Method of determining the best mix of regular and contract employees

Abstract

A process is disclosed for implementation on a suitably programmed digital computer for producing a worker staffing plan for an organization over a long-term workload forecast when the organization employs workers of different employment relation types, such as regular employees, both full and part time, and contract employees hired from another concern. Data is entered into the computer pertaining to (a) the work forecast; (b) types of employees, including the productivity, training cost, annual cost and termination cost of each type; (c) demographic data, where available and appropriate, for each type such as worker age and experience or length of service; and (d) attrition or retention data for each employment type by demographic group. A linear programming analysis is then conducted on the computer to produce a hiring and termination schedule for each worker type for each work period to meet the workload requirements of the organization at minimum cost.

Claims

What is claimed is:

1. A method, for implementation on a programmed computer with a database, for determining the number of employees of each of a variety of at least two types that should be utilized by an organization where each worker type has a different employment arrangement, a capability for completing work and a different cost that together affect the overall cost and management prerogatives of the organization, said method comprising;

entering into said computer database data identifying the number of periods of time to be included in the analysis, T, and identifying for each period of time t between 0 and T a worker requirement forecast, W.sub.t, where workload changes from period to period,

entering into said computer database data identifying each worker type, i, the initial number of employees of each type, q.sub.i, the productivity of each said type, w.sub.i, and a cost, c.sub.i, of each said type,

entering into said computer database a retention rate, p.sub.i, based on the employment experience of said organization for each worker type, and

producing on said computer using linear programming a hiring, y.sub.it, and termination, z.sub.it, schedule using the data in said database for each said time period and for workers of each type to both ensure that the total number of workers, x.sub.it, satisfies the workload requirements and minimizing ##EQU6##

subject to the constraints ##EQU7##

y.sub.it.gtoreq.0 for all i in the set of worker types, I, and for all t in the set {1, . . . , T},

z.sub.it.gtoreq.0 for all i in the set I and for all t in the set {1, . . . , T},

x.sub.i0 =q.sub.i for all i in the set I, and

x.sub.it =x.sub.i,t-1 p.sub.i -z.sub.it for all i in the set I and for all t in the set {1, . . . , T}.

2. A method as recited in claim 1 comprising entering into said computer database data identifying the number of periods of time to be included in the analysis, T, and identifying for each period of time t between 0 and T a worker requirement forecast, W.sub.t, where workload changes from period to period,

entering into said computer database data identifying each worker type, i, the productivity specifically for each combination of worker type and age and length of service group, w.sub.ijk, and a cost specifically for each combination of worker type and age and length of service group, c.sub.ijk,

entering into said computer database demographic data comprising at least, when known, worker hiring age groups indexed by j where j varies from the youngest age at which employees are hired, H.sup.min, to the oldest age at which employees are hired, H.sup.max, and worker length of service groups indexed by k where k varies from 0 to the maximum length of service, S, and data identifying the number of workers of each worker type in each said age and length of service group currently employed by the organization, q.sub.ijk,

entering into said computer database a retention rate, p.sub.ijk, based on the employment experience of said organization, for each combination of worker type and age and length of service group,

entering into said computer database data for each worker type i indicating the fraction of employees, r.sub.ij, of that type who are hired at age j, and

producing on said computer using linear programming a hiring, y.sub.it, and termination, z.sub.ijkt, schedule using the data in said database for each said time period and for workers of each type to both ensure that the total number of workers, x.sub.ijkt, satisfies the workload requirements and minimizing ##EQU8##

subject to the constraints ##EQU9##

y.sub.it.gtoreq.0 for all i in the set of worker types, I, and for all t in the set {1, . . . , T},

z.sub.ijkt.gtoreq.0 for all i in the set I, for all j in the set {H.sup.min, . . . , H.sup.max }, for all k in the set {0, . . . , S} and for all t in the set {1, . . . , T},

x.sub.i,j,k,0 =q.sub.ijk for all i in the set I, for all j in the set {.sup.min, . . . , H.sup.max }, and for all k in the set {0, . . . , S},

x.sub.i,j,0,t =y.sub.ij r.sub.it for all i in the set I, and for all j in the set {H.sup.min, . . . , H.sup.max }, and for all t in the set {1, . . . , T}, and

x.sub.ijkt =x.sub.i,j,k-1,t-1 p.sub.ijk -z.sub.i,j,k-1,t for all i in the set I, and for all j in the set {H.sup.min, . . . , H.sup.max }, for all k in the set {1, . . . , S} and for all t in the set {1, . . . , T}.

3. A method as recited in claim 1 comprising entering into said computer database data identifying the number of periods of time to be included in the analysis, T, and identifying for each period of time t between 0 and T a worker requirement forecast, W.sub.t, where workload changes from period to period,

entering into said computer database data identifying each worker type, i, the initial number of employees of each type, q.sub.i, the productivity of each said type, w.sub.i, the training cost of each worker type, c.sup.y.sub.i, the annual cost of each worker type, c.sup.x.sub.i, and the termination cost of each worker type, c.sup.z.sub.i,

entering into said computer database a retention rate, p.sub.i, based on the employment experience of said organization for each worker type, and producing on said computer using linear programming a hiring, y.sub.it, and termination, z.sub.it, schedule using the data in said database for each said time period and for workers of each type to both ensure that the total number of workers, x.sub.it, satisfies the workload requirements and minimizing ##EQU10##

subject to the constraints ##EQU11##

y.sub.it.gtoreq.0 for all i in the set of worker types, I, and for all t in the set {1, . . . , T},

z.sub.it.gtoreq.0 for all i in the set I and for all t in the set {1, . . . , T},

x.sub.i0 =q.sub.i for all i in the set I and

x.sub.it =x.sub.i,t-1 p.sub.i -z.sub.it for all i in the set I and for all t in the set {1, . . . , T}.

4. A method as recited in claim 1 comprising entering into said computer database data identifying the number of periods of time to be included in the analysis, T, and identifying for each period of time t between 0 and T a worker requirement forecast, W.sub.t, where workload changes from period to period,

entering into said computer database data identifying each worker type i,

entering into said computer database demographic data comprising at least, when known, worker hiring age groups indexed by j where j varies from the youngest age at which employees are hired, H.sup.min, to the oldest age at which employees are hired, H.sup.max, and worker length of service groups indexed by k where k varies from 0 to the maximum length of service, S, and data identifying the number of workers of each worker type in each said age and length of service group currently employed by the organization, q.sub.ijk,

entering into said computer database a retention rate, p.sub.ijk, based on the employment experience of said organization, for each combination of worker type and age and length of service group,

entering data into said computer database identifying the productivity for each combination of worker type and age and length of service group, w.sub.ijk, the training cost for each worker type, c.sup.y.sub.i, the annual cost for each combination of worker type and age and length of service group, c.sup.x.sub.ijk, and the termination cost for each combination of worker type and age and length of service group, c.sup.z.sub.ijk,

entering into said computer database data for each worker type i indicating the fraction of employees, r.sub.ij, of that type who are hired at age j, and

producing on said computer using linear programming a hiring, y.sub.it, and termination, z.sub.ijkt, schedule using the data in said database for each said time period and for workers of each type to both ensure that the total number of workers, x.sub.ijkt, satisfies the workload requirements and minimizing ##EQU12##

subject to the constraints ##EQU13##

y.sub.it.gtoreq.0 for all i in the set of worker types, I, and for all t in the set {1, . . . , T},

z.sub.ijkt.gtoreq.0 for all i in the set I, for all j in the set {H.sup.min, . . . , H.sup.max }, for all k in the set {0, . . . , S} and for all t in the set {1, . . . , T},

x.sub.i,j,k,0 =q.sub.ijk for all i in the set I, for all j in the set {H.sup.min, . . . , H.sup.max }, and for all k in the set {0, . . . , S},

x.sub.i,j,0,t =y.sub.it r.sub.ij for all i in the set I, and for all j in the set {H.sup.min, . . . , H.sup.max }, and for all t in the set {1, . . . , T}, and

x.sub.ijkt =x.sub.i,j,k-1,t-1 p.sub.ijk -z.sub.i,j,k-1,t for all i in the set I, and for all j in the set {H.sup.min, . . . , H.sup.max }, for all k in the set {1, . . . , S} and for all t in the set {1, . . . , T}.

5. A method as recited in claim 1 a method as recited in claim 4 comprising entering into said computer database data identifying the number of periods of time to be included in the analysis, T, and identifying for each period of time t between 0 and T a worker requirement forecast, W.sub.t, where workload changes from period to period,

entering into said computer database data identifying each worker type, i,

entering into said computer database demographic data comprising at least, when known, worker hiring age groups indexed by j where j varies from the youngest age at which employees are hired, H.sup.min, to the oldest age at which employees are hired, H.sup.max, and worker length of service groups indexed by k where k varies from 0 to the maximum length of service, S, and data identifying the number of workers of each worker type in each said age and length of service group currently employed by the organization, q.sub.ijk,

entering into said computer database a retention rate, p.sub.ijk, based on the employment experience of said organization, for each combination of worker type and age and length of service group,

entering data into said computer database identifying the productivity specifically for each combination of worker type and age and length of service group, w.sub.ijk, and a cost specifically for each combination of worker type and age and length of service group, c.sub.iji,

entering into said computer database data for each worker type i indicating the fraction of employees, r.sub.ij, of that type who are hired at age j,

entering into said computer database the training cost for each work type, c.sup.y.sub.i, the annual cost for each combination of worker type and age and length of service group, c.sup.x.sub.ijk, and the termination cost of each worker type, c.sup.z.sub.ijk,

entering into said computer database data on management policies including the maximum number of employees of any given type i that can be hired in a single period, a.sub.i, the maximum fraction of employees of type i that management is willing to terminate in a single period, b.sub.i, the minimum length of service across the organization that the management is willing to tolerate, c, and the maximum number of employees of type i that the management is willing to include on the staff in period t, d.sub.it, and

producing on said computer using linear programming a hiring, y.sub.it, and termination, z.sub.ijkt, schedule using the data in said database for each said time period and for workers of each type to both ensure that the total number of workers, x.sub.it, satisfies the workload requirements and minimizing ##EQU14##

subject to the constraints ##EQU15##

y.sub.it.gtoreq.0 for all i in the set of worker types, I, and for all t in the set {1, . . . , T},

z.sub.ijkt.gtoreq.0 for all i in the set I, for all j in the set {H.sup.min, . . . , H.sup.max }, for all k in the set {0, . . . , S} and for all t in the set {1, . . . , T},

x.sub.i,j,k,0 =q.sub.ijk for all i in the set I, for all j in the set {H.sup.min, . . . , H.sup.max }, and for all k in the set {0, . . . , S},

x.sub.i,j,0,t =y.sub.it r.sub.ij for all i in the set I, and for all j in the set {H.sup.min, . . . , H.sup.max }, and for all t in the set {1, . . . , T},

x.sub.ijkt =x.sub.i,j,k-1,t-1 p.sub.ijk -z.sub.i,j,k-1,t for all i in the set I, and for all j in the set {H.sup.min, . . . , H.sup.max }, for a11 k in the set {1, . . . , S} and for all t in the set {1, . . . , T},

y.sub.it.ltoreq.a.sub.i, for all i in the set I and for all t in the set {1, . . . , T}, ##EQU16## ##EQU17##

Description

TECHNICAL FIELD

This invention pertains to the determination of suitable, low cost mixes of different employee types, such as mixes of regular employees and contract employees, to accomplish varying estimated quantities of work over a substantial forecast period.

BACKGROUND OF THE INVENTION

There is a trend in business organizations toward purchasing services from outside suppliers (contracting out) since at least 1980. For example, the W. E. Upjohn Institute for Employment Research found that 44% of employers in the United States use independent contract workers. Many employers predict even greater use of contract employees and other flexible staffing arrangements in the future.

Most employers hire contract workers to handle workload fluctuations and absences of regular staff. Some employers blend full-time and contract employees for greater cost control, improved productivity, and improved customer service. Employers also turn to contract labor for specialized skills possessed by the outside contractors. For example, janitorial, machine maintenance, engineering and drafting, accounting, and computer skills are frequently obtained using contract employees.

In manufacturing industries like the automobile industry, engineering design departments are often faced with the need to blend the regular employees of the company with employees supplied by outside contractors. Engineering design departments typically operate under strict headcount limits for regular employees and contract with an engineer supply firm for the remainder of a temporary workforce. A manufacturing company limits its salaried headcount, in part, because of the tremendous long-term expense that a regular workforce represents. Such a company usually offers a substantial compensation package for its regular employees so as to be competitive with other industrial companies. Thus, its employee retention levels exceed those of other companies. The high retention level results in very long average work lives for salaried employees. A large salaried workforce with long average work lives and high compensation translates into huge future costs for the company.

The second reason to use contract employees is to keep employees "off the books." Information about the number of employees at a company is widely disseminated and frequently mentioned by stock analysts. To achieve desirable levels, senior management often establishes a corporate headcount target. The corporate headcount target is broken down into targets for every group, division, staff, and department. Each department head is provided a headcount target and a dollar budget. Few, if any, limits are established for contract employees in the corporate budgeting process.

On the other hand, there are many important reasons to limit the use of contracting. Contract employees generally cost more per year than regular employees do. Contract employees also typically have significantly higher attrition rates, which disrupts projects and increases recruiting and training costs.

To limit these negative effects, engineering management sets goals for the maximum percentage of the engineering workforce that should be made up of contract employees (leveraging percentage). These goals are based on the strategic importance of each area of engineering. In general, management believes that areas where a company is creating new knowledge and areas that require critical skills should not rely on contractors. For instance, functions with few critical skills, such as data conversion, are 80-100% staffed by contract employees. Leading edge areas of a corporation's business and competitive interests should use a minimum of contract workers.

In some cases, the headcount limits set by senior management to limit liability and keep employees "off the books" are in direct conflict with engineering management's desire to use regular employees for critical areas. This conflict leads managers to ask the following questions. What is the optimal mix of contract and regular employees? How much do headcount limits increase staffing costs?

Accordingly, it would be desirable for organizations mixing contract and regular employees to develop a decision support tool that determines the minimum-cost staffing plan. It is an object of this invention to provide such a decision support tool within a framework of linear programming.

SUMMARY OF THE INVENTION

This invention provides a procedure to be practiced on a suitably programmed computer for determining a low cost mix of available different types of employees, for example, regular employees and contract employees, in an operation to produce the workload requirements of the concern.

Large engineering and manufacturing concerns, for example, may require hundreds or thousands of employees to fulfill their workload requirements. And the workload requirements may vary significantly over a period of months or years. Such concerns usually use workers having different employment arrangements such as those described above. It is a significant problem to determine a suitable balance of the different types of workers to achieve the varying work output of the organization at a minimum cost of hiring, training, using and terminating employees under such differing working arrangements.

This invention identifies long term workload requirements of an organization in combination with certain characteristics of different worker types and capabilities. The invention organizes the requirements and characteristics in a computer database suitable for linear programming analysis to determine an optimal number of each worker type for each period of months or years within the forecast time. In accordance with the invention, a method is provided that accomplishes such an analysis.

The subject method starts with the preparation of a long-term work forecast of an organization in which there are substantial changes in workload from month to month or year to year. The estimated work requirements by forecast period are entered into the database of a computer using a suitable application program such as, e.g., Microsoft Excel.RTM. or the like.

Each suitable potential worker type available to perform the forecast work, such as full time regular employee, part time regular employee or contract employee is identified. Preferably this analysis is undertaken for a single specific job, such as engineering designer. Data is entered into the computer database identifying each such worker type. If there are differences in productivity between worker types, productivity values are entered into the database. Data concerning the costs of supporting each type of worker are entered into the database. Examples of relevant costs include the training costs, the wages or operating costs, and termination costs of each type.

In addition to cost data, the process of this invention uses certain demographic data in order to estimate attrition rates for the worker types to be employed. This analysis is applicable to sufficiently large worker populations where attrition rates can be used with confidence. Accordingly, the process includes entering into the computer database (when known and if appropriate) demographic data comprising worker age demographic groups, worker length of service demographic groups, and the number of workers of each worker type in each said demographic group currently employed by the organization. Using these demographic categories, an attrition rate, based on the employment experience of said organization, is entered into the database for each combination of worker type and demographic group.

After entry of the worker type, cost data and attrition data, a linear program analysis is used to determine the low cost population combination of each type of worker to accomplish the work output for each work period. The analysis will produce the number of workers of each type that must be maintained, hired, trained or terminated during each period. Finally, a summary is prepared for each month or year under analysis stating such numbers of workers and the respective costs.

Linear programming has been developed and used for nearly 50 years as a mathematical approach to the general and widespread problem of allocating limited resources among competing activities or needs in an optimal way. It uses a mathematical model consisting of linear equations and inequalities to describe the problem of concern. The word "linear" means that all the mathematical functions in the model are required to be linear functions. The word "programming" in linear programming is a synonym for planning or analysis, and the analysis is done mathematically using, as stated, linear equations and linear inequalities as constraints on the equations. In a typical linear programming problem, trial solutions are tested iteratively to reach a optimal solution to the linear equation(s) that constitute the model.

In accordance with the subject invention, a set of parameters have been identified for use in a linear programming analysis of the regular employee-contract employee population balancing type problem. Furthermore, an illustrative set of linear equations and constraints are disclosed and applied in an illustration of a specific embodiment of the invention.

Other objects and advantages of the invention will be come apparent from the following description of an illustrative preferred embodiment.

DESCRIPTION OF A PREFERRED EMBODIMENT

Following is a linear programming representation of an optimization problem for regular/contract workforce planning that can assist in determining the best staffing strategy for a particular situation. This problem representation can be solved to determine the minimum-cost plan that will meet the workforce requirements. As input, the problem requires a complete set of data on workload, workforce costs, productivity and demographics. Once this data is entered, the model is solved to determine the optimal plan using standard linear programming software. This plan consists of the number of employees to hire and terminate in each year of a ten-year, or other selected, planning horizon.

There are at least two potential uses for this model. First, it can be used to direct staffing policy in any organization. Finding the minimum-cost staffing plan would be an arduous chore without such an automatic tool. By knowing what the minimum-cost strategy is, management can make more informed choices.

A second use of this model is to determine the cost of the management policies such as headcount limits. To observe the effects of these policy constraints, the user can enter data on these policies. The model will then report the minimum-cost plan that will meet the additional policy constraints. Since these policies restrict the number of plans that can be considered, they can only serve to maintain or increase the cost of the plan. (They may, however, improve the performance of the plan on measures other than cost.) The model is an excellent tool for playing "what if" games to learn about the impacts of such policy constraints.

The data used in the process is to be input into computer memory in a form suitable for linear programming analysis. Thus, mathematical notation such as the following can be employed.

There are four indices used to describe the worker type groups, the worker length of service groups and the worker hiring age groups. The notation for these indices is as follows:

Indices

i ranges over the set I of available employee types, i.e. regular and contract.

j ranges over the set {H.sup.min, . . . , H.sup.max } where H.sup.min and H.sup.max are the minimum and maximum hiring ages groups. j normally is a range of ages, e.g., 25-29 years.

k ranges over {0, . . . , S} where S is the maximum length of service in years for any employee.

t ranges over the set {0, . . . , T} where T is the maximum length of the planning horizon. Each period, t, can represent any unit of time such as one month or one year.

The following mathematical notation is used to describe the data to be input into the computer database:

Input Data on Workforce Costs

c.sup.x.sub.ijk =one-period cost of an employee of type i hired while in age group j who has k years of service (including salary, benefits, contract costs, ongoing training, etc.)

c.sup.y.sub.i =cost of hiring an employee of type i

c.sup.z.sub.ijk =cost of terminating an employee of type i who was hired while in age group j and has k years of service

Following is a specific example of a staffing problem involving different types of employees. In this example only two types of employees, regular and contract employees, are considered for simplicity of illustration. However, only a single type of job, for example, an engineering designer is treated in the problem. Also in this example, it is assumed that a startup company is involved that initially has no engineering designer employees, regular, contract or other. However, the company does have data of the type used in this example.

Tables 1 and 2 show an example set of input cost data for workforce costs. The costs are in thousands of dollars per year per employee. Table 1 summarizes hiring costs and annual salaries for employees with engineering design experience levels. Table 2 presents similar data for termination costs by experience level for regular and contract employee engineering designers. Table 2 also is broken down into age categories to illustrate this possibility, and there is pay variation by age group.

                                                            TABLE 1
                                    Input Data on Employee Costs - Hiring and
     Annual Costs
                 Regular
     Worker     Employee                   Regular Employee Cost per Year
                                Contract Employee
    Years of   Hiring Cost               (Wages, Benefits, Training, etc.)
              Contract Employee   Cost per Year
       of     (Recruiting,                          Hired at age
                 Hiring Cost     (Contract Costs)
     Service    Training)    15-19   20-24   25-29   30-34   35-39   40-44
     45-49    50+   Hired at any age   Hired at any age
        0          22         40      42      45      48      50      54
     57      60           22                 96
        1                     42      44      47      50      53      56
     59      63                              96
        2                     43      46      49      52      55      58
     61      65                              96
        3                     45      48      51      54      57      60
     64      68                              96
        4                     47      50      53      56      59      63
     66      70                              96
        5                     49      52      55      58      61      65
     69      73                              96
        6                     51      54      57      60      64      68
     72      76                              96
        7                     53      56      59      63      66      70
     75      79                              96
        8                     55      58      62      65      69      73
     78      82                              96
        9                     57      60      64      68      72      76
     81      86                              96
       10                     59      63      67      71      75      79
     84      89                              96
       11                     62      65      69      73      78      82
     87                                      96
       12                     64      68      72      76      81      86
     91                                      96
       13                     67      71      75      79      84      89
     94                                      96
       14                     69      73      78      82      87      93
     98                                      96
       15                     72      76      81      86      91      94
     102                                     96
       16                     75      79      84      89      92      95
                                           96
       17                     78      83      88      90      93      96
                                           96
       18                     81      86      88      91      94      96
                                           96
       19                     84      87      89      92      95      97
                                           96
       20                     85      88      90      93      96      98
                                           96
       21                     86      88      91      94      97
       22                     87      89      92      95      98
       23                     88      90      93      96      98
       24                     89      91      94      97      99
       25                     89      92      95      98      100
       26                     90      93      96      99
       27                     91      94      97      100
       28                     92      95      98      101
       29                     93      96      99      102
       30                     94      97      100     103
       31                     95      98      101
       32                     96      98      102
       33                     96      98      103
       34                     96      98      104
       35                     96      98      105
       36                     96      98
       37                     96      98
       38                     96      98
       39                     96      98
       40                     96      98
       41                     96
       42                     96
       43                     96
       44                     96
       45                     96
       46                     96
       47                     96
       48                     96


                                         TABLE 2
                         Input Data on Employee Costs - Termination Costs
                               Regular Employee Termination Costs
                                      (Severance Package)
     Contract Employee
    Worker Years                          Hired at age
     Termination Costs
     of Service    15-19   20-24   25-29   30-34   35-39   40-44   45-49    50+
       Hired at any age
          0         20      20      20      20      20      20      20      20
               0
          1         21      21      21      21      21      21      21      21
               0
          2         22      22      22      22      22      22      22      22
               0
          3         22      22      22      22      22      22      22      22
               0
          4         23      23      23      23      23      23      23      23
               0
          5         24      24      24      24      24      24      24      24
               0
          6         25      25      25      25      25      25      25      25
               0
          7         26      26      26      26      26      26      26      26
               0
          8         27      27      27      27      27      27      27      27
               0
          9         28      28      28      28      28      28      28      28
               0
         10         30      30      30      30      30      30      30      30
               0
         11         31      31      31      31      31      31      31
               0
         12         32      32      32      32      32      32      32
               0
         13         33      33      33      33      33      33      33
               0
         14         35      35      35      35      35      35      35
               0
         15         36      36      36      36      36      35      35
               0
         16         37      37      37      37      37      35
               0
         17         39      39      39      39      37      35
               0
         18         41      41      41      39      37      35
               0
         19         42      42      41      39      37      35
               0
         20         44      44      41      39      37      35
               0
         21         46      44      41      39      37
         22         47      44      41      39      37
         23         49      44      41      39      37
         24         49      44      41      39      37
         25         49      44      41      39      37
         26         49      44      41      39
         27         49      44      41      39
         28         49      44      41      39
         29         49      44      41      39
         30         49      44      41      39
         31         49      44      41
         32         49      44      41
         33         49      44      41
         34         49      44      41
         35         49      44      41
         36         49      44
         37         49      44
         38         49      44
         39         49      44
         40         49      44
         41         49
         42         49
         43         49
         44         49
         45         49
         46         49
         47         49
         48         49

                                     TABLE 3
                             Input Data on Workload
    Planning Period     1     2     3     4     5     6     7     8     9    10
    Number of Units of 1982  1915  1873  1688  1577  1383  1273  1297  1066
     1009
    Work Required


                                               TABLE 4
                                     Input data on Employee Productivity
                                        Regular Employee
                                Units of Work Produced Per Year
         Contract Employee
    Worker Years                          Hired at age
     Units of Work Produced Per Year
     of Service    15-19   20-24   25-29   30-34   35-39   40-44   45-49    50+
             Hired at any age
          0        0.90    0.90    0.90    0.90    0.90    0.90    0.90    0.90
                   0.90
          1        0.94    0.94    0.94    0.94    0.94    0.94    0.94    0.94
                   0.91
          2        0.97    0.97    0.97    0.97    0.97    0.97    0.97    0.97
                   0.92
          3        1.01    1.01    1.01    1.01    1.01    1.01    1.01    1.01
                   0.92
          4        1.05    1.05    1.05    1.05    1.05    1.05    1.05    1.05
                   0.92
          5        1.09    1.09    1.09    1.09    1.09    1.09    1.09    1.09
                   0.92
          6        1.14    1.14    1.14    1.14    1.14    1.14    1.14    1.14
                   0.92
          7        1.18    1.18    1.18    1.18    1.18    1.18    1.18    1.18
                   0.92
          8        1.23    1.23    1.23    1.23    1.23    1.23    1.23    1.23
                   0.92
          9        1.28    1.28    1.28    1.28    1.28    1.28    1.28    1.28
                   0.92
         10        1.33    1.33    1.33    1.33    1.33    1.33    1.33    1.33
                   0.92
         11        1.39    1.39    1.39    1.39    1.39    1.39    1.39
                   0.92
         12        1.44    1.44    1.44    1.44    1.44    1.44    1.44
                   0.92
        13-48      1.50    1.50    1.50    1.50    1.50    1.50    1.50
                   0.92

                             TABLE 5
          Input Data on Management Policies - Hiring and
    Termination Limits and Average Length of Service Requirement
                         Policy Parameter
          Regular Employee Hiring Limit            500
          Contract Employee Hiring Limit           5000
          Regular Employee Termination Limit          0.25
          Contract Employee Termiantion Limit          1
          Minimum Average Length of Service          0


                                            TABLE 6
                          Input Data on Management Policies - Headcount Limits
    Planning Period         1       2       3       4       5       6       7
         8       9      10
    Maximum Headcount for  99999   99999   99999   99999   99999   99999
     99999   99999   99999   99999
    Regular Employees
    Maximum Headcount for  99999   99999   99999   99999   99999   99999
     99999   99999   99999   99999
    Contract Employees

                                                   TABLE 7
                       Input Data on Worker Demographics - Survival or
     Retention Rates
                                        Regular Employee
                                         Survival Rates
    Worker Years                          Hired at age
     Contract Employee Survival Rates
     of Service    15-19   20-24   25-29   30-34   35-39   40-44   45-49    50+
             Hired at any age
                   0.94    0.88    0.96    0.94    0.96    0.96    0.97    0.98
                   0.60
          0        0.90    0.90    0.96    0.95    0.97    0.97    0.97    0.98
                   0.80
          1        0.87    0.93    0.97    0.96    0.97    0.97    0.97    0.97
                   0.80
          2        0.86    0.95    0.97    0.97    0.97    0.97    0.98    0.96
                   0.80
          3        0.86    0.96    0.98    0.97    0.97    0.97    0.98    0.94
                   0.80
          4        0.88    0.96    0.98    0.98    0.98    0.97    0.98    0.91
                   0.80
          5        0.90    0.97    0.98    0.98    0.98    0.97    0.98    0.89
                   0.80
          6        0.93    0.97    0.98    0.99    0.98    0.97    0.97    0.89
                   0.80
          7        0.95    0.97    0.98    0.99    0.98    0.97    0.96    0.90
                   0.80
          8        0.96    0.98    0.98    0.99    0.98    0.98    0.94    0.92
                   0.80
          9        0.96    0.98    0.98    0.99    0.99    0.98    0.91    0.00
                   0.80
         10        0.97    0.98    0.99    0.99    0.99    0.98    0.89
                   0.80
         11        0.97    0.98    0.99    0.99    0.99    0.98    0.89
                   0.80
         12        0.97    0.98    0.99    0.99    0.99    0.97    0.90
                   0.80
         13        0.98    0.99    0.99    0.99    0.99    0.96    0.92
                   0.80
         14        0.98    0.99    0.99    0.99    0.99    0.94    0.00
                   0.80
         15        0.98    0.99    0.99    0.99    0.98    0.91
                   0.80
         16        0.98    0.99    0.99    0.99    0.98    0.89
                   0.80
         17        0.98    0.99    0.99    0.99    0.97    0.89
                   0.80
         18        0.99    0.99    0.99    0.99    0.96    0.90
                   0.80
         19        0.99    0.99    0.99    0.99    0.94    0.00
         20        0.99    0.99    0.99    0.98    0.91
         21        0.99    0.99    0.99    0.98    0.90
         22        0.99    0.99    0.99    0.97    0.89
         23        0.99    0.99    0.99    0.95    0.90
         24        0.99    0.98    0.98    0.91    0.00
         25        0.99    0.98    0.97    0.88
         26        0.99    0.98    0.96    0.86
         27        0.99    0.97    0.95    0.85
         28        0.99    0.97    0.93    0.86
         29        0.98    0.97    0.90    0.00
         30        0.98    0.97    0.86
         31        0.98    0.96    0.84
         32        0.97    0.95    0.83
         33        0.97    0.92    0.85
         34        0.97    0.88    0.00
         35        0.97    0.83
         36        0.96    0.80
         37        0.95    0.79
         38        0.92    0.81
         39        0.88    0.00
         40        0.83
         41        0.80
         42        0.79
         43        0.81
         44        0.85
         45        0.91
         46        0.96
         47        0.00
         48        0.00


                                         TABLE 8
                      Input Data on Worker Demographics - Initial Population
                                        Regular Employee
                                       Initial Population
     Contract Employee
    Worker Years                          Hired at age
     Initial Population
     of Service    15-19   20-24   25-29   30-34   35-39   40-44   45-49    50+
       Hired at any age
                     0       0       0       0       0       0       0       0
               0
          0          0       0       0       0       0       0       0       0
               0
          1          0       0       0       0       0       0       0       0
               0
          2          0       0       0       0       0       0       0       0
               0
          3          0       0       0       0       0       0       0       0
               0
          4          0       0       0       0       0       0       0       0
               0
          5          0       0       0       0       0       0       0       0
               0
          6          0       0       0       0       0       0       0       0
               0
          7          0       0       0       0       0       0       0       0
               0
          8          0       0       0       0       0       0       0       0
               0
          9          0       0       0       0       0       0       0       0
               0
         10          0       0       0       0       0       0       0
               0
         11          0       0       0       0       0       0       0
               0
         12          0       0       0       0       0       0       0
               0
         13          0       0       0       0       0       0       0
               0
         14          0       0       0       0       0       0       0
               0
         15          0       0       0       0       0       0
               0
         16          0       0       0       0       0       0
               0
         17          0       0       0       0       0       0
               0
         18          0       0       0       0       0       0
               0
         19          0       0       0       0       0       0
               0
         20          0       0       0       0       0
         21          0       0       0       0       0
         22          0       0       0       0       0
         23          0       0       0       0       0
         24          0       0       0       0       0
         25          0       0       0       0
         26          0       0       0       0
         27          0       0       0       0
         28          0       0       0       0
         29          0       0       0       0
         30          0       0       0
         31          0       0       0
         32          0       0       0
         33          0       0       0
         34          0       0       0
         35          0       0
         36          0       0
         37          0       0
         38          0       0
         39          0       0
         40          0
         41          0
         42          0
         43          0
         44          0
         45          0
         46          0
         47          0
         48          0

                             TABLE 9
       Input Data on Demographics - Hiring Age Distribution
         Fraction of Regular Employees Hired by Age Group
                           Hired At Age
     15-19   20-24   25-29   30-34   35-39   40-44   45-49   50+
     0.12    0.29    0.27    0.17    0.06    0.04    0.05   0.00

                                       TABLE 10
                     Linear Programing Output for Specific Example
                                       ##STR1##
              Year       0    1     2     3     4     5     6     7     8     9
        10
     Regular  Hire           500   500   500   264   500   --    386   259   --
        57
      Staff   Terminate      --    --    --    --    --    398   --    --    62
        --
              Quit           --    34    63    86    90    108   77    89    91
        73
              Total      0   500   966  1,403 1,580 1,990 1,485 1,794 1,964
     1,811 1,795
    Contract  Hire          1,750  26    --    --    415   --    --    --    --
        --
      Staff   Terminate      --    --    600   205   --    249   --    --    --
        --
              Quit           --    700   220   51    --    166   --    --    --
        --
              Total      0  1,750 1,076  256   --    415   --    --    --    --
        --
       Total Staff      0  2250  2042  1659  1580  2406  1485  1794  1964  1811
      1795
      Total   Hire       0   49    12    11     6    20    --     9     6    --
         1
      Costs   Terminate  0   --    --    --    --    --     9    --    --     1
        --
      ($M)    Annual     0   191   148   91    77    138   74    90    101   97
        100
              Total      0   240   160   102   83    158   83    99    107   98
        101

• Inventors
  Kintner, Hallie J.; Feit, Eleanor M.;
• Assignee
  General Motors Corporation (Detroit, MI)
• Published
  May-4-2004
• Current US Classes:
  705/7
  705/8
  705/9
• Application #
  431251
• International Classes
  G06F 017/60
• Field of Search
  705/9 705/8 705/7
• Examiner
  Hafiz; Tariq R.
• Agent
  Marra; Kathryn A.
• US Patent References:
  5117353
  5325292
  5765140
  5884276
  5911134
  5913201
  6219649
  6275812