Production
Planning and
Shipping

CASE 4

.

MR.DANG VU TUNG
SIE - HUST


GROUP 5

2


INTRODUCTION

MODEL FORMULATION

SOLUTION

SENSITIVITY ANALYSIS


INTRODUCTION

MODEL FORMULATION

SOLUTION

The potential issues:
- Get more material
- Get more inspection capacity
- Add extra machine hours
- Handle RAYco’s demand increases

Four Types of Products:
Small
Medium
Large
Precision

Assumption: Produce less than or equal to
customer’s demand
5


INTRODUCTION

MODEL FORMULATION

SOLUTION

SENSITIVITY ANALYSIS


DECISION
VARIABLES

DATA

x_22 = precision from Huntington to Rayco

x_5 = medium from Ashland to Honco

x_23 = precision from Huntington to Honco

x_6 = medium from Ashland to MMco

x_24 = precision from Huntington to MMco

x_7 = large from Ashland to Rayco

x_25 = small from Johnson City to Rayco

x_8 = large from Ashland to Honco

x_26 = small from Johnson City to Honco

x_9 = large from Ashland to MMco

x_27 = small from Johnson City to MMco

x_10 = precision from Ashland to Rayco

x_28 = medium from Johnson City to Rayco

x_11 = precision from Ashland to Honco

x_29 = medium from Johnson City to Honco


FUNCTION

Objective: Maximize Total Profit

Max Z = Profit Per Unit (Revenue − Cost) * xj for j = (1,2,3,...,36),
Where Revenue = Sales price/Unit, and Cost = Shipping cost/Unit + Production cost/Unit.
Therefore our objective function is
z = 2x_1 + 0.4x_2 + 0.9x_3 + x_4 + 0.4x_5 − 0.1x_6 +3x_7 + 2.4x_8 + 3.9x_9 + 2x_10 − 1.6x_11 −
0.1x_12 + 2.8x_13 + 1.5x_14 + 2x_15 − 0.2x_16 − 0.5x_17 − x_18 + 0.8x_19 + 0.5x_20 + 2x_21 +
3.8x_22 + 0.5x_23 + 2x_24 + 1.6x_25 + 0.5x_26 + 0.7x_27 + 1.6x_28 + 1.5x_29 + 0.7x_30 +
1.6x_31 + 1.5x_32 + 2.7x_33 + 4.6x_34 + 1.5x_35 + 2.7x_36


CONSTRAINTS

CONSTRAINTS

+ Resources Constraints:
+ Sales and shipping constraints
Maximum Small Product Sales to RAYco : 17(x_1 + x_13 + x_25) ≤ 200
Maximum Medium Product Sales to RAYco : 18(x_4 + x_16 + x_28) ≤ 300
Maximum Large Product Sales to RAYco : 22(x_7 + x_19 + x_31) ≤ 500
Maximum Precision Product Sales to RAYco : 29(x_10 + x_22 + x_34)≤ 200
Maximum Small Product Sales to HONco : 16(x_2 + x_14 + x_26) ≤ 400
Maximum Medium Product Sales to HONco : 18(x_5 + x_17 + x_29) ≤ 300
Maximum Large Product Sales to HONco : 22(x_8 + x_20 + x_32) ≤ 200

Maximum Precision Product Sales to HONco : 26(x_11 + x_23 + x_35) ≤ 400
Maximum Small Product Sales to MMco : 16(x_3 + x_15 + x_27) ≤ 200
Maximum Medium Product Sales to MMco : 17(x_6 + x_18 + x_30) ≤ 400


SOLUTION

SENSITIVITY ANALYSIS


OPTIMAIL SOLUTION
X1 = 11.76 (rounded up 12)
X4 = 16.67 (rounded up 17)
X7 = 22.73 (rounded up 23)
X10 = 6.897 (rounded up 7)
X15 = 12.5
X21 = 13.04 (rounded up 13)
X24 =11.11 (rounded up 11)
Others equal 0

OPTIMAL VALUE
The maximum profit is Z = 195,48
Number of unit sales is 94.71

Result: Would not meet small, medium, large, precision demand for HONco
and medium for MMco.


Suggestion
-

Production & Shipping

Assuming that we round up the products to integer values,

SENSITIVITY ANALYSIS


Material
"If you could get more material, how much would you like? What would you be willing to pay for it?”
No, it is not necessary to get more material because the shadow price of the toal material constraint is 0.
This is also because we have a lack of 3500 − 11.764706 = 3488.235294 units for the total material constraint.


Inspection Capacity
"If you could get more inspection capacity, how much would you like? How would you use it? What would you be
willing to pay for it?”
No, it is not necessary to get more inspection capacity because the shadow price of the inspection constraint is
0.
This is also because we have a lack of 1500 − 58.055197 = 1441.944803 units for the inspection capacity
constraint.


Machine Hours
"At what plant(s) would you like to add extra machine hours? How much would you be willing to pay per hour?
How many extra hours would you like?”
No, it is not necessary to add extra machine hours at any plants because the shadow price of the machine hours
for each plant constraint is 0.
This is also because we have a lack of 10000 − 360.73207 = 9639.26793 units for the machine hours for plant 1
constraint and 12500 − 291.84783 = 12208.15217 units for the machine hours for plant 2.


RAYco's Demand +50%
"Marketing is trying to get RAYco to consider a 50% increase in its demand. Can we handle this with the current
system or do we need more resources? How much more money can we make if we take on the additional