# Linear Programming - Transportation Problem, NW corner

3. Emily Alice PLC is a printing company which specializes in the design and production of special effect booklets for marketing promotions. A new client orders 60,000 booklets which are to be sent to their offices in London, Manchester and Newcastle. These offices require 15000, 21000 and 24000 copies respectively.

Each of its printing works at Hill and Bath can produce up to 35,000 copies by the deadline. Given the following table of transportation costs (in pence per booklet), determine how many copies should be produced at Hull and at Bath and how should these be distributed if the total transportation cost is to be minimized.

London Manchester Newcastle

Hull 8 7 4

Bath 4 6 7

Use the North-West corner method to find the first basic feasible solution and state the minimum transportation cost.

© BrainMass Inc. brainmass.com October 25, 2018, 8:25 am ad1c9bdddfhttps://brainmass.com/math/linear-programming/linear-programming-transportation-problem-nw-corner-539515

#### Solution Preview

Because, total demand (= 60,000) < total supply (= 70,000)

Hence, a dummy demand column to be created with cost = 0

London (C1) Manchester (C2) Newcastle (C3) Dummy (C4) Supply

Hull (R1) 8 7 4 0 35,000

Bath (R2) 4 6 7 0 35,000

Requirements 15,000 21,000 24,000 10,000 Total=70,000

Start allocating from North-West corner, i.e., with (R1,C1): Minimum of C1_requirements(=15,000) and R1_supply(=35,000) = 15,000.

Hence, maximum possible units that can be allocated to R1,C1 = 15,000, allocate it. Hence remainder(C1_requirements ) = 0; remainder(R1_supply) = 35,000 - 15,000 = 20,000. Strike-off remaining cells of C1.

London (C1) ...

#### Solution Summary

Using North-West corner method, a Linear programming problem is solved here.

Sales, Probability, Forecasting Models, EOQ, Programming

1. If the sale of ice cream and pizza are independent, then ice cream sales decrease by 60% during the winter months and pizza sales will

a. increase by 60%

b. increase by 40%

c. decrease by 60%

d. cannot tell from information

2. Suppose that we determine the probability of a warm winter based on the number of warm winters experienced over the past 10 years, in this case we have used (please explain)

a. relative frequency

b. classical method

c. logical method

d. subjective probability

3. Assume that you have tried three different forecasting models. For the first, the MAD = 2.5, for the second, the MSE = 10.5, and for the third, the MAPE = 2.7. We can then say:

a. the third method is the best.

b. the second method is the best.

c. method two is least preferred.

d. none of the above

4. For the basic EOQ model, which of the following relationships is not true:

a. the optimal number of orders per year equals annual demand divided by the EOQ

b. the reorder point equals daily demand times the lead time in days

c. average inventory levels equals one half the order size

d. the average dollar level of inventory equals unit price times order quantity

5. Which of the following is a technique used to determine forecasting accuracy

a. the optimal number of orders per year equals annual demand divided by the EOQ

b. the reorder point = daily demand times the lead time in days

c. average inventory = ½ the order size

d. average dollar of inventory = unit price times order quantity

6. The use of LP in solving assignment problems yields what kind of solutions?

a. redundant

b. unbounded

c. either -1 or 1 for each variable

d. either 0 or 1 for each variable

7. infeasibility in a linear programming problem occurs when

a. there is an infinite solution

b. constraint is redundant

c. more than one solution is equal

d. there is no solution that satisfies all the constraints given

8. Which of the following problem types is such a special case of linear programming that a special algorithm developed to solve it?

a. production mix problem

b. assignment problem

c. ingredient mix problem

d. media selection problem

9. Linear programming is used by managers involved in portfolio selection to

a. maximize return on investment

b. maximize investment limitations

c. maximize risk

d. minimize risk

10. The selection of specific medial from among a wide variety of alternatives is the type of LP problem known as:

a. production mix

b. investment banker problem

c. wall street problem

d. an effective media mix

11. Explain how a multiple optimal solution is recognized when using the simplex algorithm (what is this?

12. Transportation models can be used for which of the following decisions

a. Facility location

b. Production mix

c. Media selection

d. Portfolio selection

13. Goal programming is characterized by

a. All maximization problems

b. Setting of lower and upper bounds

c. The deviation from a high priority goal must be minimized before the next highest priority goal may be considered

d. maximizing as in LP

14. Which of the following statements is true comparing the transportation and assignment algorithms to the simplex algorithm?

a. Similar computational effort, faster, and similar computer memory usage

b. Less computational effort, similar speed, and less computer memory usage

c. Less computational effort, faster and similar computer memory usage

d. Less computational effort, faster and less computer memory usage

15.The most common objectives for the assignment problem are the minimization of ___________

a. Uncertainty or inexperience

b. Total costs or inexperience

c. Total costs or total line

d. Total time or inexperience

16. Which of the following accurately describes steps of the northwest corner rule, after making the initial allocation of units in the northwest cell?

a. Move down first, and then move right

b. Move right first and then move down

c. Move right or down first, depending on whether the demand requirement or the supply capacity respectively, is exhausted first

d. Move right or down first, depending on whether the supply capacity or the demand requirement ,respectively is exhausted first

17. The branch and bound method is often used when

a. Linear programming problems cannot be graphically solved

b. There are fewer than three variables

c. One or more variables are negative

d. Solving integer programming problems

18. A transportation problem is not

a. Is a special case of the linear programming problem

b. Can be solved by linear programming, but is solved more efficiently by a special purpose algorithm

c. May give an initial feasible solution rather than the optimal solution

d. Used to determine facility locations

Describe a transportation problem. The assignment problem is a special case of the transportation problem. So, then, why is it not recommended to use the transportation algorithm to solve the assignment problem?

Executive Furniture Corporation which manufactures office desks at three locations: Des Moines, Evansville and Ft Lauderdale. The firm distributes the desks through regional warehouses located in Albuquerque, Boston and Cleveland. An estimate of the monthly production capacity at each factory and an estimate of the number of desks that are needed each month at each of the three warehouses is as shown:

FACTORIES WAREHOUSES

(sources) (Destinations)

100 units Des Moines Albuquerque 300 units

300 units Evansville Boston 200 units

300 units Ft Lauderdale Cleveland 200 units

Capacities shipping results requirements

The firm has found that production costs per desk are identical at each factory, and hence the only relevant costs are show in the table above. They are assumed to be constant regardless of the volume shipped. (chapter 10 Transportation and Assignment Models, Quantitative Analysis for Management, 10th Edition, Barry Render).

View Full Posting Details