CHAPTER8

تحليله و المكان اختيار تخطيط

McGraw-Hill/IrwinOperations Management, Eighth Edition, by William J. StevensonCopyright © 2005 by The McGraw-Hill Companies, Inc. All rights

reserved.

المواقع تقييم والحجم التكلفه تحليل النقل نموذج

والمنتج الخام المواد حركة تكاليف على يعتمد قرارالنهائى

التقدير عامل المدخالت ونوعية كمية على يعتمد قرار اتخاذ

الثق6ل موقع نظرية الحد الى التوزيع تكلفة تقليل على يعتمد قرار

االدنى

الموقع تقييم

ال قيمة والحجم تحليل تكلفه والمتغيرة الثابتة التكاليف تحديد التكلفة اجمالى اجمالية تكلفة اقل تحديد

التكلفة حجم تحليل

االربعة للمواقع والمتغيرة الثابتة التكاليفالمتوقعة

L o c a t i o n F i x e dC o s t

V a r i a b l eC o s t

ABCD

$ 2 5 0 , 0 0 01 0 0 , 0 0 01 5 0 , 0 0 02 0 0 , 0 0 0

$ 1 13 02 03 5

الحل

F i x e dC o s t s

V a r i a b l eC o s t s

T o t a lC o s t s

ABCD

$ 2 5 0 , 0 0 01 0 0 , 0 0 01 5 0 , 0 0 02 0 0 , 0 0 0

$ 1 1 ( 1 0 , 0 0 0 )3 0 ( 1 0 , 0 0 0 )2 0 ( 1 0 , 0 0 0 )3 5 ( 1 0 , 0 0 0 )

$ 3 6 0 , 0 0 04 0 0 , 0 0 03 5 0 , 0 0 05 5 0 , 0 0 0

Example 1: Solution

800700600500400300200100

0

Annual Output (000)

$(000)

8 10 12 14 166420

A

BC

B SuperiorC Superior

A Superior

D

Method of Factor Rating

In factor rating method, first we must identify the Most Important Factors in

evaluating alternative sites for the new facility.

Then we should assign a weight between 0 and 100 to each of these

factors.

Example

Weights reflecting the relative importance of each factor have been assigned as

follows:

Example

Based on these criteria, the three Alternative sites were scored

between 0 and 100 points :

Example

Now we will multiply each score by its corresponding factor weight:

Weighted scores are calculated as: (Site Score)x(Factor Weight)

Example

What happens if we change the factor weights. Lets use the following factor

weights:Skilled labor: 0.45;Raw Materials: 0.40;

and Market: 0.15Then the following results are obtained:

Example

Since factor weights, selected factors, and assigned scores are all determined

subjectively, the managers should be very careful in selecting these items and

numbers.

Center of Gravity Method

The center of gravity method is used to find a location that Minimizes the Sum of

Transportation Cost in between new facility and old facilities.

Transportation cost is assumed to be a linear function of the Number of Units Shipped AND the Traveling Distance.

Center of Gravity Method

The location of the firm’s existing facilities are converted into x and y

coordinates.The following center of gravity equations

are Then used for calculating the x and y coordinates for the new facility:

Center of Gravity Method

Center of Gravity Method

Here, Cx : x coordinate for new locationCy : y coordinate for new locationi: index for existing locationsn: total number of existing locationsxi: x coordinate of existing ith location ,

andyi: y coordinate of existing ith location.

Example

Aldrich Manufacturing Company plans to build a Warehouse to serve its

Distribution Centers in Columbus (Ohio), Frankfort (Kentucky), Nashville

(Tennessee), and Richmond (Virginia) .

Example

Example

The number of units to be shipped monthly from Harrisburg to the

Distribution Centers are shown in the following table:

)Weighted Coordinates are calculated as: (Annual Shipping Volume) (x or y

coordinate)(

Example

Example

Using the equations of center of gravity:Cx = 2,040,000 / 10,000 = 204 (x

coordinate for new facility)Cy = 1,185,000 / 10,000 = 118.5 (y

coordinate for new facility)The nearest city to (204, 118.5)

Charleston at West Virgina.

Example

This method only considers the distances traveled. It does not consider the other factors such as the availability

of roads on the selected location. Therefore, applying solely this method may not be applicable in every cases.

Transportation Model

A special form of linear programming, that is

Transportation Model, can be used to

compare the total transportation cost

associated with each alternative site.

Transportation Model

The transportation model technique can be used to determine how many units should be shipped from each plant to

each warehouse To Minimize Total Transportation Cost.

Example

Straub Ltd. has three plants running at full capacity in Des Moines, Racine, and

Gary.These plants supply four Distribution

warehouses in St. Paul, Milwaukee, Chicago, and Detroit.

Example

Straub plans to build a new plant. It has narrowed down the choice of sites to two

possibilities: Kalamazoo and Duluth.We will now determine which site results in the

lowest transportation Cost by using the unit transportation costs, warehouse demands, and plant capacities shown in the following:

Example

Example

Example

We will approach this problem in the following manner:

We will first assume that the selected plant is the Kalamazoo plant, and

calculate the total transportation cost.

Example

Later, we will assume the selected plant is Duluth. Then we will compare the transportation costs for both plants.

Now, the first step is to find the Optimal number of units to ship between each

plant-warehouse combination. This also gives the optimal transportation cost for

the problem.

Example

We can use any of the computerized LP tools for finding the optimum values for

this problem.Some of these include WINQSB, Lindo,

OM Expert, and Excel.We use WINQSB to solve this

transportation model. The result is as follows:

Example

Example

The total transportation cost will be $10,225 if the new plant is built in Kalamazoo.

)This can be calculated simply by multiplying the shipment in each cell by its unit cost(

On the other hand, The optimal number of units to ship between each plant and Duluth

Warehouse is found as follows:

Example

Example

The total transportation cost will be $13,825 if the new plant is built in Duluth.

Therefore, the Kalamazoo plant will incur the lowest transportation cost.