IE 515- Network Flows and Algorithms Fall 2018 Programming Project 1: The Bin Packing Problem Due Date: Beginning of class on November 14, Wednesday Project Description: The bin packing problem requires that we pack n items of lengths a, a,.., a, (assume that each a, s 1) into bins of unit length using the minimum possible number of bins. Several approximate methods, called heuristics, are available for solving the bin packing problem. The first-fit heuristic is one of the more popular of these heuristics. It works as follows. Arrange items in an arbitrary order and examine them one by one in this order. For an item being examined, scan the bins one by one and put the item in the bin where it fits first. If an item fits in none of the bins that currently contain an item, we introduce a new bin and place the item in it. Questions: (a) (80 points) Write a MATLAB code for the first-fit heuristic and apply the code in order to solve the problem of 20 items with the following lengths. [0.36 0.88 0.12 0.22 0.12 0.56 0.18 0.33 0.06 0.79 0.60 0.14 0.31 0.22 0.13 0.52 0.69 0.01 0.79 0.31] Note: While applying your code for the above example, DO NOT change the order of items in the array. IE 515- Network Flows and Algorithms Fall 2018 Programming Project 1: The Bin Packing Problem Due Date: Beginning of class on November 14, Wednesday Project Description: The bin packing problem requires that we pack n items of lengths a, a,.., a, (assume that each a, s 1) into bins of unit length using the minimum possible number of bins. Several approximate methods, called heuristics, are available for solving the bin packing problem. The first-fit heuristic is one of the more popular of these heuristics. It works as follows. Arrange items in an arbitrary order and examine them one by one in this order. For an item being examined, scan the bins one by one and put the item in the bin where it fits first. If an item fits in none of the bins that currently contain an item, we introduce a new bin and place the item in it. Questions: (a) (80 points) Write a MATLAB code for the first-fit heuristic and apply the code in order to solve the problem of 20 items with the following lengths. [0.36 0.88 0.12 0.22 0.12 0.56 0.18 0.33 0.06 0.79 0.60 0.14 0.31 0.22 0.13 0.52 0.69 0.01 0.79 0.31] Note: While applying your code for the above example, DO NOT change the order of items in the array