Refuelling Schedule for Airports

By Kiran R K Jitha Babu Shyam S Sreeraj S

CHAPTER 1
INTRODUCTION
1.1 REFUELLING
Refuelling is an important aspect with respect to the airports since it determines the ground time of an aero plane. Aircraft fuelling can take up to 90 minutes of ground time. Hence, precise planning and allocation is absolutely essential.

Once a flight lands in an airport it has to be refueled for the next flight. The quantity of fuel required depends on the distance it has to travel to reach the next station and type of flight.

Aviation fuel is a specialized type of petroleum-based fuel used to power aircraft. It is generally of a higher quality than fuels used in less critical applications such as heating or road transport, and often contains additives to reduce the risk of icing or explosion due to high temperatures, amongst other properties.

Aviation fuels consist of blends of over a thousand chemicals, primarily Hydrocarbons (paraffins, olefins, naphthenes, and aromatics) as well as additives such as antioxidants and metal deactivators, and impurities. Principal components include n-octane and isooctane. Like other fuels, blends of Aviation fuel are often described by their Octane rating. Avgas is sold in much lower volumes, but to many more individual aircraft, whereas Jet Fuel is sold in high volumes to large aircraft operated typically by airlines, military and large corporate aircraft. [3]

Aviation fuel is often dispensed from a tanker or bowser which is driven up to parked aero planes and helicopters. Some airports have pumps similar to filling stations that aircraft must taxi up to. Some extremely large airports also have permanent piping to parking areas for large aircraft.

Regardless of the method, aviation fuel is transferred to an aircraft via one of two methods: over wing and under wing. Over wing fuelling is used on smaller planes, helicopters, and all piston-engine aircraft. Over wing fuelling is similar to automobile fuelling — one or more fuel ports are opened and fuel is pumped in with a conventional pump. Under wing fuelling, also called single-point, is used on larger aircraft and for jet fuel exclusively. For single-point fuelling, a high-pressure hose is attached and fuel is pumped in at up to 50 PSI. Since there is only one attachment point, fuel distribution between tanks is either automated or it is controlled from a control panel at the fueling point or in the cockpit. As well, a dead man's switch is used to control fuel flow.

Refuelling is basically done in two ways: 1. Using the hydrant dispenser. 2. Using the refuelling tanks.

Aircraft refuelers can be either a self contained fuel truck or a hydrant truck or cart. Fuel trucks are self contained, typically containing up to 10,000 US gallons of fuel, and have their own pumps, filters, hoses, etc. A hydrant cart or truck hooks into a central pipeline network and provides fuel to the aircraft. There is a significant advantage with hydrant systems when compared to fuel trucks, as fuel trucks must be periodically replenished. In most of the airports there will be two types of bays; those with fuel outlets and those without fuel outlets. Hydrant dispensers can be used only in the bays which have fuel outlets. Most airports also have their own dedicated oil depots (or "tank farms") where aviation fuel (jet A1) is stored prior to being discharged into aircraft fuel tanks. Fuel is transported from the depot to the aircraft via a hydrant system. A hydrant is an outlet from a fluid main often consisting of an upright pipe with a valve attached from which fluid (fuel) can be tapped.The hydrant dispenser (or cart) is traditionally a self propelled vehicle which is driven on to the aircraft parking apron (or ramp) area and connected by hoses to the fuel hydrant at a hydrant pit valve in the ground and to the aircraft fuel intake coupling. The dispenser contains pressure control, filtration and metering equipment as well as an elevating platform to allow the operator to reach the under wing couplings (for large aircraft).

The refuelling tank is a comprehensive apparatus provided with a fuel tank and pump. This refueller is driven to the required position near the aero plane and its tank is connected to the fuel tank of aero plane and the fuel is pumped by refueller’s pump. Refuellers can range in fuel capacity from around 5,000 litres up to approximately 80,000 litres. They have on board pressure control, pumping, filtration and metering equipment, sometimes together with an elevating platform to allow the operator to reach the under wing couplings. For operating the refuelling tank a driver, an officer and another worker is required.

The refuelling tanks come in different capacities and they have a limitation. For refuelling operations where more fuel has to be supplied than the maximum capacity of the refuelling tank, hydrant dispensers of unlimited capacity are used. This can be connected to the main tank and outlet is connected to aero plane’s fuel tank and fuel is pumped. If refuelling tank is used in this case one refuelling tank is emptied and then it is disconnected and another refuelling tank is connected to the fuel tank. This becomes a tedious and time consuming job where large quantities of fuel have to be filled into an aero plane.

1.2 SCHEDULING
A schedule is a list of employees who are working on any given day, week, or month in a workplace. A schedule is necessary for the day-to-day operation of any facility.

The process of creating a schedule is called scheduling. An effective workplace schedule balances the needs of employees, tasks, and in some cases, customers. A daily schedule is usually ordered chronologically, which means the first employees working that day are listed at the top, followed by the employee who comes in next, etc.

A schedule is most often created by a manager. In larger operations, a Human Resources manager or scheduling specialist may be solely dedicated to writing the schedule. In some cases scheduling software is used to allow organizations to better manage staff scheduling. Employee scheduling software supports shift and employee assignments and improves staff utilization. Organizations commonly use spreadsheet software or employee scheduling software to create and manage shifts, assignments, and employee preferences. [4]

1.3 OPTIMIZATION
In mathematics, the term optimization, or mathematical programming, refers to the study of problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an allowed set.
An optimization problem can be represented in the following way
Given: a function f : A [pic]R from some set A to the real numbers
Sought: an element x0 in A such that f(x0) ≤ f(x) for all x in A ("minimization") or such that f(x0) ≥ f(x) for all x in A ("maximization").

Such a formulation is called an optimization problem or a mathematical programming problem. Many real-world and theoretical problems may be modeled in this general framework. The function f is called an objective function, or cost function. A feasible solution that minimizes (or maximizes, if that is the goal) the objective function is called an optimal solution. [5]

CHAPTER 2
PROBLEM DEFINITION
Indian Oil Corporation is responsible for providing aviation fuel to flights in Indian airports.
We are considering the refuelling crew scheduling from Indian Oil Corporation’s point of view. The staff available for the Indian Oil Corporation can be classified into two: • Blue collar workers and • White collar workers (Officers)

The Blue collar workers are further classified into o Driving hands and o Non driving hands

The officers are classified into two o Authorized officers and o Unauthorized officers

IOC is facing difficulties in scheduling their crew for refuelling since they have banned new recruitments of unskilled labour. The demand of workforce for each day is much higher than total available workforce in the Blue Collar category which is 9 workers. Therefore every worker has to work overtime hours. This overtime is unevenly distributed. Some workers has to work for 24 hours at a single stretch.

They are manually scheduling their refuelling crew. The problem is to schedule this manpower in a systematic and optimized manner.
CHAPTER 3
LITERATURE REVIEW
3.1 Generating, scheduling and rostering of shift crew - duties: Applications at the Hong Kong International Airport

In the context of manpower planning, goal programming (GP) is extremely useful for generating shift duties of fixed length. A fixed-length duty consists of a fixed number of contiguous hours of work in a day, with a meal/rest break somewhere preferably around the middle of these working hours. It is such properties that enable the straightforward, yet flexible GP modeling. We propose GP models for an integrated problem of crew duties assignment, for baggage services section staff at the Hong Kong International Airport. The problem is solved via decomposition into its duties generating phase—a GP planner, followed by its GP scheduling and rostering phase. The results can be adopted as a good crew schedule in the sense that it is both feasible, satisfying various work conditions, and ‘‘optimal’’ in minimizing idle shifts.

This paper of optimization modeling for staffing is motivated by the need to produce daily work plan of the baggage service agents at the passenger terminal. The complete BSS crew system consists of its three component GP models: the Duties Generation Problem (DGP), the Crew Scheduling Problem (CSP) and the Crew Rostering Problem (CRP).
DGP in its simplest form (computes and) allocates duties (of given fixed structure of work pattern, rather than crew or staff needing further varying requirements of scheduling) to cover known demands. Demands are given, for equally spaced (such as hourly or half-hourly) time intervals of (the working time of) a day. As such, DGP is the prerequisite to CSP and CRP in that it provides the planning inputs needed in subsequent scheduling and rostering of staff. [2]

3.2 An integer programming model for hierarchical workforce scheduling problem
In this paper, an integer programming model for the hierarchical workforce problem under the compressed workweeks is developed. The model is based on the integer programming formulation developed by Billionnet [A. Billionnet, Integer programming to schedule a hierarchical workforce with variable demands, European Journal of Operational Research 114 (1999) 105–114] for the hierarchical workforce problem. In this model, workers can be assigned to alternative shifts in a day during the course of a week, whereas all workers are assigned to one shift type in Billionnet’s model. The main idea of this paper is to use compressed workweeks in order to save worker costs. A compressed workweek (alternative shifts) is a workweek arrangement which lets labour work fewer days a week, but usually a longer day to fully or partially compensate the hours lost due to the extra free days. If the only one shift (i.e., 8 hours) is allowed for scheduling of labour, assuming that employees can only take 2 off-days, then they will be working 5-day. If alternative shift types like 8 hours, 10 hours and 12 hours are used simultaneously, it will be possible to reduce labour cost.
The objective of this model is to determine an optimal hierarchical workforce in which a higher qualified worker can substitute for a lower qualified one, but not vice versa. [1]

CHAPTER 4
STUDY AND ANALYSIS OF EXISTING SYSTEM
4.1 INTRODUCTION TO THE PRESENT SYSTEM
Indian Oil Corporation provides about 75% of fuel for refuelling operations in Indian airports. The company controls over 97 airports out of 117 in the country. It meets the requirements of 21 domestic, 64 international and 250 private airlines. We are considering the refuelling crew scheduling from Indian Oil Corporation’s point of view. The staff available for the Indian Oil Corporation can be classified into two: 1) Officers 2) Blue collar workers 1. Officers:- The officers can be broadly classified into two: those who have authorization to guide the refuelling operations in the field and those who do not have authorization and can work only inside the office. As per the rule there should be at least one authorized officer whose presides over the refuelling operations and sign the papers at the beginning and end of operations. 2. Blue collar workers:-These workers there are two types a) Driving hands b) Non driving hands a) Driving hands:- These are workers who have driving license for heavy vehicles. They drive the refuelling tank to the required locations. b) Non driving hands:- These are workers who do not have a driving license and cannot single handedly use the refuelling tanks.

IOC has banned the recruitment of staff in the worker category. So now the authorities are finding it difficult to schedule the crew for refuelling operation.

For using the hydrant dispenser there should be one worker who is a driving hand and an authorized officer. For using the refuelling tanks there should be one driving hand, one authorized officer and an additional worker who may be a driving hand or a non driving hand.

The refuelling operation is done on a three shift basis per day. 1) First shift is from 6am to 2pm 2) Second shift is from 2pm to 10pm 3) Third shift is from 10pm to 6am

Normal working hour per day for a worker is a shift per day. But due to shortage of staff and improper scheduling, most of the workers are made to work overtime. In this state also there are some irregularities as some workers work overtime more than the others. Also there is a difficulty in scheduling the workers such that sufficient number of driving hands and authorized are present in each shift along with non driving hand and unauthorized officers. Since this complex scheduling work is done manually, the scheduling of crew obtained is full of flaws and violates several principles like ▪ Avoiding overtime of workers ▪ Even if overtime work is required, it is distributed equally among the workers.

4.2 Study and analysis of the present system
4.2.1 Study
IOC faces an acute shortage of blue collar workers for refuelling at the Trivandrum airport. They now have six officers and nine blue collar workers.

Of the six officers available, three are authorized for presiding over refuelling operations. Two of them are unauthorized and they look into office matters and financial transactions of IOC.

Of the nine blue collar workers, seven of them are driving hands with license for driving heavy vehicles and two of them are non driving hands.

The refuelling process is done on a shift basis comprising of 3 shifts per day. First shift from 6am to 2 pm, Second shift from 2pm to 10pm,Third shift from 10pm to 6am.First and the second shift consist of 5 workers and the third shift consist of 3 workers. As 13 workers are required and only 9 are available, many of the workers have to do overtime work. The workers are paid wages at rate of Rs 190 per hour for each extra hour. Therefore some are ready to work for even 24 hours. But this is avoided most of the time since this leads to fatigue and refuelling job requires concentration. Any small damage to the aero plane being refueled will lead to payment of compensations which may be in crores.

The first and the second shift should consist of at least 3 driving hands each and the third shift should consist of 2 driving hands, and the non driving hands are scheduled to satisfy the required number of workers.

4.2.2 Detailed Analysis Of Present System
(i) Blue Collar Workers
There are 9 blue collar workers available for refuelling operations, say A,B,C,D,E,F,G,H and I. Refuelling operation is done on a shift basis as explained earlier. First two shifts of the day requires 5 blue collar workers and last shift requires 3 blue collar workers. The constraints for scheduling are given below. 1. A worker can work only for 2 shifts at a stretch. 2. Each worker is entitled for one day off per week. 3. First two shifts should compose of atleast 3 driving hands and last shift should compose of 2 driving hands.

The schedule of workers for a week on an average is shown :

TABLE 4.1: SAMPLE SCHEDULE FOR A WEEK
|day |shift |working |off |

[pic]

The average overtime of a worker

The average overtime of a worker is calculated as follows:
Total man-hours per week = 13 workers x 8 hours x 7 days = 728 man-hours
Required working hours per week for a worker = 728manhours ÷ 9 workers = 81 hours
Normal working hours of a worker on ‘a shift a day basis’ and one day off per week = 8 hours x 6 days = 48 hours
Average overtime of a worker = 81 − 48 = 33 hours per week

Distribution of overtime between workers
Distribution of overtime among the workers, for a week is given:

TABLE 4.2: DISTRIBUTION OF OVERTIME

|worker |Working hours per week |overtime |
|A |88 |40 |
|B |80 |32 |
|C |88 |40 |
|D |88 |40 |
|E |64 |16 |
|F |80 |32 |
|G |88 |40 |
|H |72 |24 |
|I |80 |32 |

Figure 4.1: Distribution of Overtime

The distribution of overtime is unequal. The overtime work should be distributed evenly among the workers such that each worker has overtime equal to the average overtime, ie 33 hours per week.

(ii) Officers
The officers can be broadly classified into two: those who have authorization to guide the refuelling operations in the field and those who do not have authorization and can work only inside the office. As per the rule there should be at least one authorized officer whose presides over the refuelling operations and sign the papers at the beginning and end of operations.

Of the six officers available, three are authorized for presiding over refuelling operations. Two of them are unauthorized and they look into office matters and financial transactions of IOC.

First shift of the day requires 2 officers and last two shifts require 1 officer. For all the three shifts, there should be atleast one authorized officer. Since there are only three authorized officers, this calls for their overtime working for one shift.

The average overtime of authorized officer
The average overtime of authorized officers is calculated as follows:
Demand for authorized officers in a day = 1 per shift X 3 shifts = 3 authorized officers / day
Total demand for authorized officers in a week = 3 authorized officers / day X 7 days = 21 authorized officers / week
No. of authorized officers = 3
Required working shifts for an authorized officer = 21 authorized officers / week ÷ 3 authorized officers = 7 shifts / week
Normal working hours of authorized officer on ‘a shift a day basis’ and one day off per week = 6 shifts / week
Average overtime of authorized officer = 1 shift / week

The overtime working of officers is not as critical as the overtime working of blue collar workers, as the officers are required to do only one shift overtime in a week.

(iii) Hydrant Dispensers And Refuelling Tanks
In airports there will be two types of bays; those with fuel outlets and those without fuel outlets. Hydrant dispensers can be used only in the bays which have fuel outlets .In the Trivandrum International airport,7 out of 9 bays have fuel outlet. In these 7 bays, hydrant dispensers can be used.

For refuelling operations where more fuel has to be supplied than the maximum capacity of the refuelling tank, hydrant dispensers of unlimited capacity are used. If refuelling tank is used, one refuelling tank is emptied and then it is disconnected and another refuelling tank is connected to the fuel tank. This becomes a tedious and time consuming job where large quantities of fuel have to be filled into an aero plane.

For using the hydrant dispenser there should be one worker who is a driving hand and an authorized officer. For using the refuelling tanks there should be one driving hand, one authorized officer and an additional worker who may be a driving hand or a non driving hand.

Types of aircrafts used in Trivandrum International airport
(i) Airbus
A310:

The Airbus A310 is a medium to long-range widebody airliner. Launched in 1978, it was the second aircraft created by the Airbus consortium of European aerospace companies, which is now fully owned by EADS. The A310 is a shortened derivative of the A300, the first twin-engined widebody airliner. The A310 (along with the A300) ceased production in July 2007. Freighter sales for which the A310 competed are to be fulfilled by a new A330-200F derivative.

The A310's range exceeds that of all the A300 models, except for the A300-600, which surpasses the A310-200. This feature has led to the aircraft being used extensively on transatlantic routes. The A300 and A310 introduced the concept of commonality: A300-600 and A310 pilots can qualify for the other aircraft with one day of training.

Like its sister aircraft, the A300, the A310 has reached the end of its market life as a passenger and cargo aircraft. There have been no new A310 passenger orders since the late 1990s, and only a few freighter orders remain. The A310 (along with the A300) ceased production in July of 2007, though five orders from Iraqi Airways remain on the books. The remaining freighter sales are to be fulfilled by the new A-330-200F derivative.

The aircraft was formally launched in July 1978 for LUFTHANSA and SWISSAIR. A further development of the A300, the aircraft was initially designated the A300 B10. Essentially a "baby" A300, the main differences in the two aircraft are • Shortened fuselage - same cross section, providing capacity of about 200. • Redesigned wing - designed by British Aerospace who rejoined Airbus consortium • Smaller vertical fin
The A310 was marketed as an introduction to widebody operations for developing airlines. The A310 was replaced in Airbus' lineup by the highly successful A330-200, which shares its fuselage cross-section. Between 1983 and the very last aircraft produced 1998, 255 A310s were delivered by Airbus.

The A300 and A310 established Airbus as a competitor to Boeing and allowed it to go ahead with the more ambitious A320 and A330/A340 families. [6]

TABLE 4.3: SPECIFICATIONS OF A310
| |A310-200 |A310-200F |A310-300 |A310-300F |
|Crew |2 |
|Length |46.66 m (153 ft 1 in) |
|Cross section |5.64 m (17ft 4in) |
|Passengers (2cl) |240 |33t cargo |240 |33t cargo |
|MTOW |141,974 kg (312,342 lb) |164,000 kg (361,600 lb)* |
|Empty weight |80,142 kg |72,400 kg |83,100 kg |73,900 kg |
| |(176,312 lb) | |(183,300 lb) | |
|Max fuel |55,200 l (14,603 US g) |75,470 l (19,940 US g) |
|Cruise speed (M) |0.80 (850 km/h.) |
|Max speed (M) |0.84 (901 km/h.) |
|Range |6,800 km |5,550 km |9,600 km |7,330 km |
| |(3,670 nm) | |(5,200 nm) | |
| |Trans-continental | |Trans-atlantic | |

A320

The Airbus A320 families of short- to medium-range commercial passenger airliners are manufactured by Airbus Family members include the A318, A319, A320, and A321, as well as the ACJ business jet.

First delivered in 1988, the A320 pioneered the use of digital fly by wire flight control in a commercial aircraft. With more than 3,000 aircraft of the A320 family built, it is the second best-selling jet airliner family of all time after the family's primary competition, the Boeing 737. [7]
TABLE 4.4: SPECIFICATIONS OF A320
|Measurement |A318-100 |A319-100 |A320-200 |A321-200 |
|Cockpit crew |Two |
|Seating capacity |117 (1-class) |142 (1-class) |180 (1-class) |220 (1-class) |
| |107 (2-class) |124 (2-class) |150 (2-class) |185 (2-class) |
|Length |31.45 m (103 ft 2 in) |33.84 m (111 ft) |37.57 m (123 ft) |44.51 m (146 ft) |
|Typical empty weight |39,300 kg |40,600 kg |42,400 kg |48,200 kg |
|Cruising speed |Mach .78 |
|Max. speed |Mach .82 |
|Take off run at MTOW |1,355 m (4,446 ft) |1,950 m (6,398 ft) |2,090 m (6,857 ft) |2,180 m (7,152 ft) |
|Range fully loaded |5,950 km or 3,200 nmi |6,800 km or 3,700 nmi |5,700 km or 3,100 nmi |5,600 km or 3,000 nmi |
| |(5,900 km) |(6,900 km) |(5,700 km) |(5,600 km) |
|Max. fuel capacity |23,860 liters or 6,300 |29,840 liters or 7,885 |29,680 liters or 7,842 US gal |
| |US gal |US gal | |

A330

The Airbus 330 is a large-capacity, wide-body, medium-to-long-range commercial passenger airliner. It was developed at the same time as the four-engined Airbus 340, and will likely be replaced by the Airbus 350. [8]

TABLE 4.5 : SPECIFICATIONS OF A330

|Aircraft dimensions |A330-200 |A330-300 |A330-200F |
|Overall length |58.8 m (192 ft 11 in) |63.6 m (208 ft 8 in) |58.8 m (192 ft 11 in) |
|Wheel track |10.69 m (35 ft 1 in) |
|Cruising Speed |Mach 0.82 (541 mph, 470 knots, 871 km/h at 35,000 ft cruise altitude) |
|Maximum Cruise Speed |Mach 0.86 (568 mph, 493 knots, 913 km/h at 35,000 ft cruise altitude) |
|Takeoff run at MTOW |2,220 metres/7300ft |2,500 metres (8,202 ft) |- |
| |
|Design weights |
|Maximum ramp weight |230.9 (233.9 ) t |
|Maximum fuel capacity |139,100 l |97,170 l |139,100 l |
|Typical operating weight empty |119.6 t |122.2 (124.5) t |109 t |
|Typical volumetric payload |36.4 t | | |

A340
The Airbus A340 is a long-range four-engined widebody commercial passenger airliner manufactured by Airbus, a subsidiary of EADS. It seats between 261 and 380 passengers, and has a range between 6,700 and 9,000 NM. It is similar in design to the twin-engined A330. Initial A340 versions share the fuselage and wing of the A330 while later models are longer and have larger wings. [9]

TABLE 4.6: SPECIFICATION OF A340

|Measurement |A340-200 |A340-300 |A340-500/-500HGW |A340-600/-600HGW |
|Cockpit crew |Two |
|Typical empty weight |129,000 kg |129,275 kg |170,400 kg |177,000 kg |
| |284,396 lb |295,503 lb |375,668 lb |390,218 lb |
|Maximum take-off weight |275,000 kg |276,500 kg |372,000/380,000 kg |368,000/380,000 kg |
| |606,300 lb |609,600 lb |820,100 /837,800 lb |811,300/837,800 lb |
|Cruising speed |M .82 (484 kn, 896 km/h, 557 mph) |M .83 (490 kn, 907 km/h, 564 mph) |
|Take off run at MTOW |2,990 m |3,000 m |3,050 m |3,100 m |
| |9,810 ft |9,840 ft |10,000 ft |10,170 ft |
|Range fully loaded |14,800 km 8,000 NM |13,700 km 7,400 NM |16,020/16,700 km 8,650/9,000 NM |14,900/15,900 km 7,750/7,900 NM |
|Max. fuel capacity |155,040 L 40,957 gal|140,640 L 37,153 gal|214,810/222,000 L |195,881/204,500 L |
| | | |56,750/58,646 gal |51,746/54,023 gal |

(ii) BOEING

BOEING 737

The Boeing 737 is a short to medium range, single aisle, narrow body jet airliner. Developed from Boeing's 727 and 707, the 737 has nine variants, from the early -100 to the most recent and largest, the -900. Currently series -600 through -900 are being produced.

First envisioned in 1964, the 737 entered service in 1968, and 25 years after the announcement of its first sale it has become the most ordered and produced commercial passenger jet in the world. Continuously manufactured by Boeing since 1967 with over 7,000 ordered and over 5,000 delivered (as of 2007), there are over 1,250 of the type airborne at any given time. On average, a 737 departs or lands somewhere every five seconds. [10]

TABLE 4.7 : SPECIFICATIONS OF BOEING 737

|Measurement |737-100 |737-400 |737-500 |737-600 |737-700/ |737-800 |737-900ER |
| | | | | |737-700ER | | |
|Length |94ft(28.6m) |119ft 6 |101ft 8in(31.1m) |102ft 6in(31.2m)|110ft 4in(33.6m)|129ft 6in(39.5m)|138ft 2in (42.1 m) |
| | |in(36.5m) | | | | | |
|Empty Weight |61,864 |73,040 lb(33,200|68,860 |80,031 lb(36,378|84,100 lb(38,147|91,108 lb(41,413|98,495 lb |
| |lb(28,120 kg) |kg) |lb(31,300kg) | kg) | kg) | kg) |(44,676 kg) |
|Cruising speed|0.74 (485 mph, 780 km/h) |0.785 (514 mph, 828 km/h) |0.78(511 mph,823 km|
| | | |/h) |
|Maximum speed |0.82 (544 mph, 876 km/h, 473 kt) |
|Max.fuel |4725US gal |6,130 US gal |6,296 US gal |6,875 US gal |7,837 US gal |
|capacity |(17860 L) |(23,170 L) |(23,800 L) |(26,020 L) |(29,660 L) |

Boeing 747

The Boeing 747, sometimes nicknamed the "Jumbo Jet", is among the world's most recognizable aircraft, and was the first wide-body commercial airliner ever produced. Manufactured by Boeing's Commercial Airplane unit in the United States, the original version of the 747 was two and a half times the size of the Boeing 707, one of the common large commercial aircraft of the 1960s. The aircraft is so large that its wingspan is longer than the length of the Wright Brothers' first flight. First flown commercially in 1970, it held the passenger capacity record for 37 years, until it was surpassed by the Airbus A380.
The four-engine 747 uses a double deck configuration for part of its length. It is available in passenger, freighter and other versions. The 747's hump created by the upper deck allows for a front cargo door on freighter versions, and serves as additional seating in most versions. The 747-400, the latest version in service, is among the fastest airliners in service with a high-subsonic cruise speed of Mach 0.85 (567 mph or 913 km/h). It has an intercontinental range of 7,260 nautical miles (8,350 mi or 13,450 km). The 747-400 passenger version can accommodate 416 passengers in a typical three-class layout or 524 passengers in a typical two-class layout.
The 747 was expected to become obsolete after 400 were sold because of the development of supersonic airliners, but it has outlived many of its critics' expectations, and production passed the 1,000 mark in 1993. As of December 2007, 1,399 aircraft had been built, with 122 more in various configurations on order. The latest version of the aircraft, the 747-8, is scheduled to enter service in 2009. [11]

TABLE 4.8 : SPECIFICATIONS OF BOEING 747

|Measurement |747-100 |747-200B |747-300 |747-400 |747-8I |
| | | | |747-400ER | |
|Cockpit Crew |Three |Two |
|Length |231 ft 10 in (70.6 m) |250 ft 8 in (76.4 m) |
|Weight empty |358,000 lb |383,000 lb |392,800 lb |393,263 lb |410,000 lb |
| |(162,400 kg) |(174,000 kg) |(178,100 kg) |(178,756 kg) |(185,972 kg) |
| | | | |ER: 406,900 lb | |
| | | | |(184,600 kg) | |
|Cruising speed |Mach 0.84 |Mach 0.85 |Mach 0.855 |
|(at 35,000 ft |(555 mph, 895 km/h, 481 knots ) |(567 mph, 913 km/h, 487 kt) |(570 mph, 918 km/h, 493 kt) |
|altitude) | |ER: Mach 0.855 | |
| | |(570 mph, 918 km/h, 493 kt) | |
|Maximum speed |Mach 0.89 |Mach 0.92 | |
| |(587 mph, 945 km/h, 510 kt) |(608 mph, 977 km/h, 527 kt) | |
|Takeoff run at |10,466 ft (3,190 m) |10,893 ft |9,902 ft (3,018 m) |10,138 ft (3,090 m) |
|MTOW | |(3,320 m) |ER: 10,138 ft (3,090 m) | |
|Range fully |5,300 nmi |6,850 nmi |6,700 nmi |7,260 nmi |8,000 nmi |
|loaded |(9,800 km) |(12,700 km) |(12,400 km) |(13,450 km) |(14,815 km) |
| | | | |ER: 7,670 nmi | |
| | | | |(14,205 km) | |
|Max. fuel |48,445 U.S. gal |52,410 U.S. gal |57,285 U.S. gal |64,225 U.S. gal |
|capacity |(40,339 imp gal/183,380 L) |(43,640 imp gal/199,158 L) |(47,700 imp gal/216,840 L) |(53,478 imp gal/243,120 L) |
| | | |ER: 63,705 U.S. gal | |
| | | |(53,045 imp gal/241,140 L) | |

BOEING 767
The Boeing 767 is an American mid-size, wide-body twinjet airliner produced by Boeing’s Commercial Airplanes Division. Passenger versions of the 767 can carry from 181 to 375 passengers and have a range of 5,200 to 6,590 nautical miles (9,400 to 12,200 km) depending on variant and seating configuration. It entered into airliner service in 1982. [12]

TABLE 4.9 : SPECIFICATIONS OF BOEING 767

| |767-200 |767-200ER |767-300 |767-300ER |767-300F |767-400ER |
|Length |159 ft 2 in (48.5 m) |180 ft 3 in |201 ft 4 in |
| | |(54.9 m) |(61.4 m) |
|Empty Weight, |176,650 lb |181,610 lb |189,750 lb |198,440 lb |190,000 lb |229,000 lb |
|operating |(80,130 kg) |(82,380 kg) |(86,070 kg) |(90,010 kg) |(86,180 kg) |(103,870 kg) |
|Maximum take-off|315,000 lb |395,000 lb |350,000 lb |412,000 lb |412,000 lb |450,000 lb |
|weight |(142,880 kg) |(179,170 kg) |(158,760 kg) |(186,880 kg) |(186,880 kg) |(204,120 kg) |
|Range |5,200 NM |6,590 NM |5,230 NM |5,975 NM |3,255 NM |5,625 NM |
| |(9,400 km) |(12,200 km) |(9,700 km) |(11,065 km) |(6,025 km) |(10,415 km) |
| |transatlantic |transpacific |transatlantic |transpacific |transcontinental |transpacific |
|Cruise speed |Mach 0.80 (470 kn, 530 mph, 851 km/h at 35,000 ft cruise altitude) |
|Maximum Cruise |Mach 0.86 (493 kn, 568 mph, 913 km/h at 35,000 ft cruise altitude) |
|speed | |
|Takeoff run |5,600 ft (1,710 m) |7,900 ft (2,410 m) |9,501 ft (2,896 m)|
|at MTOW | | | |

(iii) ATR
Aerei da Trasporto Regionale or Avions de Transport Régional (ATR) is an Italian-French based aircraft manufacturer. It was formed in 1981 by Aérospatiale of France (now EADS) and Aeritalia (now Alenia Aeronautica) of Italy. Its primary products are the ATR 42 and ATR 72 aircraft. Alenia Aeronautica's manufacturing facilities in Pomigliano d'Arco, near Naples, Italy produce the aircraft fuselage and tail sections.Aircraft wings are assembled at EADS Sogerma in Bordeaux in western France for Airbus France. Final assembly, flight-testing, certification and deliveries are the responsibility of ATR in Toulouse, France. [13]
Maximum fuel capacity is 6,370ltr
(iv) EMB
The Embraer EMB 202 Ipanema is an agricultural aircraft used for aerial application, particullary crop dusting. It is produced by Indústria Aeronáutica Neiva, a subsidiary of Embraer located in the Brazilian city of Botucatu. The latest version of this aircraft is the first ethanol-powered fixed-wing aircraft, which could give it an economical advantage over the gasoline version. The aircraft is widely employed in Brazil, having market share of about 80%, and the 1,000th delivery was completed on March 15, 2005. Besides aircraft, alcohol-conversion kits for gasoline-powered Ipanemas are also sold. It's common to think that the Ipanema name comes from the Rio de Janeir beach, but it actually comes from a farm with the same name, where it was first tested. [15]

Specifications (EMB-202A)

General characteristics

• Crew: One pilot • Capacity: 950 kg (2,094) lb of chemicals • Length: 7.43 m (24.37 ft) • Wingspan: 11.69 m (38.45) • Height: 2.22 m (7.28 ft) • Loaded weight: 1,800 kg (3,968 lb) • Powerplant: 1× modified Lycoming IO-540-K1J5, Hartzell constant speed propeller, 320 hp (240 kW)

Performance

• Cruise speed: 222 km/h (138 mph) • Stall speed: 88 km/h (55 mph) • Range: 610 km (379 mi) • Usable fuel capacity: 264 lt of ethanol fuel (70 US gal.) • Fuel consumption: 98 lt/h (26 US gal.) • Take-off distance: 354 m (1,161 ft) • Landing distance: 170 m (558 ft)

CHAPTER 5
APPROACH TO PROBLEM SOLUTION
Integer programming studies linear programs in which some or all variables are constrained to take on integer values. If in linear programming, the unknown variables are all required to be integers, then the problem is called an integer programming (IP) or integer linear programming (ILP) problem.

Billionnet’s mathematical model is an integer programming model used for scheduling of hierarchical workforce. The objective of this model is to determine an optimal hierarchical workforce in which a higher qualified worker can substitute for a lower qualified one, but not vice versa. Daily labour requirements within a week may vary, but each worker must receive n of days in the week. [1]

Minimize Z=[pic]kwk
Subject to
[pic]klj + ykj = wk
[pic]kj >= wkn
[pic]klj = dlj
Xklj, ykj, wk integer (k=1….m, l=k….m, j=1…..7)

Goal programming is a branch of multiobjective optimization, which in turn is a branch of multi-criteria decision analysis (MCDA), also known as multiple-criteria decision making (MCDM).
In the context of manpower planning, goal programming (GP) is extremely useful for generating shift duties of fixed length. A fixed-length duty consists of a fixed number of contiguous hours of work in a day, with a meal/rest break somewhere preferably around the middle of these working hours. It is such properties that enable the straightforward, yet flexible GP modeling. The problem is solved in three steps. First the duties are generated and then crew scheduling is done. This gives the start time of work and number of workers required per each hour. Then the crew roster is prepared. In this model duties generation phase is solved using goal programming[2]

[pic]
FIGURE 5.1 : STAGES IN THE MODEL
5.1 ALTERNATIVES
The method of solution is Integer programming, more precisely Binary Integer programming. In scheduling, a worker (or an officer) either works in a particular period or time slot or he does not work. ie the variable can have only two values, either 1 or 0. Thus this problem becomes a case of Binary Integer programming.

5.1.1 alternative 1
Hourly basis
In the hourly basis, scheduling is done based on the hourly demand. The hourly demand is obtained from the demand generation programme (DGP). The input of DGP is the hourly flight schedule. The demand for each hour is calculated and given as output. Scheduling is done based on this hourly demand.

5.1.1 alternative 2
Shift basis
In the shift basis, workers are allocated or scheduled on the basis of demand for a shift. The demand for each shift is obtained from the DGP by inputting the flight schedule for that shift. The input of DGP is the shift flight schedule. The demand for each hour is calculated and the maximum hourly demand in a shift is the demand for that shift. The shift demand is output. Scheduling is done based on this shift demand.

Shift work is an employment practice designed to make use of the 24 hours of the clock, rather than a standard working day. The work shift, is the time period during which a person is at work. A day may be divided into three shifts each of eight hours, and an employee works just one of those shifts; they might for example be 06:00 to 14:00, 14:00 to 22:00, 22:00 to 06:00 (times are given in the 24-hour clock). Generally, "first shift" refers to the day shift, with "second shift" running from late afternoon to nightfall, and "third shift" being the night shift. On occasion, more complex schedules are used, perhaps involving employees changing shifts, in order to operate during weekends as well, in which case there will be four or more sets of employees. The swing shift, also known as "second shift", is an employment schedule during the afternoon and evening, such as 4 p.m. to midnight or 2 p.m. to 10 p.m. This swing shift is the least desirable of all three possibilities. As a matter of fact, graveyard is preferred twice as much as swing. The graveyard shift means a shift of work running through the early hours of the morning, especially one from 10 pm until 6 am. [14]

5.2 Selection of the Solution alternative
As there are practical difficulties in scheduling on hourly basis, the preferred alternative is that based on shift basis. Thus the model developed is based on Binary Integer programming on shift basis.

CHAPTER 6
SOLUTION IMPLEMENTATION
6.1 MODEL DEVELOPMENT

6.1.1 Model for Blue Collar Workers’ shifts
i) Shift Basis
VARIABLES:

i shift 1-21 j worker 1-9 x(i,j) binary variable 0,1 = 1, if worker j works on ith shift = 0, if worker j does not work on i th shift
Dj demand for ith shift
Mwj Max. working shifts for jth worker

Objective FUNCTION:
Min z = [pic]
Constraints:
1. Demand constraint [pic]≥ Dj [pic] For each shift the number of workers allotted should be greater than or equal to the demand of workers for that shift

2. Max working hours constraint

[pic]≤ Mwj [pic] Each worker can work only upto a particular number of shifts per week,

3. No continuous working for more than 2 shifts [pic] [pic] No worker can work more than 2 shifts continuously per day.
4. Leave Constraint
[pic] [pic] , where k = (j mod 7) + 1 Each worker is given 1 day leave every week.

ii) Hourly Basis
VARIABLES:
i hour 1-168 j worker 1-9 x(i,j) binary variable 0,1 = 1, if worker j works on ith hour = 0, if worker j does not work on i th hour
Dj demand for ith hour
Mwj Max. working hours for jth worker
OBJECTIVE
Min [pic]

CONSTRAINTS
1. Demand constraint [pic] ≥ Di [pic] For each hour the number of workers allotted should be greater than or equal to the demand of workers for that hour.

2. Max working hours constraint
[pic] ≤ Mwj [pic]
Each worker can work only upto a particular number of hours per week.

3. No continuous working for more than 2 shifts [pic] [pic] k= 0,1,2,3,4,5,6
No worker can work more than 2 shifts (16 hours) continuously per day.

4. Leave Constraint
[pic][pic] where l= (j mod 7 ) +1
Each worker is given 1 day leave every week.
5. If x(i,j) = 0, and i mod 8 ≠ 1 x (i+1,j) = 0[pic]
A worker can start working only at starting hour of each 8 hour shift.
6. If x(i,j) = 0 and x(i+1,j) = 1 [pic]
Each worker works continuously for minimum 8 hours after he starts work

6.1.2 MODEL FOR OFFICERS’ SHIFTS
VARIABLES
i shift 1 - 21 a authorized officer 1 - 3 u unauthorized officer 1 - 2 x (i,a) binary variable 0,1 = 1, if authorized officer ‘a’ works on ith shift = 0, if authorized officer ‘a’ does not work on ith shift y (i,u) binary variable 0,1 = 1, if unauthorized officer ‘u’ works on ith shift = 0, if unauthorized officer ‘u’ does not work on ith shift
Daj demand for authorized officers on ith shift
Dtj total demand for officers on ith shift
Mwa , Mwu maximum working shifts / week for authorized and unauthorized officers respectively

OBJECTIVE FUNCTION
Min z = [pic]
CONSTRAINTS
1. Demand constraints for authorized officers.
[pic] Dai [pic] The number of authorized workers allotted per shift should be greater than or equal to demand for that shift.

2. Demand Constraints for total number of officers
[pic] Dti [pic] The sum of authorized and unauthorized workers allotted per shift should be equal to or greater than the demand for that shift.

3. Continous working hours constraint. [pic] [pic] No authorized worker should work continuously for more than 2 shifts. [pic] i=1- 19, [pic] No unauthorized worker should work continuously for more than 2 shifts.

4. Leave constraint [pic] [pic] For authorized officers. [pic] For unauthorized officers.

6.2 TOOLS USED FOR IMPLEMENTATION
6.2.1 CPP
C++ is a general-purpose programming language. C++ is regarded as a mid-level language, as it comprises a combination of both high-level and low-level language features.[1] It is a statically typed, free-form, multi-paradigm, usually compiled language supporting procedural programming, data abstraction, object-oriented programming, and generic programming.

Bjarne Stroustrup developed C++ in 1979 at Bell Labs as an enhancement to the C programming language and named it "C with Classes". In 1983 it was renamed to C++. Enhancements started with the addition of classes, followed by, among other features, virtual functions, operator overloading, multiple inheritance, templates, and exception handling. The C++ programming language standard was ratified in 1998 as ISO/IEC 14882:1998, the current version of which is the 2003 version, ISO/IEC 14882:2003. A new version of the standard (known informally as C++0x) is being developed.
In The Design and Evolution of C++ (1994), Bjarne Stroustrup describes some rules that he uses for the design of C++: • C++ is designed to be a statically typed, general-purpose language that is as efficient and portable as C • C++ is designed to directly and comprehensively support multiple programming styles (procedural programming, data abstraction, object-oriented programming, and generic programming) • C++ is designed to give the programmer choice, even if this makes it possible for the programmer to choose incorrectly • C++ is designed to be as compatible with C as possible, therefore providing a smooth transition from C • C++ avoids features that are platform specific or not general purpose • C++ does not incur overhead for features that are not used (the "zero-overhead principle") • C++ is designed to function without a sophisticated programming environment

6.2.2 MS EXCEL
Microsoft Excel (full name Microsoft Office Excel) is a spreadsheet application written and distributed by Microsoft for Microsoft Windows and Mac OS X. It features calculation, graphing tools, pivot tables and, except for Excel 2008 for Mac OS X, a macro programming language called VBA (Visual Basic for Applications). It is overwhelmingly the dominant spreadsheet application available for these platforms and has been so since version 5 in 1993 and is bundled as part of Microsoft Office. Excel is one of the most popular microcomputer applications to date.

Export and migration of spreadsheets

APIs are also provided to open excel spreadsheets in a variety of other applications and environments other than Microsoft Excel. These include opening excel documents on the web using either ActiveX controls, or plugins like the Adobe Flash Player. Attempts have also been made to be able to copy excel spreadsheets to web applications using comma-separated values.

A valuable aspect of Excel is the ability to write code using the programming language Visual Basic for Applications (VBA). This code is written using an editor viewed separately from the spreadsheet. Manipulation of the spreadsheet entries is controlled using objects. With this code any function or subroutine that can be set up in a Basic- or Fortran-like language can be run using input taken from the spreadsheet proper, and the results of the code are instantaneously written to the spreadsheet or displayed on charts (graphs). The spreadsheet becomes an interface or window to the code, enabling easy interaction with the code and what it calculates.

6.2.3 LINGO
LINGO is a simple tool for utilizing the power of linear and nonlinear optimization to formulate large problems concisely, solve them, and analyze the solution. Optimization helps you find the answer that yields the best result; attains the highest profit, output, or happiness; or achieves the lowest cost, waste, or discomfort. Often these problems involve making the most efficient use of your resources— including money, time, machinery, staff, inventory, and more. Optimization problems are often classified as linear or nonlinear, depending on whether the relationships in the problem are linear with respect to the variables.

In general, an optimization model will consist of the following three items: • Objective Function - The objective function is a formula that expresses exactly what it is you want to optimize. In business oriented models, this will usually be a profit function you wish to maximize, or a cost function you want to minimize. Models may have, at most, one objective function.

• Variables - Variables are the quantities you have under your control. You must decide what the best values of the variables are. For this reason, variables are sometimes also called decision variables. The goal of optimization is to find the values of a model’s variables that generate the best value for the objective function, subject to any limiting conditions placed on the variables.

• Constraints - Almost without exception, there will be some limit on the values the variables in a model can assume—at least one resource will be limited (e.g., time, raw materials, your department’s budget, etc.). These limits are expressed in terms of formulas that are a function of the model’s variables. These formulas are referred to as constraints because they constrain the values the variables can take.

LINGO is a comprehensive tool designed to make building and solving mathematical optimization models easier and more efficient. LINGO provides a completely integrated package that includes a powerful language for expressing optimization models, a full-featured environment for building and editing problems, and a set of fast built-in solvers capable of efficiently solving most classes of optimization models.

(i) Interfacing With Spreadsheets

|As we have mentioned, it can be cumbersome and impractical to try to maintain your data in a LINGO model file. This is particularly true|
|if you have more than just a small handful of data—as is the case with most practical models. Spreadsheets are adept at handling small |
|to moderate amounts of data. Spreadsheets are also very useful tools for manipulating and presenting the results generated by your |
|model. For these reasons, LINGO has a number of features that allow the user to import data from spreadsheets and export solutions back |
|out to spreadsheets. These features include real-time Object Linking and Embedding (OLE) links to Excel, OLE automation links that can |
|be used to drive LINGO from Excel macros, and embedded OLE links that allow you to import the functionality of LINGO into Excel. At |
|present, all of these features are supported only under Windows versions of LINGO. |
| |
| |
| |
|(ii) Embedding LINGO Models in Excel |

|LINGO is capable of functioning as an OLE server. This means you can embed a LINGO model in any application that can function as an OLE |
|container. Excel is one such application. Embedding a LINGO model into Excel is convenient in that the LINGO model is always immediately|
|available once the spreadsheet is opened. You don't have to worry about also starting LINGO and finding the correct LINGO model that |
|corresponds to the spreadsheet. |
| |
|To embed a LINGO document in an Excel file, select the Excel command Insert|Object. You will be presented with a list of embeddable |
|objects available on your system. Select the LINGO Document object from this list. |

Click the OK button and a blank LINGO model window will be embedded within the spreadsheet. You can enter text directly into this window just as you would in LINGO, or you can paste it in from another application. When you save the Excel sheet, the embedded LINGO model will automatically be saved with it. Similarly, whenever you read the sheet back into Excel, the embedded LINGO model will be restored, as well.The spreadsheet will contain the data for the model, and it will also contain an embedded LINGO model to perform the optimization and install the solution back into the spreadsheet.

The version used in this project work is demo version, having the following limitations:

Constraints 150

Variables 300

Integer Variables 30

Nonlinear Formulas 30

Global Variables 5

6.2.4 GAMS

The General Algebraic Modeling System (GAMS) is a high-level modeling system for mathematical programming problems.The General Algebraic Modeling System (GAMS) is specifically designed for modeling linear, nonlinear and mixed integer optimization problems. The system is especially useful with large, complex problems. GAMS is available for use on personal computers, workstations, mainframes and supercomputers. GAMS allows the user to concentrate on the modeling problem by making the setup simple. The system takes care of the time-consuming details of the specific machine and system software implementation.

GAMS is especially useful for handling large, complex, one-of-a-kind problems which may require many revisions to establish an accurate model. The system models problems in a highly compact and natural way. The user can change the formulation quickly and easily, can change from one solver to another, and can even convert from linear to nonlinear with little trouble.

GAMS is designed to
• Provide an algebraically based high-level language for the compacrepresentation of large . and complex models
|• |Allow changes to be made in model specifications simply and safely |

|• |Allow unambiguous statements of algebraic relationships |
|• |Provide an environment where model development is facilitated by subscript based expandability allowing the modeler to begin |
| |with a small data set, then after verifying correctness expand to a much broader context. |

|• |Be inherently self documenting allowing use of longer variable, equation and index names as well as comments, data definitions |
| |etc. GAMS is designed so that model structure, assumptions, and any calculation procedures used in the report writing are |
| |documented as a byproduct of the modeling exercise in a self-contained file. |
|• |Be an open system facilitating interface to the newest and best solvers while being solver independent allowing different |
| |solvers to be used on any given problem |

|• |Automate the modeling process including |
|? |permitting data calculation; |

|? |verifying the correctness of the algebraic model statements; |
|? |checking the formulation for obvious flaws; |

|? |interfacing with a solver; |
|? |saving and submitting an advanced basis when doing related solutions; |

|? |permitting usage of the solution for report writing. |
|• |Permitting portability of a model formulation between computer systems allowing usage on a variety of computers ranging from |
| |PCs to workstations to super computers. |

|• |Switching solvers is also very simple requiring changing a solver option statement or changing from using LP to using NLP. |
|• |Facilitating import and export of data to and from other computer packages |

|• |Allow use by groups of varying expertise |
|• |Provide a example models that may assist modelers through provision of a model library. |
| | |

GAMS permits one to express a formulation in general algebraic terms using symbolic summation notation. This allows modelers to concisely state problems, largely independent of the data and exact application context. Such formulations are inherently expandable, easily subjected to context changes, and easily augmented as will be discussed just below. However, use of algebraic modeling can be a two edged sword. GAMS algebraic requirements and summation notation are difficult for some users. Some people will always desire to deal with the exact problem context, not an abstract general formulation. This does lead to a strategy most modelers use when employing GAMS modeling. Namely, GAMS exercises are usually supported by small hand formulations that capture problem essence and serve as an aid in GAMS model formulation.
The version used in this project work is demo version, having the following limitations: Model limits: o Number of constraints and variables: 300 o Number of nonzero elements: 2000 (of which 1000 nonlinear) o Number of discrete variables: 50 Global solver limits: o Number of constraints and variables: 10

6.3 PROGRAM CODES
6.3.1 DEMAND GENERATION PROGRAM
The demand of blue collar workers for each shift is generated by a CPP program. The flight schedule for each day is entered. The demand of each shift is obtained as the output of the demand generation program.
#include
#include
#include
#include void main()
{
clrscr(); int hr[7][50],min[7][50],d[7][24],i,k,h,n[7],shift[21],hour[168]; for(h=0;h