Essays on Applying Markowitz Portfolio Model in Management Science Math Problem

The paper “ Applying  Markowitz Portfolio Model in Management Science” is an informative variant of the math problem on finance & accounting.   The given problem can be written in the following manner in the matrix where elements of the matrix are the costs of transportation per motor: Plants (1) (2) (3) (4) Supply A x11   120 x12   130 x34   x14   x13   x32   x22   x31   41 59.5 500 B x21   61 40 x23   100 x24   110 700 C 102.5 90 x33   122 42 800 Demand 400 900 200 500 2000 Since the total demand for motors is equal to the total supply of the motors, so it is a balanced transportation problem that requires the transportation cost to be minimized. The problem can be expressed in the following model: x21 + x22 + x23 + x24 = 700; x31 + x32 + x33 + x34 = 800; x11 + x21 + x31 = 400; x12 + x22 + x32 = 900; x13 + x23 + x33 = 200; x14 + x24 + x34 = 500; XIJ > = 0; where XIJ’ s are the number of motors transported. Step 1: Finding Initial of Basic Feasible Solution: To find the initial feasible solution Vogel’ s Approximation Method (VAM) is used, which, gives the following matrix where the numbers inside the boxes are the number of motors to be transported from the harbor to the assembly plant. Plants (1) (2) (3) (4) Supply D1 D2 D3 D4 A 120 130 41 59.5 500 18.5 60.5 - - B 61 40 100 110 700 21 21 21 21 C 102.5 90 122 42 800 48 48 48 12.5 Demand 400 900 200 500 2000         D1 41.5 50 59 17.5           D2 41.5 50 - 17.5           D3 41.5 50 - 68           D4 41.5 50 - -           Since the number of allocations is equal to the (no.

of rows + no. of columns - 1 = 6), hence we move to the next step to test the optimality of the solution. Step 2: Optimality Test: The optimality is tested by calculating the opportunity costs of unallocated cells using the formula: OC = Cij – (Ui + Vj), where Cij’ s are the costs in each cell and Ui’ s & Vj’ s are the difference between the lowest cost and the second-lowest-cost in each row and columns. Plants (1) (2) (3) (4) Supply Ui A 120 0 130 22.5 41 59.5 500 U1=17.5 B                                                       Since Opportunity Costs (OC) in each unallocated cell is non-negative, hence the initial feasible solution is the optimal solution.