Stat 279 Operations Research

Problem 1.

Nanaq Europe-                     

Regions                       Electric motors

Gaydon (UK)                          140,000

Rouen (France)                       130,000

Dresden (Germany)                160,000

Nanaq International

Regions                                   Refrigerators.

Jung (Sweden)                                                130,000

Reynosa (Mexico)                               120,000

Pohang (South Korea)                                    145,000

East Tamaki (New Zealand)               25,000

Supplied by Nanuq Europe                     To Nanaq InternationalSupply(SS)
Jung ReynosaPohangEast Tamaki
Gaydon80240180280780
Rouen40210200320770
Dresden20250140200610
Demand(DD)1407005208002160

Total demand for motors.

DD=140 + 700+520+800= 2,160 motors

  1. Total supply for motors.

SS= 780+770 +610 = 2,160 motors.

  1. Use LCM (Least cost method) to construct a transportation tableau.

Identify the least cost in the whole table.

NoSupplierDestinationCost (Euros)Allocation
1.DresdenJung20140
2.DresdenPohang140470
3.GaydonPohang18050
4.RouenReynosa210700
5.GaydonEast Tamaki280730
6.RouenEast Tamaki32070

 Transportation Tableau.

Supplied by Nanuq Europe                     To Nanaq InternationalSupply(SS)
Jung ReynosaPohangEast Tamaki
Gaydon00180280780
Rouen02100320770
Dresden2001400610
Demand(DD)1407005208002160

Transportation cost tableau.

Unit cost (Q)Allocation (C)Total Cost $ (C*Q) Euros
201402,800
14047065,800
180509,000
210700147,000
280730204,400
3207022,400
∑C = 1,150∑Q = 2,160∑TC = 451,400

Interpret the starting solution from the least cost method.

Total minimum cost:

(140*20) + (470*140) + (50*180) + (700 * 210) + (730* 280)+ (70*320)

= 451,400Euros.

Stat 279 Operations ResearchUsing the Least cost method to solve the transportation problem, it can be concluded that to obtain the minimum cost of transporting to Nanuq International, it will cost $ 451,400 and the supplies should originate from the suppliers in Europe as indicated by the tableau above. It will have to transport a total of 2,160 electric motors. 

  1. Obtain the optimal solution using excel. Cut and paste the excel output into word document and interpret the solution.

Conclusion:

  • 140 Electric motors should be transported from Rouen to Jung.
  • 70 Electric motors should be transported from Gaydon to Reynosa
  • 630 Electric motors should be transported from Rouen to Reynosa
  • 190 Electric motors should be transported from Gaydon to East Tamaki
  • 610 Electric motors should be transported from Dresden to East Tamaki.

Excel:

  1. According to excel, the total cost is 423, 500

Problem 2.

Calculate the total cost according to the excel solution. Also comment on any excess supply or demand.

According to excel solution, the Total minimum cost is $ 167,000

According to excel, the following persons should be assigned the following projects;

Person Assigned                   Work Project.
Mary                        2
Elizabeth                        4
 Steven                              1
Joshua                               3

 REFERENCE LIST.

  1. Mokhtar S. B., John, J. J., &Hanif, D. S. (2011). Linear Programming and Network Flows (3rd). Hoboken, New Jersey: John Wiley & Sons Inc.

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