(1) Morgan Trucking Company operates a special pickup and delivery service betwe

Question

(1) Morgan Trucking Company operates a special pickup and delivery service between Chicago and six other cities located in a four-state area. When Morgan receives a request for service, it dispatches a truck from Chicago to the city requesting service as soon as possible. With both fast service and minimum travel costs as objectives for Morgan, it is important that the dispatched truck take the shortest route from Chicago to the specified city. Assume that the following network (not drawn to scale) with distances given in miles represents the highway network for this problem. Formulate a model to find the shortest-route distance from Chicago (node C) to node Miami (node M) 6 5.5 5 5.5 6

Explanation / Answer

Let Xyz be the binary variable determinig the selection of path from Node Y to Node Z.

Our objective is to minimize the distance or determine the shortest path from Node C to Node M. Thus our Objective function is-

Min Z = 4* Xcb + 5*Xca + 5*Xae + 5.5* Xbe + 1*Xbd + 6*Xbf + 2*Xdf + 6* Xeh + 4*Xdh + 4*Xfg + 5.5 *Xgm + 8*Xhm

Our Constraints are- (From all Nodes)

Xca + Xcb = 1

Xca = Xae

Xcb = Xbf+ Xbd + Xbe

Xae + Xbe = Xeh

Xbd = Xdf + Xdh

Xeh + Xdh = Xhm

Xbf + Xdf = Xfg

Xfg = Xgm

Xgm + Xhm = 1

Xyz ~ (0,1)

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