Workforce Planning

A software company is anticipating increased demand for its products. However, management is concerned about their programmers' adequacy to meet the increased demand given the history of workforce turnover (5 percent of the programmers leave the company at the end of each month).

Rather than hiring new workers, management is contemplating enrolling some or all of their programmers in a month-long intensive training program. After successfully completing the training program, a programmer would receive a salary increase and sign a contract not to leave the company for at least six months. Successfully trained programmers would therefore be immune from normal turnover and layoffs.

Management believes that successful completion of the program would increase a programmer's productivity by 20 percent and plans to implement a no-layoff policy to encourage participation. However, only 90 percent of the programmers are predicted to complete the training program successfully. Those who enroll in training but do not complete the program successfully will return to the workforce at their pre-training skill level. (For simplicity, we assume that they are not candidates for a normal turnover during their training month but are candidates for normal turnover after the training month, and they can enroll in the training program again later.)

The monthly demand for untrained programmers for the next six months is shown in the table below. If trained programmers are available, their higher productivity allows management to satisfy demand with fewer programmers. For example, the demand in January can be satisfied with 100 untrained programmers or with 82 untrained and 15 trained programmers (since 82 + 1.20 * 15 = 100).

	Number of Untrained Programmers Required
Month	Jan	Feb	Mar	Apr	May	Jun
Programmers	100	100	115	125	140	150

A programmer cannot be engaged in production and participate in the training during the same month. At the beginning of January, there are 145 (untrained) programmers in the workforce. The company's monthly payroll costs are $3,000 per untrained programmer (engaged in either production or the training program) and $3,300 per trained programmer.

Questions:

1. Determine a training schedule and a layoff schedule for January through June that meets the workforce requirements at the minimum cost. What is the optimal cost? (Define decision variables as continuous variables.)
2. If the company could shift demand from June to April (i.e., June demand = 125 and April demand = 150), determine the optimal training schedule and the layoff schedule. Would the cost be higher or lower and by how much? (Define decision variables as continuous variables.)

Assumptions:

1. Layoff:
   1. A layoff is a decision that the company makes. People who are laid off by the company will not return to the company in the next six months.
   2. Layoff decisions are made by the company at the beginning of each month, simultaneously, as the training decisions are made.
   3. People who get laid off at the beginning of the month will leave the system at the beginning of the month and will not receive a salary in that month.

1. Turnover:
   1. Turnover means employees leave the company voluntarily for various reasons (e.g., they might be pursuing better opportunities elsewhere).
   2. Each month, after laying off some untrained employees and sending some untrained employees to the training program, the company has the remaining untrained employees and trained employees work in production. Those remaining untrained employees will have a 5 percent turnover at the end of the month; they will receive a salary for that month because they leave at the end of the month.

Questions: (a) Determine a training schedule and a layoff schedule for January through June that meets the workforce requirements at the minimum cost. What is the optimal cost? (Define decision variables as continuous variables.) (b) If the company could shift demand from June to April (i.e., June demand = 125 and April demand = 150), determine the optimal training schedule and the layoff schedule. Would the cost be higher or lower and by how much? (Define decision variables as continuous variables.) Assumptions: 1. Layoff: a. A layoff is a decision that the company makes. People who are laid off by the company will not return to the company in the next six months. b. Layoff decisions are made by the company at the beginning of each month, simultaneously, as the training decisions are made. c. People who get laid off at the beginning of the month will leave the system at the beginning of the month and will not receive a salary in that month. 2. Turnover: a. Turnover means employees leave the company voluntarily for various reasons (e.g., they might be pursuing better opportunities elsewhere). b. Each month, after laying off some untrained employees and sending some untrained employees to the training program, the company has the remaining untrained employees and trained employees work in production. Those remaining untrained employees will have a 5 percent turnover at the end of the month; they will receive a salary for that month because they leave at the end of the month.This assignment consists of one problem. You are required to solve the problem by building linear program models and then solving them using Pu'LP. Each team needs to submit the following les to this assignment through learni'VashU: Python models. You should submit two separate files, one for each problem. An electronic copy of a short report. In the report, you should: 0 Provide a network diagram representation of each problem. Legible, handdrawn pictures are acceptable. 0 Formulate (in math) a linear program model for each problem (variables, objective function, constraints). Legible, handwritten math formulations are acceptable. 0 State any assumptions you made if the problem statement is not 100 percent clear about certain aspects of the problem 0 Present the optimal solution in an easytocommunicate format. This is a group deliverable. Work with your designated team members only. Workforce Planning A software company is anticipating increased demand for its products. However, management is concerned about their prograaners' adequacy to meet the increased demand given the history of workforce turnover (5 percent of the programmers leave the company at the end of each month]. Rather than hiring new workers, management is contemplating enrolling some or all of their programn'lers in a month-long intensive training program. After successfully completing the training program, a programmer would receive a salary increase and sign a contract not to leave the company for at least six months. Successfully trained programmers would therefore be immune from normal turnover and layoffs. Management believes that successful completion of the program would increase a programmer's productivity by 20 percent and plans to implement a nolayotf policy to encourage participation. However, only 90 percent of the programmers are predicted to complete the training program successfully. Those who enroll in training but do not complete the program successfully will return to the workforce at their pretraining skill level. (For simplicity, we assume that they are not candidates for a normal turnover during their training month but are candidates for normal turnover after the training month, and they can enroll in the training program again later.) The monthlyr demaniifor untrained programmersybr the next six months is shown in the table below. Iftraineil programmers are available, their higher productivity allows management to satisfy demand with fewer programmers. For example, the demand in JTaniiary can be satised with 100 untrained programmers or with 32 untrained and 15 trained programmers {since 8'2 + 1.20 *15 = 100). Number of Untrained Programmers Required Month Jan Feb Mar Apr Delay ]un Programmers 100 100 115 125 140 150 A programmer cannot be engaged in production and participate in the training during the same month. At the beginning of january, there are 145 (untrained) programmers in the workforce. The company's monthly payroll costs are $3,000 per untrained programmer (engaged in either production or the training program) and $3,300 per trained programmer