Linear Programming (PRAN)

Document Sample
Linear Programming (PRAN) Powered By Docstoc
					Linear Programming
PRAN (Aseptic Juice Pack – 250ml)

North South University
Nazmus Sakib
MGT314                                            KZn

Submitted To             From                           Page | 2
Kais Zaman               Nazmus Sakib
School of Business       ID: 091-0866-030
North South University   North South University

Linear Programming
MGT314                                      KZn

Table of Contents
                                                  Page | 3

Contents                      Page Number
Introduction                  4
PRAN                          5
Production Process            6
Linear Programming            10
Optimal Production for PRAN   11
Sensitivity Analysis

Linear Programming
MGT314                                                                   KZn


                                                                               Page | 4
The main objective of this study is to calculate the optimal
level of production for “PRAN Aseptic Juice Pack 250ml” using
Linear Programming. To begin with, I needed some production and
Sales related information. So I visited the organization and
collected      relevant   information.   Though   it   was   an   incomplete
quest for information because of reluctant company personnel, I
managed to assume other needed information.

After I had an idea about Juice production process, I checked to
see if     there are any machinery or raw material constraints.
Several machines were constrained by work hour and raw material
for mix fruit juice was not enough. So, I took the products as
variables and set constraints on Machine hour while maximizing
the profit.

Before going to the main part of this report, little discussion
on “PRAN” group, its juice production process and what is linear
programming is necessary.

Linear Programming
MGT314                                                                                   KZn


           Programme for Rural Advancement Nationally
                                                                                               Page | 5

“PRAN” is currently the most well-known household name among the
millions of people in Bangladesh and abroad also. Since its
inception in 1980, PRAN Group has grown up in stature and became
the largest fruit and vegetable processor in Bangladesh. It also
has the distinction of achieving prestigious certificate like
ISO 9001:2000, and being the largest exporter of processed agro
products      with     compliance     of    HALAL   &   HACCP       to    more    than    70
countries from Bangladesh.

PRAN is the pioneer in Bangladesh to be involved in contract
farming and procures raw material directly from the farmers and
processes through state of the art machinery at our several
factories into hygienically packed food and drinks products. The
brand “PRAN” has established itself in every category of food
and beverage industry and can boost a product range from Juices,
Carbonated       Drinks,     Confectionery,       Snacks,      and       Spices    to   even
Dairy products.

Today, its consumers not only value “PRAN” for its authentic
refreshing           juice   drinks    products         ,     but    also         for    its
mouthwatering quality confectionery products with high visual
appeal     and       exciting   texture.      “PRAN”        intend       to   expand     its
presence to every corner of the world and strive to make “PRAN”
a truly international brand to be recognized globally.

Linear Programming
MGT314                                                                       KZn

                     Production Process

Whole of the manufacturing maintain by our employees and all the Page | 6
raw materials will be purchased from our country and abroad and
we produced our product in our factory.


Three basic disciplines are used in the process:

1. Mass transfer

2. Heat transfer

3. Squeezing the Pulp

Juice extraction:

                     Firstly the oil is removed. This process is
                     carried    out   without       causing    damage   to   the
                     fruit. It is done to avoid undesirable flavors
                     and   obtain     the   highest     possible     level    of

                     Secondly     the       juice     is      extracted.     The
                     technology used involves cutting and squeezing
                     the orange/mango and is different to many of
                     the In-line systems used. The HRS process does
                     not   damage     the   peel     and   therefore    avoids
contamination of the juice.

Linear Programming
MGT314                                                                                  KZn

Thirdly the juice is separated from the husk and the seeds. With
this process we reduce the bitter constituents, obtaining a low
reading for quick fiber and a low viscosity in NFC.

The    resultant     juice   has   a   minimum      content      of      the        bitter Page | 7
constituents, an agreeable color, minimum natural oil content
and an increased number of intact juice cells. The Limonina
content is also reduced. The average cell size in the pulp is
increased with a higher percentage of floating pulp.

We must also highlight the fact that the process does not use
water during the extraction processes, the energy consumption
has been optimized and the contaminants contained in residual
water have been minimized.


Once the orange juice has been obtained we have to remove the
bitterness from the juice. This is done by a process designed to
eliminate the Limonina, narangina y hesperidina from the juice.

                                       The         process       starts               with
                                       stabilized      fresh        juice       and     15
                                       Bricks reconstituted juice. They
                                       are     centrifuged          in        order     to
                                       separate out the pulp from the
                                       juice. Lewis Bayer resin is added
                                       to    the    juice     and        it    is     then
                                       circulated      to    a   storage            vessel
                                       where     the   thermal        treatment         is
                                       carried out.

Linear Programming
MGT314                                                                                KZn


One of the key aspects related to the treatment of the pulp is
                                                                                            Page | 8
the mass transfer. HRS Spiratube has developed a piston pump
particularly suited to this purpose, a pump which is hygienic
and can develop pressures of up to 40 Bar.


The    Pasteurizers          MX     series     produced    by    HRS     Spiratube    are
characterized          by    the    high     speed   of   treatment,      carrying    out
product de-aeration when the product is cold and because little
maintenance is necessary.

 HRS has developed a new series of Pasteurizers, designated the
MX    series    in     which       special    attention    has    been    paid   to   the
following features:


The CIP (Clean in Place) cleaning system used by HRS Spiratube
is    centralized          with    automatic    control    of    the   parameters.     An
outstanding feature of this design is that it has automated
practically          all    of    the   cleaning     operations    required      in   the

Linear Programming
MGT314                                            KZn

                                                        Page | 9
Graphical outlook of the manufacturing process:

Linear Programming
MGT314                                                                                    KZn

                          Linear Programming

A mathematical technique designed to help operations managers Page | 10
plan and make decisions relative to the trade-offs necessary to
allocate resources.

All LP problems have four properties in common:

1.    LP    problems     seek    to     maximize      or        minimize   some    quantity
(usually     profit      or    cost).    We   refer        to    this   property    as   the
objective function of an LP problem. The major objective of a
type-cal firm is to maximize dollar profits in the long run.

2.    The   presence     of     restrictions,         or    constraints,      limits      the
degree      to   which    we    can     pursue    our       objective.      For    example,
deciding how many units of each product in a firm’s product line
to manufacture is restricted by available labor and machinery.
We want, therefore, to maximize                   or minimize a quantity (the
objective        function)        subject        to        limited      resources        (the

3. There must be alternative courses of action to choose from.
For example, if a company produces three different products,
management may use LP to decide how to allocate among them its
limited production resources (of labor, machinery, and so on).
If there were no alternatives to select from, we would not need

4. The objective and constraints in linear programming problems
must be expressed in terms of linear equations or inequalities.

Linear Programming
MGT314                                                           KZn

                     LP in action for PRAN
While studying its production process, I found some machinery
constraints. Fruit extraction, Pulp treatment and Pasteurization
                                                                       Page | 11
Department are limited by their capacity. Each department has a
capacity ceiling in terms of machine hour.

Machine                          Maximum Machine Hour per week
Extraction                       10,000
Pulp Treatment                   12,000
Pasteurization                   15,000

So, extraction, pulp treatment and Pasteurization machine cannot
run longer than 10,000 , 12,000 and 15,000 hours a week.

“PRAN” has varieties of product lines among which I choose to do
the LP application on “Aseptic Juice Pack 250ml”. In this line
there are 3 (three) products. These are Mango Juice, Orange
Juice and Mix Fruit Juice. I studied their previous demands to
find out the demand for this month. The Demand Chart is given

Product                          Weekly Demand
Mango Juice                        *
Orange Juice                     30,000
Fix Fruit Juice                   6,000

I also studied their cost of goods sold and Sales price to
compute “contribution margin” earned from each product.

Linear Programming
MGT314                                                                         KZn

                                              Mango       Orange       Mix Fruit
Price/Unit                                    14.00       14.00        14.00
(Company Price)
Variable Cost            Raw Materials        8.50        9.00         7.00
                                                                                     Page | 12
                         Process Cost         2.00        2.50         1.50
                         Labor                1.50        1            2.50
Unit Contr.
Margin                                        2.00        1.50         3.00

Now, these three products consume machine hours in different

Max. Demand                      30,000   6,000

Optimal              65128       7744     6000
                     Mango       Orange   Mix                 Used              Capacity
Extraction           0.11        0.25     0.15        =       10000    <=       10000
Pulp Treatment 0.15              0.10     0.2         =       11744    <=       12000
Pasteurization 0.2               0.1      0.2         =       15000    <=       15000
CM/U                 2           1.5      3

Total                130256      11615    18000               159872

This illustrates a MS Excel solver model for solving linear
programming problem. The Formal Solution page is given below.

Linear Programming
MGT314                                                           KZn

                                                                       Page | 13

That means, this model suggest that the company produces 65128
units of Mango Juice, 7743 units of Orange Juice and 6000 units
of Mix Fruit Juice. This production mix yield the highest
“Contribution Margin” which is BDT 1,59,871.

This solver model also provides a Sensitivity Analysis Report.
This Report Suggest that how much change from different limits
can bring how much change in maximized value.

Linear Programming
MGT314                                                           KZn

                                                                       Page | 14

According to this sensitivity report provided by excel solver,
for each hour increased capacity for Extraction Facility can
bring BDT 2.56 increase in Contribution Margin. Also, BDT 8.59
increase will be consumed if Pasteurization Facility is enhanced
with one more hour.

Here mix fruit juice production is constrained by its weekly
demand. BDT 0.90 increased contribution margin can be assumed
for every demand increase for Mix Fruit Juice.

Linear Programming
MGT314                                                          KZn

Here is another piece of report that excel produced.

                                                                      Page | 15

Extraction and Pasteurization is running in its full capacity
while we can witness a big slack in “pulp treatment” department.

Linear Programming
MGT314                                                           KZn


As well as its product Aseptic 250ml Juice Pack, PRAN is doing         Page | 16
very good in business. They have good supply chain management
system to meet their production. So, raw material is not a
constraint. But some critical machines have less capacity.

PRAN should take corrective action to reduce the slack time

Linear Programming

Shared By: