This case study is about increasing efficiency by optimizing how a pallet is packed. Although a

large data set is provided with the case it is only possible to solve the optimization problem for a

small number of items. These items are provided in the Excel file. You are going to develop the

model for the following $10$ items assuming there are $5$ pallets on which they can be packed.

Item SKU: $220187,271440,4004137,4011282,1321030,611077,146178,4013167,515173,$

$16114$

Design your model so that when you enter the SKU in a cell the necessary data is picked up from

the data sheet.

The model you are going to develop is called the bin$-$packing problem. The problem described in

the case is a $3-$D bin$-$packing problem but that would be too hard to model and solve. Therefore,

you are required to develop a $1-$D bin$-$packing model that only considers the weight of the items.

In addition to the weight capacity of the pallets, take into account the following constraints:

$$ Family group $2$ items cannot be in the same bin with family group $3$ items.

$$ Items of family group $1$ should not be in the same bin.

a$)$ Formulate and solve the model so that the number of pallets used is minimized.

b$)$ Formulate and solve the model so that the maximum weight of pallets is minimized.

c$)$ Create a Pareto frontier taking into account maximum weight and number of pallets used.