ISYE 3104 Summer 2003 Homework 5 Solution

Chapter 9Layout Strategy

DISCUSSION QUESTIONS

  1. How would you obtain data and determine the number of trips in:

(a)a hospital?

(b)a machine shop?

(c)an auto-repair shop?

Most organizations have some procedure for documenting movement of their product. For instance, a hospital has doctor’s orders indicating the tests and procedures that a patient is to undergo. A machine shop has routing documents indicating the operations that an order is to follow as the product moves through the shop. And an auto repair shop knows what repairs, parts, and labor are used on a particular job and as a result where the job was done and the trips made necessary.

In each of the above examples a matrix would be made showing the number of trips. And the distance (or time or cost) of each trip would be determined.

  1. What are the two major trends influencing office layout?

Two major trends influencing office layout are: technology and virtual companies.

  1. What layout variables would you consider particularly important in an office layout where computer programs are written?

Some of the layout variables you might want to consider as particularly important in an office where computer programs are to be written are:

  • Ease of communication
  • Provision of privacy and a quiet work environment
  • Lighting –especially as it related to glare on CRT screens
  • Consideration of ergonomic or human factor issues in equipment layout and construction

PROBLEMS

Problem 9.2

What is the appropriate layout of the new building?

Based on the above matrix, we can establish the following closeness ratings among the different processes:

M / W / D / L / G / B
M
W
D
L
G
B / - / A
- / E
U
- / U
E
U
- / I
U
A
O
- / E
U
O
U
U
-

To compute the optimal solution of this problem, in a strict sense, one would employ the following mathematical programming formulation:

Parameters:

dij : distance between available areas (rooms) i and j, i,j{1,…,6}

fkl : number of trips between processes ik and l, k,l  {1,…,6}

Variables:

xkibinary variable with a value of 1 indicating that process k is assigned to location i, k,i  {1,…,6}

Objective:min i,j,k,l dij*fkl*xki*xlj

Constraints

i xki = 1, k (i.e., every process k must be assigned to one and only one location)

k xki = 1, i (i.e., every location i must be assigned to one and only one process)

xki{0,1},  i, k (i.e., the decision variables are all binary)

The above formulation is known as a quadratic assignment problem. (it is an assignment because as it is stated by the problem constraints, we are essentially trying to match the processes with the available areas/rooms, and it is quadratic because the objective is a quadratic function of the decision variables). However, the non-linear structure (quadratic) of the objective, combined with the binary nature of the decision variables, makes it a computationally hard problem. i.e., there are no readily available efficient algorithms for its solution.
Problem 9.4

You have been asked to evaluate these two kitchen layouts and to prepare a recommendation for your boss, Mr.Reid, so that he can proceed to place the contract for building the kitchens.

ΣΣTij x Dij = 600 with rooms fixed (504, if not fixed; 560, if the sink is fixed in one location)

ΣΣTij x Dij = 602 (if rooms are fixed; 566 if not; and 595 if the sink is fixed in one location)

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