Using LINGO for Business Students

Abstract

For business majors doing a survey course involving linear, integer, and possibly non-linear optimization, it is quite common to use the Solver in Excel for solving optimization models. In addition to this, or even indeed instead of doing this, we propose using optimization software which closely mimics the structure of the underlying algebraic model. For this, we suggest LINGO, not with the use of sets, but alternatively using only a basic set of commands, which is called scalar mode. We argue that this is simpler than using a solver add-in for Excel. Also, we argue that scalar mode in LINGO is much simpler than LINGO with the definition of sets, because the students do not have to learn and apply several concepts needed in order to apply the sets approach. We also give an example of when the transition to sets would be appropriate.

Appendix

This section gives the problem description that was used for the creation of the two-variable cement model [17].

A cement company makes two types of cement, which they market under registered tradenames, but for our purposes we will simply call them Type 1 and Type 2. Cement is sold by the Tonne (a Tonne is 1000 kilograms), and production is measured in Tonnes per Day, abbreviated as TPD. The company has contractual sales obligations to produce at least 40 TPD of Type 1 cement, and at least 30 TPD of Type 2 cement.

The physical capacity of the plant, which is governed by such things as conveyor belt speed, storage size, and so on, is limited to 200 TPD. A new labour agreement has increased the length of breaks, and restricts and makes more costly the use of overtime. The company therefore wishes to find its best production plan using the new work rules with everyone working a 40-h week. Work is measured in this company by the labour-hour, which is one person working for 1 h. Each type of cement is made in three departments, labeled A, B, and C. To make each Tonne of Type 1 cement requires three labour-hours in Department A, one and a half labour-hours in Department B, and four labour-hours in Department C. The amounts of work per Tonne of Type 2 cement are two, five, and six labour-hours in Departments A, B, and C respectively.

Based on the current authorized strength in each department, and factoring in allowances for breaks, absenteeism, and so on, Department A has 585 labour-hours available each day. Departments B and C are allowed to use up to 500 and 900 labour-hours per day respectively. These are the most they can use for the making of cement. If a department has some time leftover (i.e., if the time to make the cement is less than the number of labour-hours available), then the workers will be idle for a few minutes at the end of the day. The three departments require workers with very different training and skills, so the possibility of transferring employees from one department to another is not something that is factored into the planning process.

Taking the market price of each type of cement and from this subtracting all the variable costs of making the cement leaves the company with a profit of $8 per Tonne of Type 1 cement, and $10 per Tonne of Type 2 cement. There are also fixed costs (taxes, security, and so on) which total $1400 per day. The company wants to know how much should be produced of each type of cement, so that the profit is maximized.