Suppose that a less than truckload company has to carry 100 different items to a certain destination. The volume of these items are denoted by vi (i = 1, 2, 3, …, 100). The capacity of each truck is equal to V and vi <= V for all the items. The company wants to assign the items to the trucks such that the total volume of the items assigned to a truck is not more than its capacity. The company’s goal is to minimize the maximum empty space on any of the utilized trucks.

(a) Formulate a mathematical model to help company achieve its goal. Define your decision variables clearly.

(b) Consider the first three items (i = 1, 2, 3). They are either assigned to the same truck or assigned to three different trucks. How would you modify your model to handle this restriction?

(c) If items 4 and 5 are assigned to same truck, then items 6 and 7 should be assigned to same truck as well (not necessarily to the same truck with items 4 and 5). How would you modify your model to handle this restriction?

Answer rating: 100% (QA)

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