a) Change in basic C(I,J)
Performing sensitivity analysis on a basic C(I,J) value determines a range to which the arc (I,J) remains in the optimal solution. If the C(I,J) value is perturbed such that the range is violated, then the arc (I,J) will leave the current basis.
In our current basis, we have the arcs: (3,2), (4,3), (1,4), (1,7), (7,5), (1,8), (8,6)
We found a range for the arc (1,4). Currently, C(1,4) is 7. Using the GAMS we determined that this arc remains in the optimal solution when its associated C(1,4) value is between 0 and 14.
b) Change in non-basic C(I,J)
Performing sensitivity analysis on a non-basic C(I,J) value determines a range to which the arc (I,J) remains non-basic. If this range is breached, then the arc (I,J) will enter the basis. We found a range for the arc (1,6). Using the GAMS we determined that this arc remains non-basic when its associated C(1,6) value is greater than 6.c) Change in right-hand-side (RHS) value
Performing sensitivity analysis on an RHS value determines a range to which the entire basis remains optimal.
In our model, it is only possible to perform sensitivity analysis on the RHS values of the FLOW and RESTRICT equations. The MEET, LEAVE and BACK RHS values must remain the same because it constrains the customer's order to be fulfilled by only one delivery vehicle.
RHS ranging for the FLOW equations:
In our solution to the network model, currently there are three drivers: Driver 1 has the path: 1-4-3-2 Driver 2 has the path: 1-7-5 Driver 3 has the path: 1-6-8
Driver 1 is carrying the maximum number of pizzas when he leaves Pedro's Pizza. Thus, if we were to increase customer 3's and/or customer 2's demand, then our optimal solution would change. Since customer 2 and customer 3 order only 1 pizza, the optimal solution would change if we were to decrease either of their orders because then they would not require any pizza.
Driver 2 is only carrying 2 pizzas when he leaves Pedro's Pizza. If customer 7 and/or customer 5 were to increase their order such that Driver 2 is still carrying 4 pizzas or less, the optimal solution would not change. On the other hand, if their orders total to more than 4 pizzas, the optimal solution would change and another driver would have to be put into action. Conversely, if either customer 7 or 5 were to decrease their order to 0, the optimal solution would change as well.
Driver 3 is carrying the maximum number of pizzas when he leaves Pedro's Pizza. Thus, if we were to increase customer 6 and/or customer 8's demand, then our optimal solution would change. Since customer 6 currently has 3 pizzas on order, he can decrease his order to 1 and the optimal solution would not change. Customer 8 currently has 1 pizza on order and thus if he decreases his order then the optimal solution would change.
RHS ranging for the RESTRICT equations:
Currently we restrict the pizza driver to carry only 4 pizzas at one time because Pedro's pizza oven can only cook 4 pizzas at a time. Thus, when 4 pizzas are ready, we would like the driver to begin the delivery process. If Pedro decides to buy another pizza oven, then it would be possible for the driver to carry more than 4 pizzas at a time. Thus, he can deliver to more customers. Hence, any increase in Pedro's capacity for making pizzas will change the optimal solution.
d) Addition of a node
If the node we add to the problem has a demand greater than 0 then the optimal solution will change.