Modify the heuristics for the 1BP problem for the case where each bin j, j = 1,...,n, has a capacity qj and a cost f_{j}. Apply the modified version of the BFD heuristic to the following problem. Brocard is a road carrier mainly operating in France and Benelux.
The vehicle fleet is composed of 14 vans of capacity equal to 800 kilograms and 22 vans of capacity equal to 500 kilograms. The company has to deliver 34 parcels of different sizes from Paris to Frankfurt (the distance between these cities is 592 kilometres). The characteristics of the parcels are reported in Table.
As only five companyowned vans (all having a capacity of 800 kilograms) will be available on the day of the delivery, Brocard has decided to hire additional vehicles from a thirdparty company. The following additional vehicles will be available:
• two trucks with a capacity of three tons each, whose hiring total cost (inclusive of drivers) is € 1.4 per kilometre;
• one truck with trailer, with a capacity of 3.5 tons, whose hiring total cost (inclusive of drivers) is € 1.6 per kilometre.
Which trucks should Brocard hire?
Table : List of the parcels to be loaded and corresponding weight (in kilograms) in the Brocard problem. 
Parcel

Weight

Parcel

Weight

1

228

18

170

2

228

19

170

3

228

20

170

4

217

21

170

5

217

22

95

6

217

23

95

7

217

24

95

8

210

25

95

9

210

26

75

10

210

27

75

11

210

28

75

12

195

29

75

13

195

30

75

14

195

31

75

15

170

32

55

16

170

33

55

17

170

34

55
