1. CHAPTER 8 تخطيط اختيار المكان و تحليله McGraw-Hill/Irwin Operations Management, Eighth Edition, by William J. Stevenson Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.

2. تقييم المواقع تحليل التكلفه والحجم نموذج النقل قرار يعتمد على تكاليف حركة المواد الخام والمنتج النهائى عامل التقدير اتخاذ قرار يعتمد على كمية ونوعية المدخلات نظرية موقع الثقل قرار يعتمد على تقليل تكلفة التوزيع الى الحد الادنى

3. تقييم الموقع تحليل قيمة التكلفه والحجم تحديد التكاليف الثابتة والمتغيرة اجمالى التكلفة تحديد اقل تكلفة اجمالية

4. تحليل حجم التكلفة التكاليف الثابتة والمتغيرة للمواقع الاربعة المتوقعة

5. الحل

6. Example 1: Solution 800 700 600 500 400 300 200 100 0 Annual Output (000) $(000) 8101214166420 A B C B Superior C Superior A Superior D

7. 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.

8. Example Weights reflecting the relative importance of each factor have been assigned as follows:

9. Example Based on these criteria, the three Alternative sites were scored between 0 and 100 points:

10. Example Now we will multiply each score by its corresponding factor weight: Weighted scores are calculated as: (Site Score)x(Factor Weight)

11. 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: 0.15 Then the following results are obtained:

12. 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.

13. 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.

14. 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:

15. Center of Gravity Method

16. Here, Cx : x coordinate for new location Cy : y coordinate for new location i: index for existing locations n: total number of existing locations xi: x coordinate of existing ith location, and yi: y coordinate of existing ith location.

17. Example Aldrich Manufacturing Company plans to build a Warehouse to serve its Distribution Centers in Columbus (Ohio), Frankfort (Kentucky), Nashville (Tennessee), and Richmond (Virginia).

18. Example

19. 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))

20. Example

21. 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.

22. 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.

23. 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.

24. 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.

25. 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.

26. 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:

27. Example

29. 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.

30. 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.

31. 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:

32. Example

33. 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:

34. Example

35. 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.