**1. Introduction**

The bus schedule is one of the operations planning process in bus transport that deals with the proper assignment of busses to routes to serve the expected passenger demand. The planning process in public transportation consists of different recurrent and complex tasks. It starts at a strategic level by collecting or forecasting the number of passengers at each transfer point, which is most of the time fully unknown and adds to the complexity of the planning process [1–3].

The decision-making process of the bus assignment is, however, a trade-off between service quality and operating costs for the bus operating companies [4]. It is because using too many busses incurs more operating costs while resulting in good service quality, whereas too few busses have the opposite effect. Based on the information collected from Anbessa City Bus Service Enterprise (ACBSE) currently, the enterprise serves more than 125 routes (as of 2019) that connect different parts of the city using 759 operational busses. The number of passengers shows

high variability during each period which requires fluctuating the number of assigned busses in each route. But the enterprise uses mainly a fixed number of busses scheduled per route in its operation throughout the day. This resulted in some busses moving empty while others are being overcrowded, which subsequently results in poor performance and service quality. Moreover, the transportation service in ACBSE has many challenges such as low bus utilization, unsatisfied passengers' demand, and higher operating costs.

constant *K*, specifying the capacity of the bin, what is the minimum number of bins

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

solving TSP. A VRP with a single vehicle and infinite capacity is a TSP.

the important research topics in the fields [4, 22, 23].

Logically, all the items have to be inside exactly in one bin and the total capacity of items in each bin has to be within the capacity limits of the bin. This is known as the best packing version of BPP. The TSP [3] is about a traveling salesman who needs to visit several cities. The salesman has to visit each city exactly once, start and end location, commonly called depot in VRP. The issue is to search the shortest tour within all the cities [17]. Connecting this to the VRP, customers can be allotted to vehicles by solving BPP and the order in which they are visited can be found by

VRP is a common name given to a problem in which a set of routes for a fleet of vehicles based at one or several locations called a depot, must be determined for several dispersed cities or customers [18]. The motive is to service a set of customers with a minimum-cost [16, 19]. Vehicle routes originate and terminate at a depot. It is one of the most challenging combinatorial optimization problems in distribution, and logistics [7]. Customers may be in a dispersed location and a fleet of vehicles need to serve them from a depot and return to the depot [16]. The decision here is to determine the assignment of the vehicle (s) and route (s) that a vehicle will serve them best. The commonly used illustration of the input and output of VRP is given

Since both BPP and TSP are the so-called NP-hard problems and since VRP is a combination of the two, it is also NP-hard [12, 16, 20, 21]. Since the last decades, VRP has got much interest from many scholars. Even in recent years, with the rapid advancements of globalization and supply chain systems, VRP is becoming one of

Moreover, the complexity and its application importance immense literature have devoted to the study and analysis of Bus Scheduling Problem (BSP) and many optimization models have been proposed [23]. The different models developed have tried to accomplish near-optimal solutions with an acceptable amount of computational effort and time [6]. There are many extensions for the Vehicle Schedule Problem (VSP) or VRP with several requirements in the literature over the last 50 years [16, 24]. Among many others, some of the examples are the existence of one depot [18] or more than one depots [4, 16], a heterogeneous fleet with multiple vehicle types [18] the permission of variable departure times of trips, VRP with

deterministic demand which is commonly called classical VRP [13, 18].

needed? [16].

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

in **Figures 1** and **2**.

**Figure 1.** *VRP inputs.*

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To address the challenges of bus assignment and scheduling problems in ACBSE, this paper first focuses to develop a demand-oriented Linear Programming (LP). Linear Programming is a well-accepted technique within the field of Operations Research, a specialty area within the broader field of Industrial Engineering. Then the LP-model is used to solve and optimally satisfy the existing passengers' demand in four operating periods in a day using 93 selected routes. For simplicity purpose, in this paper, the four operating periods are named as shifts.
