**10. Model validations**

The outputs of the LP-model were evaluated using different performance measuring parameters. For the validation purpose, various assessments were made between the existing performances and the LP improved systems. The comparisons made, in this research, were based on bus utilization, distance and trips covered and the different operating costs of the enterprise [32]. Each of them is discussed in the following sections.

#### **10.1 Bus utilization**

After converting and assigning busses to each route and each shift, then the improvements achieved by the LP model were compared with the existing bus utilization of ACBSE [32]. The bus utilization was calculated as the ratio of the number of passengers served by the bus to the number of passengers carrying capacity. The average daily bus utilization of the existing and the improved systems are presented in **Figure 3**. The results of the study show that the improved system has better bus utilization than the existing one. The existing system has a maximum bus utilization of about 125% on daily basis, which is very congested and crowded, while the improved system by this study has shown that a maximum bus utilization of 97% [32]. This shows how passenger congestion and service quality were improved by the new system. The average bus utilization for the improved systems is about 66.33% which is better than the existing systems that are 64.26%. Though the average utilization of both of the systems seems close to each other, in the improved most of the utilization lies between 60% and 80% whereas in the existing system had unbalanced bus utilization which is sometimes failed below 20% and other times above 120%.

compared to the existing one and reported by shift. The improved bus utilization by shift is 89.8% during the morning peak, 51.19% during the first off-peak, 82.24% during the evening peak, and 42.1% during the second off-peak periods. The improvement as compared to the existing systems is 19.75% during first off-peak and 12.15% during the second off-peak. The bus utilization of the improved system also reduced the passengers' congestions in peak hours, i.e. bus utilization is decreased from 116.1% to 89.8%. Thus, the improved system has a relatively stable and consistent bus utilization with improved service quality. The new model also indirectly improves the service quality for passengers by reducing over crowdedness while during peak periods and reduces the operating cost during off-peak

*Average bus utilization for peak and off-peak shifts; current vs improved system.*

*Linear Programming Optimization Techniques for Addis Ababa Public Bus Transport*

*DOI: http://dx.doi.org/10.5772/intechopen.93629*

In this section, the distance covered by the existing and the new system are compared. To compare this, the total kilometer covered by busses for route i per day is computed. It is the sum of the Kilometer covered during all the four shifts. **Figure 5** shows that the total distance coverage of the current and improved systems. The distance covered on each shift was computed by multiplying the number of busses allocated to a given route at that shift by the number of trips that can be made by a single bus and by the route length. The total distance covered per day for the improved system is 70,964 kilometers, while for the existing system, it is about 78,963.7 kilometers per day. This shows a reduction of 10.13% in the daily distance

In this case, the total daily trips made for the improved system is also computed for each shift by multiplying the number of busses assigned and the number of trips a single bus can make during that shift. The total trips covered for the existing systems were 5504 trips per day while 5584 for improved systems. This also shows an improvement of 80 trips per day compared with the existing system. The increased number of trips was achieved with a 10.13% reduction on the daily Kilometer. This also improves service availability in addition to saving on the

periods to the enterprise.

**Figure 4.**

operating costs.

**151**

**10.2 Distance and trip coverage**

coverage to serve the same number of passengers.

As presented in **Figure 4**, an in-depth analysis of bus utilization based on shift was carried out. The improved system exhibited significant improvement as

**Figure 3.** *Average daily bus utilization; current vs improved system.*

*Linear Programming Optimization Techniques for Addis Ababa Public Bus Transport DOI: http://dx.doi.org/10.5772/intechopen.93629*

**Figure 4.** *Average bus utilization for peak and off-peak shifts; current vs improved system.*

compared to the existing one and reported by shift. The improved bus utilization by shift is 89.8% during the morning peak, 51.19% during the first off-peak, 82.24% during the evening peak, and 42.1% during the second off-peak periods. The improvement as compared to the existing systems is 19.75% during first off-peak and 12.15% during the second off-peak. The bus utilization of the improved system also reduced the passengers' congestions in peak hours, i.e. bus utilization is decreased from 116.1% to 89.8%. Thus, the improved system has a relatively stable and consistent bus utilization with improved service quality. The new model also indirectly improves the service quality for passengers by reducing over crowdedness while during peak periods and reduces the operating cost during off-peak periods to the enterprise.

#### **10.2 Distance and trip coverage**

In this section, the distance covered by the existing and the new system are compared. To compare this, the total kilometer covered by busses for route i per day is computed. It is the sum of the Kilometer covered during all the four shifts. **Figure 5** shows that the total distance coverage of the current and improved systems. The distance covered on each shift was computed by multiplying the number of busses allocated to a given route at that shift by the number of trips that can be made by a single bus and by the route length. The total distance covered per day for the improved system is 70,964 kilometers, while for the existing system, it is about 78,963.7 kilometers per day. This shows a reduction of 10.13% in the daily distance coverage to serve the same number of passengers.

In this case, the total daily trips made for the improved system is also computed for each shift by multiplying the number of busses assigned and the number of trips a single bus can make during that shift. The total trips covered for the existing systems were 5504 trips per day while 5584 for improved systems. This also shows an improvement of 80 trips per day compared with the existing system. The increased number of trips was achieved with a 10.13% reduction on the daily Kilometer. This also improves service availability in addition to saving on the operating costs.

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

The outputs of the LP-model were evaluated using different performance measuring parameters. For the validation purpose, various assessments were made between the existing performances and the LP improved systems. The comparisons made, in this research, were based on bus utilization, distance and trips covered and the different operating costs of the enterprise [32]. Each of them is discussed in the

After converting and assigning busses to each route and each shift, then the improvements achieved by the LP model were compared with the existing bus utilization of ACBSE [32]. The bus utilization was calculated as the ratio of the number of passengers served by the bus to the number of passengers carrying capacity. The average daily bus utilization of the existing and the improved systems are presented in **Figure 3**. The results of the study show that the improved system has better bus utilization than the existing one. The existing system has a maximum bus utilization of about 125% on daily basis, which is very congested and crowded, while the improved system by this study has shown that a maximum bus utilization

of 97% [32]. This shows how passenger congestion and service quality were

was carried out. The improved system exhibited significant improvement as

improved by the new system. The average bus utilization for the improved systems is about 66.33% which is better than the existing systems that are 64.26%. Though the average utilization of both of the systems seems close to each other, in the improved most of the utilization lies between 60% and 80% whereas in the existing system had unbalanced bus utilization which is sometimes failed below 20% and

As presented in **Figure 4**, an in-depth analysis of bus utilization based on shift

to wait on bus stops until they are required for the evening peak.

*Concepts, Applications and Emerging Opportunities in Industrial Engineering*

**10. Model validations**

following sections.

**10.1 Bus utilization**

other times above 120%.

**Figure 3.**

**150**

*Average daily bus utilization; current vs improved system.*

bus. This is due to the fact that the total kilometer covered is improvement resulted

*Linear Programming Optimization Techniques for Addis Ababa Public Bus Transport*

The motivation of this research was to develop a model that can optimize the operational performances of ACBSE. Based on the major findings, it can be concluded that the existing scheduling systems of ACBSE have shown low performances on the bus utilization, operating cost, and daily trips and distance covered. These improvements have been achieved because the existing system has fixed numbers of busses assigned to routes without considering the variability of passenger demands. This had cost more the enterprise. However, the operational performance improvements of the LP-model have shown better performances over the existing one nearly in all of the above performance measuring parameters. Besides, it can be concluded that the existing bus scheduling and operations system has a lower average utilization of busses compared with the new system by 2.1%. The bus utilization per route per shift also shows significant improvement over the existing system. With regard to the cost-saving, the new model has resulted in a saving of 13.74% (151,292.19 ETB) in the operating costs of the enterprise. Moreover, the new model also resulted in a 10.13% saving on the total km covered with 80 additional available trips per day for the enterprise. In addition to these and the saving in all the parameters, the improved system has also reduced the waiting time, improve service quality, and reduce passenger congestion by scheduling busses based on the international standard bus capacity. The new system has also a significant reduction in the total kilometer covered while improving the total trips made daily. All these improvements of the new system of the LP-Model were exhibited without altering the existing routes used by the enterprise. But rerouting the existing route's design

may also bring radical improvement to the performances of the enterprise.

Sets i Routes /1 ∗ 93/ This sets routes from route 1 to route 93. j Time periods /1 ∗ 4/; Sets shifts from shift 1 to shift 4. **Sample Demand distribution per route per shift**

Table d(i, j) demand distribution on route *i* on time shift *j*

Table T(*ij*) trip factor on route *i* for time period *j*

Parameters M(*j*) minimum trips required at time period *j*

**Appendix: the GAMS sample code**

1 2 34 1 2249 1124 1968 281 2 2249 1124 1968 281 3 2249 1124 1968 281 .. . . . .. . . . .. . . . 92 1848 924 1617 231 93 1362 681 1192 170 **Sample Trip Factors (Tij)**

**Minimum Trip Required (M** *j***)**

**153**

**Defining Route i and Shift j**

\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*

in a reduction in the cost of gas oil consumed.

*DOI: http://dx.doi.org/10.5772/intechopen.93629*

**11. Conclusion**

**Figure 5.** *Distance coverage; current vs improved system.*

### **10.3 Operating costs**

Using the different operating costs of the enterprise, the other performance measuring parameters were also assessed in this research. The improvements made by the new model were also considerable. The total daily operating cost of the enterprise for each route is the sum of operating costs for all the shifts. From the comparison made, the results of the study show that the average daily operating costs of the enterprise for the existing systems are about 1,101,283.68 ETB (ETB = Ethiopian Birr and 1USD = 34.33ETB as of Jun 4, 2020) while for the improved systems is 949,991.49 ETB. The saving of the new system in this read is about 13.74% per day compared to the current system. **Figure 6** shows the improvements made by the new systems are achieved nearly in all the operating costs of the enterprise compared to the existing one.

As compared to all the operating costs, larger saving is observed on gas oil. This reduction has also a strong relationship with the total Kilometer covered by each

**Figure 6.** *Current vs improved operating cost.*

bus. This is due to the fact that the total kilometer covered is improvement resulted in a reduction in the cost of gas oil consumed.
