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Operator-Machine Assignment Problem: Minimizing Manufacturing Cost, Assignments of Introduction to Business Management

University of Alabama - HuntsvilleIntroduction to Business Management

An assignment from dr. Stafford's msc 385 class, fall 2006. Students are required to solve two versions of the operator-machine assignment problem, where they must determine the cost per unit, operator idle time, output per operator, machine idleness, and cycle time under different machine and labor cost scenarios. In part ii, students are asked to find the optimal number of machines to assign to a single operator to minimize per-unit manufacturing cost and analyze the cycle time, operator idle time, and machine idleness for that configuration. Part iii involves sensitivity analyses on labor cost (l) and machine cost (p).

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Assignment 01 Operator-Machine Assignment Problem Dr. Stafford MSC 385 Fall 2006 Page 1
ASSIGNMENT 01: OPERATOR - MACHINE ASSIGNMENT PROBLEM
Dr. Stafford MSC 385 Fall 2006
Due Date: Monday. September 11, 2006
Solve the following two questions and be prepared for a separate quiz on each question.
Question 1
A company produces a critical part on a set of multiple, identical machines. These machines are semi-automatic in
that, after they have been loaded and started, they process the part without need of further human intervention until
the part processing is completed. At that time, an operator must unload the machine, reload it, and press the start
button once more. Solve this problem twice, once for each set of parameters (rows) in the table below.
Problem Version R (min.) U (pc/cycle) Labor Cost
($/hr) Machine Cost
($/hr/machine) S (min)
A 13 3 $14 $37 3
B 19 2 $30 $25 5
Part I Currently, the company assigns one machine to each operator. For this arrangement, answer the following
questions.
1 What is the cost per unit to produce the critical part under the one man-one machine arrangement? (round
answer to nearest $0.01, if necessary)
2 What is the operator idle time (in minutes) per hour under this arrangement? (round answer to nearest 0.01
minute, if necessary)
3 What is the output per operator per 8-hour shift under this arrangement?
4 What is the machine idleness (interference) (in minutes) per machine per cycle under this arrangement?
(round answer to nearest 0.01 minute, if necessary)
5 What is the cycle time under this arrangement? (round answer to nearest 0.01 minute, if necessary)
Part II The company has decided to investigate the assignment of more than one machine to each operator. The
plan is to assign K machines to each operator such that the average manufacturing cost of the critical part is
minimized, where K = 1, 2, 3, .... Perform the necessary calculations and analyses to answer the questions
below.
6 What is the optimal number of machines to assign to a single operator in order to minimize per-unit
manufacturing cost?
7 For the optimal number of machines, what is the minimum per-unit manufacturing cost? (round answer to
nearest $0.01, if necessary)
8 For the optimal number of machines, what is the cycle time? (round answer to nearest 0.01 minute, if
necessary)
9 For the optimal number of machines, what is the amount of time per cycle (to the nearest 0.1 minute) that
the operator is idle?
10 For the optimal number of machines, what is the amount of time per hour (to the nearest 0.1 minute) that
each machine is idle?
11 What is the machine idleness (interference) per machine per cycle if 6 machines are assigned to a single
operator?
12 What is the operator idleness per hour if 3 machines are assigned to a single operator?
13 What is the cycle time, in minutes, if 7 machines are assigned to a single operator?
Part III
Perform sensitivity analyses on both L and P. Do this by holding the values of all other problem parameters constant
at their current values. Be prepared to give the ranges for both L and P for which the current optimal number of
machines assigned to a single operator remains the optimal number.

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Assignment 01 Operator-Machine Assignment Problem Dr. Stafford MSC 385 Fall 2006 Page 1

ASSIGNMENT 01: OPERATOR - MACHINE ASSIGNMENT PROBLEM

Dr. Stafford MSC 385 Fall 2006

Due Date: Monday. September 11, 2006

Solve the following two questions and be prepared for a separate quiz on each question.

Question 1

A company produces a critical part on a set of multiple, identical machines. These machines are semi-automatic in that, after they have been loaded and started, they process the part without need of further human intervention until the part processing is completed. At that time, an operator must unload the machine, reload it, and press the start button once more. Solve this problem twice, once for each set of parameters (rows) in the table below.

Problem Version R (min.) U (pc/cycle) Labor Cost ($/hr)

Machine Cost ($/hr/machine)

S (min)

A 13 3 $14 $37 3

B 19 2 $30 $25 5

Part I Currently, the company assigns one machine to each operator. For this arrangement, answer the following

questions.

1 What is the cost per unit to produce the critical part under the one man-one machine arrangement? (round answer to nearest $0.01, if necessary) 2 What is the operator idle time (in minutes) per hour under this arrangement? (round answer to nearest 0. minute, if necessary) 3 What is the output per operator per 8-hour shift under this arrangement? 4 What is the machine idleness (interference) (in minutes) per machine per cycle under this arrangement? (round answer to nearest 0.01 minute, if necessary) 5 What is the cycle time under this arrangement? (round answer to nearest 0.01 minute, if necessary)

Part II The company has decided to investigate the assignment of more than one machine to each operator. The

plan is to assign K machines to each operator such that the average manufacturing cost of the critical part is minimized, where K = 1, 2, 3, .... Perform the necessary calculations and analyses to answer the questions below.

6 What is the optima l number of machines to assign to a single operator in order to minimize per-unit manufacturing cost? 7 For the optimal number of machines, what is the minimum per-unit manufacturing cost? (round answer to nearest $0.01, if necessary) 8 For the optimal number of machines, what is the cycle time? (round answer to nearest 0.01 minute, if necessary) 9 For the optimal number of machines, what is the amount of time per cycle (to the nearest 0.1 minute) that the operator is idle? 10 For the optimal number of machines, what is the amount of time per hour (to the nearest 0.1 minute) that each machine is idle? 11 What is the machine idleness (interference) per machine per cycle if 6 machines are assigned to a single operator? 12 What is the operator idleness per hour if 3 machines are assigned to a single operator? 13 What is the cycle time, in minutes, if 7 machines are assigned to a single operator?

Part III

Perform sensitivity analyses on both L and P. Do this by holding the values of all other problem parameters constant at their current values. Be prepared to give the ranges for both L and P for which the current optimal number of machines assigned to a single operator remains the optimal number.