Class_6a

Class_6a - EMSE 154-254 Fall 2008 Integer Programming...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
EMSE 154-254 Fall 2008 Instructor: Hernan Abeledo Source: Optimization Modeling with LINGO 1 Integer Programming Models Minimum Batch Size Constraints When there are substantial economies of scale in undertaking an activity regardless of its level, many decision makers will specify a minimum “batch” size for the activity. For example, a large brokerage firm may require that, if you buy any bonds from the firm, you must buy at least 100. A zero/one variable can enforce this restriction as follows. Let: x = activity level to be determined (e.g., number of bonds purchased), y = a zero/one variable = 1, if and only if x > 0, B = minimum batch size for x (e.g., 100), and U = known upper limit on the value of x . The following two constraints enforce the minimum batch size condition: x Uy By x If y = 0, then the first constraint forces x = 0. While, if y = 1, the second constraint forces x to be at least B . Thus, y acts as a switch, which forces x to be either 0 or greater than B . The constant U should be chosen with care. For reasons of computational efficiency, it should be as small as validly possible.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
EMSE 154-254 Fall 2008 Instructor: Hernan Abeledo Source: Optimization Modeling with LINGO 2 The Simple Plant Location Problem (also known as Uncapacitated Plant Location Problem) The Simple Plant Location Problem (SPL) is a commonly encountered form of fixed charge problem. It is specified as follows: n = the number of sites at which a plant may be located or opened, m = the number of customer or demand points, each of which must be assigned to a plant, k = the number of plants which may be opened, f i = the fixed cost (e.g., per year) of having a plant at site i , for i = 1, 2, . . . , n , c ij = cost (e.g., per year) of assigning customer j to a plant at site i , for i = 1, 2, . .. , n and j = 1, 2, . .., m . The goal is to determine the set of sites at which plants should be located and which site should service each customer. An application of the SPL model is the lockbox location problem encountered by a firm with customers scattered over a wide area. (We covered this example last class). Define the decision variables: y i = 1 if a plant is located at site i , else 0, x ij = 1 if the customer j is assigned to a plant site i , else 0. A compact formulation of this problem as an IP is:
Background image of page 2
EMSE 154-254 Fall 2008 Instructor: Hernan Abeledo Source: Optimization Modeling with LINGO 3 The constraints in (2) force each customer j to be assigned to exactly one site. The constraints in (3) force a plant to be opened at site i if any customer is assigned to site i. Excepting small problems, solving this model requires a lot of computer time (and memory) because its LP relaxation (i.e., conditions (5) and (6) substituted by 0 y i 1 and 0 x ij 1) tends to have highly fractional solutions, with little similarity to the IP solution.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/02/2010 for the course EMSE 254 taught by Professor Hernanabeledo during the Fall '08 term at GWU.

Page1 / 25

Class_6a - EMSE 154-254 Fall 2008 Integer Programming...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online