**9. Assigning buses to routes**

X 4

X 93

*Concepts, Applications and Emerging Opportunities in Industrial Engineering*

*xij* þ *yij* h i

> X 93

> > *i*¼1

The output of the model indicates the total number of trips by the two types of busses needed to serve the average demand of each route on a given shift. The

The GAMS build system has different solvers such as BARON, BDMLP, and BENCH. Replace this text with your section Heading CNOPT, CPLEX, LGO, etc. that are capable of solving different varieties of problems. After trying each solver, for reporting purposes, CPLEX solver is chosen to solve the LP model developed above. The LP model is coded and programmed using the GAMS. This build system

The outputs of the model are reported by taking the upper integer value. As shown in **Table 4**, for example for route 3, 61 trips by bus type-I and 14 trips by bus type-II were required for shift one. There are also routes where no trips are required by bus type-I in the off-peak shifts. Since the LP model produces the number of trips required, the output has to be converted into the number of busses required for each route in a given shift. This has to be done by dividing the number of trips

> **Bus type-II**

L 19 9 0 10 14 11 0 3 2 19 5 5 8 15 6 0 2 3 61 14 14 24 48 17 0 7 4 18 3 6 5 15 3 2 1 5 14 3 4 6 12 3 0 2 6 51 12 0 21 41 14 0 6 � �������� � �������� � �������� 91 4 1 2 2 4 1 1 1 92 21 5 0 9 17 6 0 3 93 11 4 0 5 9 4 0 2 Total 1541 402 174 618 1231 490 18 156

**Shift 1 Shift 2 Shift 3 Shift 4**

**Bus type-I**

**Bus type-II**

**Bus type-I**

**Bus type-II**

≥ 93 ∗

X 4

*Mj* (22)

*j*¼1

*xij* ≤ 600 ∗ *PiTij* (23) *yij* ≤90 ∗ *PiTij* (24)

*Pi* ¼ 1 (25)

*xij*, *yij* ≥0 (26)

*i*¼1

*j*¼1

sample outputs of the LP model are shown in **Table 4**.

and the piece of the GAMS code are reported in the Appendix.

**Bus type-I**

**8. Model output**

**Route No.**

**Table 4.**

**148**

**Bus type-I**

*Number of trips required per route per shift.*

**Bus type-II**

Based on the results of the output of the LP-model, there are 4627 total trips required to serve the average daily passenger demand. The actual number of busses required for a given route i during a given shift *j* depends on the trip factor. That is the number of trips that can be made by each bus type during a given shift. Thus, the output needs to be transformed into the number of busses needed for each route per shift based on the feasible trips that a bus can make during a given shift *j* on each route *i*. From the output of the LP model shown in **Table 3**, the number of trips can be transformed into number busses using the following equation.

$$Number\ of\ Bus = \frac{Number\ of\ Triss}{T\_{\vec{\eta}}}\tag{27}$$

For some routes, the output of the LP is small for some route, so adjusting the actual number of busses is required for such routes to have at least two busses on a given route per shift to allocate them on both ends of the route; that is one on the going trip and the other on the returning trip. This is because the demand during a given shift *j* on each route *i* lies in both directions of the route. Sample of the number of busses per route per shift reported in **Table 5** and computed for all 93 routes in the same way.

The results showed that the actual number of busses required during peak periods is higher than that of off-peak periods. Thus, some of the busses that operate during the morning peak period have to wait on bus stops until they are required for the evening peak.


#### **Table 5.** *Number of busses per route per shift.*

Similarly, the actual number of busses required for each shift varies and the number of busses required during peak periods is higher than that of off-peak periods. Thus, some of the busses that operate during the morning peak period have to wait on bus stops until they are required for the evening peak.
