In a scenario where the order matching is static, there are six pending customer orders and six available vehicles in a dispatch area. The customer pickup positions are fixed, and the distances between each customer and available vehicle are provided in Table 1. It is assumed that there is no uncertainty regarding the travel speed of the vehicles, and all the vehicles are identical with a fixed travel speed of 5 minutes per kilometre.

a) Formulate an integer optimization problem that optimally assigns all the available vehicles to the customer orders, with the objective of minimizing the total distance travelled for pickup and solve the problem using MS Excel.

b) Additionally, assume that all customers have a predetermined waiting time limit of 6 minutes, and if the pickup time exceeds 6 minutes, the order will be cancelled. How would you modify the solutions then?

\begin{tabular}{|l|c|c|c|c|c|c|} \hline & Vehicle 1 & Vehicle 2 & Vehicle 3 & Vehicle 4 & Vehicle 5 & Vehicle 6 \\ \hline Order 1 & 200 & 900 & 1500 & 2000 & 1600 & 2200 \\ \hline Order 2 & 1000 & 1500 & 2000 & 1500 & 2000 & 1500 \\ \hline Order 3 & 1400 & 1500 & 1000 & 300 & 1500 & 1600 \\ \hline Order 4 & 1300 & 1800 & 1300 & 1000 & 1800 & 1400 \\ \hline Order 5 & 1000 & 1000 & 1000 & 1300 & 900 & 300 \\ \hline Order 6 & 1200 & 1800 & 1200 & 1600 & 1300 & 1000 \\ \hline \end{tabular} Table 1. Distance table among the 6 pending orders and 6 available vehicles (in meters)