Problem 8: (10 Points) The following network is for a transshipment probiem, whe

Question

Problem 8: (10 Points) The following network is for a transshipment probiem, whece positive numbers by nodes indicate the that node. The negative numbers by modes indicate the amount of demand at the node. Numbers on arcs indicate the cost of shipping aunit Erom node i to node amount of supply at ing to indicate fiow between sodesand 1 write an appropriate objective function for this problem e- How many decision variables exists for this problem? - How many constrains (exciuding non-segativity) exist for this problem? If each arch is capacitated by an upper bound of 2 units, how many additional constraints would be added?

Explanation / Answer

a) Let Xij indicate the flow (quantity shipped) from node i to node j

Objective: Min 11X13 + 12X14 + 10X21 + 8X34 + 1X35 + 11X42 + 9X45 + 12X52

b) There are eight decision variables (indicated by the quantity shipped along each of the arcs). These variables are: X13, X14, X21, X34, X35, X42, X45, X52

c) There are five constraints (excluding non-negativity). These five constraints are represented by each of the nodes. The cosntraints are

X13 + X14 - X21 = 5

X21 - X42 - X52 = 3

X34 + X35 - X13 = -6

X45 + X42 - X14 = 2

X52 - X34 - X45 = -4

d) Eight additional constraints would be added, one for each of the arcs. Each constraint would be Xij <= 2

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