultaneously.

First phase is to generate the alternative configurations and second phase is to find optimal operator assignment and to load cells. He solved the problem by using mathematical programming. Süer and Bera (1998) also used a two-phase approach to solve both manpower assignment and cell loading in a multi-period cellular system. The objective was to minimize the number of tardy jobs with the available capacity in each period. It was observed that number of tardy jobs decreased as number of employees increased in the cell. Vembu and Srinivasan (1997) developed heuristics to minimize the make span on a product line. They divided the line into cells such that movement in a cell is one way and single. Production times change with manpower level. They also solved the problem with enumeration methods and genetic algorithm. The developed heuristic gave closes to best solutions quickly which are found by enumeration methods and genetic algorithm.

Many complicated multi-variable optimization problems cannot be resolved easily. This has produced interest in "intelligent" search algorithms that find close optimal solutions. The Bees Algorithm established in the authors' laboratory is inspired by the food foraging behavior of honey bees and could be regarded as belonging to the category of "intelligent" optimization tools (Pham et al., 2008).

Cell formation (CF) is one of the cell loading problem in CM sector. Pham (2008) has tried to solve this problem by simultaneous the group machines and their identical part families into cells so the intercalluer travelling are minimized.

### Mathematical Models

Mathematical models use mathematics to formulate the problem. They have certain objectives and try to optimize this objective. They can be used to solve problems in a variety of application areas, which include planning, design, configuration, scheduling and resource allocation. The main advantage of mathematical models is that, upper management understands them easily since they give definite and best results (Heady, 1997). Other advantages are that they can quantify trade-offs between objectives and they can examine the implications of changing resource constraints by doing sensitivity analysis. On the other hand, they have some drawbacks. The main drawback is the huge computational time required. Many integer programming and combinatorial optimization problems are still challenging from a computational standpoint; They are NP-complete. It is widely believed that no general and efficient algorithm exists for solving them. However, manufacturing systems are dynamic systems and generally require a solution in short time.

### Mathematical Modeling Language - ILOG OPL

Traditional modeling languages such as AMPL (A Mathematical Programming Language) and GAMS (General Algebraic Modeling System) were developed to make it easy for the user to solve mathematical programming problems. The way they tried to achieve this was expressing mathematical problems in a computer language whose syntax is close to the standard presentation of these problems in books. In other words, mathematical equations are written with a computer language in a way which is similar to the algebraic notation of the equation. OPL (Optimization Programming Language) was motivated by the modeling languages AMPL and GAMS. It provides strong support for modeling linear and integer programs like AMPL and GAMS. Furthermore, it makes it possible to solve combinatorial optimization applications, such as job-shop scheduling (Mesghouni and Hammadi, 2004), and variety of resource allocation problems. OPL allows the models to be used again by separating the model and instance data. Model just declares the data and data file initializes the declared item. As a result, the same model can be used with different data files. A model and a data file are combined and form a project. This property of OPL was useful in performing the experiment since many test samples were experimented to reach a thorough comparison among Extended Models and between MACL model and genetic algorithm and bees algorithm.

### Genetic Algorithm

Evolutionary process originates by the rules of natural selection in Darwin's theory. Techniques which use the mechanics of evolution to produce optimal solutions to the problems are known as evolutionary computation. Genetic Algorithm is one of the best known evolutionary process techniques. GA has many different properties from conventional optimization and search procedures. First of all, most of the search algorithms work with solutions directly but GAs work with the coding of the solutions. Second, most of the search algorithms like simulated annealing start from a single solution whereas GAs starts the search from a population of solutions. Finally, most of the other search algorithms like Branch and Bound use deterministic transition techniques whereas GAs uses probabilistic transition techniques.

Genetic algorithms not only explore but also exploit the search space to find the best solution. Gen and Cheng (1997), state that GAs combine elements of directed and stochastic search which can make a remarkable balance between exploration and exploitation of the search space. At the beginning of genetic search, population is widely random and diverse. Exploration of the solution space is dominant. As better fitness solutions evolve, genetic search directs to the exploitation of the good solutions.

GAs start with a set of solutions called chromosomes. Chromosomes are made of coding of solutions called genes. Then GAs mimics nature, on the way to reach the optimal (or best) solution. GAs use pay off information (fitness function) to evaluate the solutions (chromosomes) and compare them. There are two kinds of operations in GA; the first type is Genetic Operations such as Crossover Operator and Mutation Operator.

The second type is Evolution Operation which is carried by the Selection Operator. Crossover operators operate on two chromosomes at a time and generate off spring by combining both chromosomes' features. Mutation operators produce random variations in chromosomes by altering one or more genes in the chromosome. Selection operators form the next generation from the current chromosomes randomly. However, chromosomes with a better fitness function have a higher chance to survive.

Advantages of GAs can be summarized as:

- They do not require much mathematics.
- They can work with many objective functions.
- They are effective at global search.
- They can be used with local heuristics or optimization techniques.
- They do not guarantee an optimal solution.
- They need problem specific parameters.

Disadvantages of GAs can be summarized as: