# Matlab code of minimum cost of shipping some standard sets of items, and also the allocation and positioning of items to/on craft.

Your first objective is to find the minimum cost of shipping some standard sets of items, and also the allo- cation and positioning of items to/on craft for each of these sets. You must determine the optimal solution for the following Sample Mixes listed in Table 2—but you must also give consideration to your solution (problem formulation and algorithms) being applied to generic, and possibly larger problems, i.e. more items, different types of item, and different sized craft.

To begin with, assume there are 4 different types of item, as described in Table 1, and the mixes of these items that need to be shipped are listed in Table 2. (see attached image)

The standard type of craft we will consider are of width 3 units and length 7 units. The number of landing craft will be limited and the cost of a trip is expensive so this should be minimised as well.

In particular you should:

(1) Consider an exhaustive search method. Can this be used to solve the Sample Mixes? Can this be used for a general problem – possibly with an increase in the number of item types?

(2) Formulate your problem as an Integer (Linear) Program.

(a) Solve the relaxed problem. What, if anything, does this tell you about the actual solution? How does the running time change as you change the Sample Mix?

(b) Solve the exact problem. Consider the running time as you change the Sample Mix. Compare your results to those obtained in (a).

(3) Consider re-formulating your problem to deal with the case where some items might be rotatable.

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