Review Vocabulary

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Corner point principle This principle states that there is a corner point of the feasible region that yields the optimal solution. (pp. 134, 135)

Feasible points A possible solution (but not necessarily the best one) to a linear-programming problem. With just two products, we can think of a feasible point as a point on the plane. (p. 142)

Feasible region The set of all feasible points—that is, possible solutions to a linear-programming problem. For problems with just two products, the feasible region is a part of the plane. Also called feasible set. (p. 132)

Indicator value of a cell The change in cost due to shipping an increased or decreased amount, using the cells in a transportation tableau that form a circuit consisting of circled cells together with a selected cell that is not circled. When an indicator value is negative, a cheaper solution can be found by shipping using this cell. (p. 155)

Linear programming A set of organized methods of management science used to solve problems of finding optimal solutions, while at the same time respecting certain important constraints. The mathematical formulations of the constraints in linear-programming problems are linear equations and inequalities. Mixture problems usually are solved by some type of linear programming. (p. 126)

Minimum constraint An inequality in a mixture problem that gives a minimum quantity of a product. Negative quantities can never be produced. (p. 131)

Mixture chart A table displaying the relevant data in a linear-programming mixture problem. The table has a row for each product and a column for each resource, for any nonzero minimums, and for the profit. (p. 129)

Mixture problem A problem in which a variety of resources available in limited quantities can be combined in different ways to make different products. It usually is desirable to find the way of combining the resources that produces the most profit. (p. 127)

Northwest Corner Rule A method for finding an initial, but rarely optimal, solution to a transportation problem starting from a tableau with rim conditions. The amounts to be shipped between the suppliers and demanders are indicated by circling numbers in the cells in the tableau. The number of cells circled after applying the method will equal the number of rows plus the number of columns minus 1. The method depends on locating at each stage the “northwest corner” of the original tableau or a part of it. (p. 152)

Optimal production policy A corner point of the feasible region where the profit formula has a maximum value. (p. 128)

Profit line In a two-dimensional, two-product, linear-programming problem, the set of all points that yield the same profit. (p. 141)

Resource constraint An inequality in a mixture problem that reflects the fact that no more of a resource can be used than what is available. (p. 131)

Rim conditions The supplies available (listed in a column at the right of a transportation tableau) and demands required (listed in a row at the bottom of a transportation tableau) in a transportation problem. The supplies available are usually taken to meet exactly the demands required. (p. 149)

Simplex method One of a number of algorithms for solving linear-programming problems. (p. 145)

Stepping stone method A method for solving a transportation problem that improves the current solution, when it is not optimal, by increasing the amount shipped using a cell with a negative indicator value. (p. 157)

Tableau A table for a transportation problem indicating the supplies available and demands required, as well as the cost of shipping from a supplier to a demander. The amounts to be shipped from different suppliers to different users are indicated by circled cells in the tableau. The number of such circled cells is always the number of rows plus the number of columns diminished by 1 for the tableau. (p. 151)

Transportation problem A special type of linear-programming problem where we have sources of supplies and users of, or demand for, these supplies. There is a cost to ship an item from a supplier to a demander. The goal is to minimize the total shipping cost to meet the demands from the supplies. (p. 149)