Training has become a major cost of doing business. A 1995 survey of all U.S. businesses with 100 or more employees revealed that approximately $52 billion was being spent on training; it has been estimated that $90 to $100 billion is being spent on training overall. Developing strategies to implement cross-training is a current topic in the operations research (OR) literature. Management consultants advocate aggressive education and professional development to remain competitive in the global and local markets. Employees now expect job and skill growth to be a major component of their duties.

Increased training costs have occurred for many reasons. Employees view training in the form of formal degrees and documented technical skills as important for job security. Technology is changing at a rapid pace. It has been claimed that high schools and universities are not producing the skills needed by industry, so the industry must train and reeducate recent graduates. For high school graduates, this may include training in technology-based skills; for college graduates, this may include developing nontechnical skills such as leadership, communications, interpersonal relations, and ethics.

Problem Environment

For a corporation, the primary purpose of training is to ensure that employees have the key skills needed to effectively manage and operate the business. There are many options for providing training. For example, to train staff members in computer skills, a corporation may use any of the following strategies:

■ hiring an outside consultant to develop and present an on-site training course,

■ using corporate personnel to develop and present an on-site training course,

■ purchasing a training course and having employees use it for self-study,

■ contracting with a local college or university to provide training, or

■ sending employees to an off-site training seminar.

The above possibilities are for a single skill. The purpose of many training programs, however, is to give employees a broad set of skills. Often the skill sets of two or more programs partially overlap. When this happens, the corporation must choose the set of programs that give employees the required skills for their jobs and the appropriate employees for each training program. In any case, training decisions made in an ad-hoc “pay-as-you-go” manner will be inefficient and generally result in additional expenses. To give the decision problem structure, the following assumptions are appropriate:

■ We have a known study period—for example, the next 3 or the next 5 years—over which we need to plan training. The study period should fit with the overall business strategy and enable accurate estimates of training needs and available resources.

■ There is a known set of skills that employees need. Among others, these may include technical, interpersonal, communication, and management skills.

■ Employees are divided into classes. In each class, we have estimates for (1) the number of employees, (2) the employee hourly wage, (3) the number of employees that require each particular skill, and (4) the maximum time available for training employees in each class during the study period.

■ There is a list of training programs. For each program, we assume we have (1) the set of skills taught, (2) the cost, (3) the development time, (4) the completion time for an employee, and (5) the maximum number of employees who can participate per decision cycle.

■ Training is equally effective for all people, thus we are concerned with which programs to offer and which employees in each class to assign to each program. If we know the quality of the training for individual skills for individual classes, then we can relax this assumption

Potential Corporate

Setting Your job is to develop models to aid businesses and corporations in determining the appropriate training programs to use. The type of model and issues often depend on the size of the corporation and the potential uses of the models. For large corporations, there are many employees in each class, so it is not necessary to model and schedule the individual employee. Concentrate instead on the assignment of classifications to programs and ignore the assignment of specific individuals to programs. Also, sufficient resources exist to develop internal training programs, hence you should consider program development costs as well as employee costs (lost work time, travel, lodging, meals, course materials) in the objective. A large corporation can use the model to plan the development of courses. This will help determine 

(1) program-development costs so that in-house programs are cost-effective and 

(2) appropriate programs for each employee classification so that, on average, there is sufficient time to complete the assigned programs within the available time. For small businesses, the focus is often different. Typically, these companies do not develop in-house programs because they do not train enough employees to justify development costs. Because the number of employees is small, it is important to model down to the employee level and schedule employees so that both training and job tasks can be completed. Your OR consulting firm has been hired to design the training program for a small company. There are no in-house classes, and vendors provide all training. The company has determined 41 skills that are important for its employees; these are listed in Table 16. There are six employees; the salary level and skills required for each person are given in Table 17. You can assume that there are 250 working days per year. There are 15 programs available for use; Table 18 contains the cost per person and the skills covered for each program. In Table 18, a 1 in the row for program p and the column for skill s implies that program p contains skill s. Table 19 lists the programs that conflict in time with other programs (for example, programs 3, 5, and 8 conflict with program 1). An employee cannot take two programs simultaneously. It is company policy that each employee is limited to 15 days for training per year.

Key Questions Your job is to develop a recommendation for the company for addressing its training needs. In particular, you should address the following key questions:

■ Which training programs should we be using? What is the assignment of personnel to those programs?

■ Identify programs with heavy use that may justify the development of an in-house course. How much would you be willing to pay for that development if you could use the program for the next three years?

■ We have the opportunity to negotiate prices for programs. Which programs would you suggest are candidates for negotiation?

■ What skills are especially expensive for us to cover? If we were to develop our own programs, what skills should be covered?

■ Would your recommendation change if we allowed more days of training per year?
 

TABLE 16 Sells List L New employee orientation 2 Performance appraisals 3 Personal computer apps 4 5 6 7 Safety 8 9 10 11 12 13 Leadership Sexual harassment Team building 14 15 16 17 18 Hiring and selection process New equipment operation Training the trainer Product knowledge Decision making Listening skills Time management Conducting meetings Quality improvements Delegation skills Problem solving Goal setting 19 20 21 Motivation Managing change TABLE 18 Enrollment Cost and Skills of Each Program Propan Erant Cost (3) Program I Program 2 Program 3 Program 4 Program 5 Program 6 Program 7 Program 8 Program 9 Program 10 Program 11 Program 12 Program 13 Program 14 Program 15 Pagan Program I Program 2 Program 3 Program 4 Program 5 Program 6 500 300 500 575 800 400 200 1,000 200 500 700 600 400 900 700 22 23 24 25 26 27 28 29 30 AR=R33831 IC 32 EE 34 35 36 37 38 39 40 41 Stress management Computer programming Diversity Data processing/MIS Planning Public speaking and presentation Strategic planning Writing skills Negotiating skills Finance Marketing Substance abuse Ethics Outplacement and retirement Creativity Purchasing Smoking cessation Financial and business literacy Reengineering Foreign language Skull1-20 11010000001111101000 00001111000000000000 00000010010000010001 01010000110010001000 00010001001000001110 10000000000110000000 10000001000000110000 00000000001111110010 11110000000001100000 00000000100000001000 00000000010100000000 00000000001001000000 SKR 01110001100000000000 10001100000000010100 10101011100000000010 100000000001000000000 011000000000000100000 111111101010000100000 100001000000010000000 000101000000100000110 000000001001100110000 010000000001010000000 111100101100000010000 000111000000000000110 Program 7 Program 8 Program 9 Program 10 Program 11 011000101101001100000 Program 12 000110000011000000000 011100000011010000000 Program 13 101010000010100000000 Program 14 Program 15 100000110000000000000 100100000000010000000 TABLE 17 Salary and Skills Required for Each Job Classification Person Salary (5) Senior Manager 250,000 Project Manager 200,000 150,000 Professional 150,000 100,000 80,000 Sales Technician Administrative Assistant Person Senior Manager Project Manager Professional Technician Administrative Assistant Program 6 (3) Program 7 (5) Program 8 (2) Program 9 (3) Program 10 (3) Program 11 (2) Program 12 (4) Program 13 (3) Program 14 (4) Program 15 (3) Skills 1-20 01010000000111010110 01001000001111100100 11001110100010100001 11000000110010001001 11101001000000000001 11101000000000000000 Skills 21-41 000111010110101101111 TABLE 19 Interfering Programs Program Number (Days Long) Program 1 (2) Program 2 (2) Program 3 (4) Program 4 (3) Program 5 (2) 011101111010100111101 000011000100101001101 0000110001001010011 111100000000000000000 000000000100000001110 3 3 1 6 1 4 2 1 5 2 6 3 8 4 9 Programs that Interfere 572797 4 10 15 8 12 5 14 9 11 8 10 12 14 12 11 6 13 15 11 13 | 14