(a) Discuss how Clark and Wrights Savings algorithm can be modified to develop shipping routes from trucks that can deliver the products where needed and pick-up the shipment to be brought back to the warehouse if space allows in a cost efficient way. Discuss the modified algorithm in general not specific to this particular example. (b) Using your ideas from part (a), develop truck routes the company should use for this shipping cycle.

During a shipping cycle, a company needs to either deliver product from its warehouse (Node 0 ) to a retail outlet or pick-up shipment from the retail outlet to be brought back to the warehouse, using its fleet of trucks each with a capacity of 100 units (Assume that company has more than 5 trucks). Note that pick up items are brought back to the warehouse - -it cannot be used to satisfy demand of other retail outlets. Table below gives the transportation costs between all pairs of points, Node 0 is the warehouse and Node 1 , Node 2,, Node 5 are the five retail outlets (assume symmetric distances). During a particular shipping cycle, following deliveries (D) and pickups (P) need to be made