BAÜ FBE Dergisi Cilt:9, Sayı:2, 48-62 Aralık 2007
Tanker scheduling by using optimization techniques and a case study Aslan Deniz KARAOĞLAN*
Abstract
Balıkesir University, Engineering and Architectural Faculty, Department of Industrial Engineering, Cagis Campus, 10145, Balikesir, Turkey
This study aims to guide companies and researchers who needs to schedule and optimize their transportation systems which are based on shipping. In this study, the problem, that is tried to solve, is providing profit maximization in transporting the different characterized cargoes to determined ports by the ship fleets which contain different kind of ships. In the first part of the study, planning and scheduling in the transportation industry is introduced and in the second part, materials and techniques to perform the scheduling, which are used by the companies that own and operate tanker or cargo ship fleets, are given. At the third part of the study the constructed scheduling model and the solution of the schedule which is computed by optimization software is given and at the following part, the concluVion is presented. The results have shown that, the presented model that is refered from the literature, can be applied successfully in real word and gives nearly optimal solutions. The case study is performed in shipping company which is established in Istanbul. Keywords: Tanker scheduling, optimization.
Optimizasyon tekniklerini kullanarak tanker çizelgeleme ve bir uygulama
Özet
Bu çalışma, gemicilik üzerine kurulu taşıma sistemlerini çizelgelemek ve optimize etmek isteyen firmalara ve araştırmacılara rehberlik etmeyi amaçlamaktadır. Problem bir çok farklı özelliğe sahip gemilerden oluşan bir filo ile farklı özelliklere sahip kargoların belirli limanlara taşınmasında kar maksimizasyonunun sağlanmasıdır. Bunun sağlanması için tanker çizelgeleme problemleri için literatürdeki modellerden faydalanılarak taşıma problemi modellenmiş ve çözüm sonucuna yer verilmiştir. Çalışmanın ilk bölümünde, taşımacılık endüstrisinde planlama ve çizelgeleme tanıtılmış ve ikinci bölümde tanker veya kargo gemi filosu işleten firmaların çizelgelemede kullandığı materyaller ve teknikler verilmiştir. Çalışmanın üçüncü bölümünde oluşturulan çizelgeleme modeli ve bir paket programla hesaplanan çözümü verilmiş ve sonraki bölümde de sonuçlar sunulmuştur. Sonuçlar incelendiğinde, literatürden alınan modelin gerçek hayata başarı ile uygulanabildiği ve elde edilen sonuçların optimale yakın olduğu görülmüştür. Çalışmanın uygulama bölümü Đstanbul’ da faaliyet gösteren bir denizcilik şirketinde gerçekleştirilmiştir. Anahtar Kelimeler: Tanker çizelgeleme, optimizasyon. *
Aslan Deniz KARAOĞLAN,
[email protected]
48
Tanker scheduling by using optimization techniques and a case study
1. Introduction The planning and scheduling models in services and the solution methodologies used tend to be different from those applied in manufacturing environments. This talk goes into four classes of models. The first class includes interval scheduling models and reservation systems. The second class involves timetabling and tournament scheduling. The third class consists of transportation models (tanker scheduling, aircraft routing and scheduling and train timetabling). The fourth and last class are the workforce scheduling models [1]. In the transportation industry planning and scheduling problems abound. The variety in the problem is due to the many modes of transportation, e.g., shipping, airlines and railroads. Each mode of transportation has its own set of characteristics. The equipment and resources involved, i.e., (i) (ii) (iii)
ships and ports, planes and airports, trains, tracks, and railway stations,
have different cost characteristics, different levels of flexibilities and different planning horizons [2]. Ship scheduling models optimize the transportation of commodities, so they are vital to world trade and millitary logistics. A ship requires a multi-million dolar capital investment and the daily operation costs of a ship can be tens of thousand dollars. Consequently, improved fleet utilization can yield significant financial benefit [3]. Scheduling tankers presents many interesting and varied problems. Among these problems are, how to determine a program of delivery dates at the respected ports and how to route the tankers in fleet [4]. There are few studies about tanker scheduling in the literature. Fagerholt [5] studied the problem of evaluating the trade-off between the level of customer service and transportation costs. An evaluation is performed on the background of data from a real ship scheduling problem, where each cargo has time windows on both the loading and the discharging. Cho and Perakis [6] presented an improved, significantly more efficient formulation of an existing model for bulk cargo or semi-bulk cargo ship scheduling problems with a single loading port. The original model, published by Ronen in 1986, was formulated as a nonlinear, mixed integer program. In this work, the authors were able to re-formulate it into a linear one, by eliminating all the non-linearities of the original model. In addition, this model has far fewer integer variables than the original one. Hwang and Rosenberger [7] presented a set-packing model that limits risk using a quadratic variance constraint. After generating first-order linear constraints to represent the variance constraint, the authors developed a branch-and-price-and-cut algorithm for medium-sized ship-scheduling problems. Sambracos et al. [8] investigated the introduction of small containers, an important new technology, in an effort to reengineer coastal freight shipping in the Aegean Sea in Greece. 49
A. D. Karaoğlan
Infrastructure problems of island ports are documented and the advantages of introducing small containers are discussed. Fagerholt [9] considered a real liner shipping problem of deciding optimal weekly routes for a given fleet of ships and proposed a solution method for solving the problem. Sherali et al. [10] explored models and algorithms for routing and scheduling ships in a maritime transportation system. The authors have constructed a mixed integer programming model for the problems of Kuwait Petroleum Corporation (KPC). Giziakis et al. [11] modeled the operation of passenger vessels as a linear programming (LP) problem on a network of 37 nodes in the Aegean Sea. In this study, the problem, that is tried to solve, is providing profit maximization in transporting the different characterized cargoes to determined ports by the ship fleets which contain different kind of ships. The company owns four ships and the ships are located in different ports. There are also six cargoes, which have to be transported to different ports. Each ship, that the company owned, has different characteristics and these differences influence the transportation problem of the company. Because all the ships can not transport all the cargoes, and also they can not enter to all ports because of their dimensions. Also the profits that are provided may not be attractive for all alternative schedules. To optimize the transportation problem of the company, the schedules are constructed by considering the characteristics of ships, cargoes and ports, and than the costs of each schedule is calculated. The model that is developed for tanker scheduling in the literature and optimization package program are used to calculate the optimal solution for the company.
2. Materials and methods A cargo is the entire content of a ship transported between two ports, and a schedule is a sequence of cargoes delivered by the same ship. Ship scheduling problems are solved by generating a set of feasible delivery schedules for each ship and optimizing a set packing problem [3]. Companies that own and operate tanker fleets typically make a distinction between two types of ships. One type of ship is company owned and the other type of ship is chartered. The operating cost of a company owned ship is different from the cost of a charter that is typically determined on the spot market. Each ship has a specific capacity, a given draught, a range of possible speeds and fuel consumptions and a given location and time at which the ship is ready to start a new trip [2]. Each port also has its own characteristics. Port restrictions take the form of limits on the deathweight, draught, lenght, beam and other physical characteristics of the ship. There may be some additional goverment rules in effect; for example, the Nigerian goverment imposes a so-called 90% rule which states that all tankers must be loaded to more than 90% of capacity before sailing [2]. A cargo that has to be transported is characterized by its type, quantity, load port, delivery port, time window constraints on the load and delivery times, and the load and unload 50
Tanker scheduling by using optimization techniques and a case study
times. A schedule for a ship defines a complete itinerary, listing in sequence the ports visited within the time horizon, the time of entry at each port and the cargoes loaded or delivered at each port [2]. The objective typically is to minimize the total cost of transporting all cargoes. This total cost consists of a number of elements, namely the operating costs for the company-owned ships, the spot charter rates, the fuel costs and the port charges. Port charges vary greatly between ports and within a given port charges typically vary proportionally with the deadweight of the ship [2]. In order to present a formal description of the problem the following notation is used. Let n denote the number of cargoes to be transported and T the number of company-owned tankers. Let Si denote the set of all possible schedules for ship i. Schedule l for ship i, l ∈ Si, is represented by the column vector [ali1,ali2,…,alin]. The constant alij is 1 if under schedule l, ship i transports cargo j and 0 otherwise. The decision variable xli is 1 if ship i follows schedule l and zero otherwise. The tanker scheduling problem can now be formulated as follows [2]: Maximize
T
∑ ∑ i =1
Subject to T
∑ ∑ i =1
l
∏
i
xl i
(Objective function)
j=1,….,n
(First set of constraints)
i=1,…..,T
(Second set of constraints)
l∈
Si
alij xli ≤ 1
l∈
Si
∑
xli ≤ 1
l∈
Si
xli ∈ {0,1}
l ∈ S i,
i=1,……,T (Remaining constraints)
The objective function specifies that the total profit has to be maximized. The first set of constraints imply that each cargo can be assigned to at most one tanker. The second set of constraints specifies that each tanker can be assigned at most one schedule. The remaining constraints imply that decision variables have to be binary 0-1. This optimization problem is typically referred a set-packing problem [2]. The algorithm used to solve this problem is a branch and bound procedure. However, before the branch and bound procedure is applied, a collection of candidate schedules have to be generated for each ship in the fleet. As stated before, such a schedule specifies an itinerary for a ship, listing the ports visited and the cargoes loaded or delivered at each port. The generation of an each collection of candidate schedules has to be done by a seperate ad-hoc heuristic that is especially designed for this purpose. The collection of candidate schedules should include enough schedules so that potentially optimal schedules are not ignored, but not so many that the set packing problem becomes intractable. Physical constraints such as ship capacity and speed, port depth and time windows limit the number of feasible candidate schedules considerably. Schedules that have a negative profit coefficient in the objective function of the set packing formulation can be omitted as well [2]. The case study has been performed in a shipping company which is located in Istanbul. The data is collected by e-mail, phone and other instrumental documents downloaded from 51
A. D. Karaoğlan
related websites . The tables which are composed from these collected data, are given below and after the presentation of these tables the LP model is composed [5, 6]. There are some assumptions in the tables given below such as the ships/tankers are ready to a new trip. And an another assumption is that the ships don’t delay during the navigation between two ports, so there is no extra cost for delays. Also, the fuel consumptions for the ships according to their deadweights and the navigation distances are assumed fixed values as given in Table 8. It is important to take notice that we consider the characteristics of ships, ports and cargoes that are given in Table 1 through Table 3, while constructing the schedules which are given in Table 4. Also these four tables and Table 8 are used to construct Table 5 by the contribution of the references [12] and [13]. In Table 1 the general characteristics of the four ships, that the company owned, is given. This data are used in matching the cargoes with the ships. For example, if Table 1 browsed, it is seen that Akıncı is a dry cargo ship. So Ammonium Nitrate, which is labeled as Cargo1 in Table 2, can not be transported by this ship. Akıncı is anchored at Ambarlı port according to Table 1. Its possible cargoes can be Cargo2, Cargo3 and Cargo6 according to Table 3. When the characteristics of ports like as “limits on the dead weight”, “draught” and etc. is matched with the characteristics of the ship Atmaca like as “draught”, “beam” and etc, it is seen that the mentioned ship called Atmaca, can perform loading and unloading cargoes (Cargo2, Cargo3, Cargo6) that are located at or will be transported to the ports called Ambarlı, Bandırma, Haydarpasa, Gemlik, Izmir. The possible schedules, that are given in Table 4 are determined similarly as performed in the ship Atmaca example. After determining the possible schedules, the cost of each schedule is calculated in Table 5 and then the profits are calculated in Table 7 by using the values that are given in Table 5 and Table 6. While calculating the costs of each schedule in Table 5, the costs of the cost items for loading and unloading ports are calculated by the contribution of the references [12] and [13], which are mentioned above.
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Table 1. Data related to the ships/tankers SHIP NAME OF NO THE SHIP / TANKER
CAPACITY DRAUGHT RANGE FUEL OF THE (MT) OF CONSUMTIONS SHIP / POSSIBLE TANKER SPEEDS
ATMACA 1 6200000 4.82 DWT (9641 kg)
11-12 kts
6 M/T FO & 1 M/T DO
SAMSUN
2
ATMACA 2 20000 Tone
16.6
18-30 kts
10 M/T FO & 1 M/T DO
BANDIRMA
READY
3
TRITON
11
READY
AKINCI
15M/T FO & 1 M/T DO 8 M/T FO & 1 M/T DO
GEMLIK
4
16-25 kts 14-20 kts
AMBARLI
READY
9
NOTE
ABLE TO CARRY LIQUID AND FREIGHT CONTAINER ONLY ABLE TO CARRY HOUSEHOLD FUEL DRY CARGO SHIP DRY CARGO SHIP
HIRING COST (IF THE SHIP / TANKER IS HIRED) -
DEATH WEIGHT (GROSS TONE) (GT) 3500
THE LENGHT OF THE SHIP / TANKER (MT) 80
16.2
-
9200
150
30.3
-
8500
110
22.4
-
7100
100
20.1
Table 2. Data related to the ports PORT NAME OF THE NO PORT 1 2 3
AMBARLI SAMSUN IZMIT
LIMITS ON THE DEADWEIGHT (GT) N/A 9500 9000
DRAUGHT LENGHT (MT) CONSTRAINT FOR THE SHIPS/TANKERS 14 N/A 18 150 m 25 N/A
4
GEMLIK
9000
17
N/A
5 6 7 8 9
HAYDARPASA MERSIN ISKENDERUN BANDIRMA IZMIR
8600 N/A N/A N/A N/A
13 18 23 22 25
120 m N/A N/A N/A N/A
BEAM COMPANY LAWS IF EXISTS N/A N/A N/A N/A N/A 2 tugboat must be hired N/A 2 tugboat must be hired N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A
TIME NEEDED TO ENTER THE PORT FOR THE SHIPS/TANKERS ~ 45 Min 6 Hours Canal + 45 Min to Dock 5 Hours Canal + 45 Min to Dock
NOTE
5 Hours Canal + 45 Min to Dock
-
60 Min 30 Min 30 Min 30 Min 30 Min
-
-
BEAM (MT)
Tanker scheduling by using optimization techniques and a case study
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1
TIME AT WHICH THE SHIP IS READY TO START A NEW TRIP READY
20000 Tone 15000 Tone
GIVEN LOCATION
Table 3. Data related to the cargoes CARGO TYPE OF QUANTITY LOAD NO THE CARGO PORT 1 AMMONIUM 6000000 SAMSUN NITRATE dwt (9330 kg)
DELIVERY PORT MERSIN
LOAD DELIVERY LOADING UNLOADING NOTE DATE TIME TIME TIME 11.01.2007 96 HOURS 48 HOURS 96 HOURS -
2
LIVE STOCK 5000 Unit =1900 Tone
AMBARLI
BANDIRMA
12.01.2007 12 HOURS
3
1000 Tone
4
BULK FREIGHT (Solid) OIL
5 6
-
BANDIRMA HAYDARPASA 13.01.2007 13 HOURS
24 HOURS
-
10000 Tone
IZMIR
ISKENDERUN
12.01.2007 96 HOURS
48 HOURS 40 HOURS
-
OIL
8000 Tone
IZMIR
ISKENDERUN
12.01.2007 96 HOURS
36 HOURS 30 HOURS
-
BULK FREIGHT (Solid)
500 Tone
GEMLIK
IZMIT
12.01.2007 8 HOURS
24 HOURS 20 HOURS
A. D. Karaoğlan
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10 HOURS 12 HOURS
Table 4. Schedules
X X
X
X X
X
X
X
X
4. SCHEDULE
1. SCHEDULE
SHIP NO:4 4. SCHEDULE
3. SCHEDULE
2. SCHEDULE
1. SCHEDULE
4. SCHEDULE
3. SCHEDULE
2. SCHEDULE
4. SCHEDULE
3. SCHEDULE
1. SCHEDULE
X
X
SHIP NO:3
3. SCHEDULE
X
2. SCHEDULE
TYPE OF CARGO AMMONIUM NITRATE LIVESTOCK BULK FREIGHT (Solid) OIL OIL BULK FREIGHT (Solid)
SHIP NO:2
2. SCHEDULE
CARGO1 CARGO2 CARGO3 CARGO4 CARGO5 CARGO6
SHIP NO:1 1. SCHEDULE
SCHEDULES
X
Table 5. Costs SHIP NAME OF THE NO SHIP/TANKER 1
COSTS ACCORDING TO THE 1. SCHEDULE ($)
COSTS ACCORDING TO THE 2. SCHEDULE ($)
COSTS ACCORDING TO THE 4. SCHEDULE ($)
Tanker scheduling by using optimization techniques and a case study
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ATMACA 1 (4500 GT) FUEL COSTS=SAMSUN-MERSIN FUEL COSTS= SAMSUN-AMBARLI=3000 BANDIRMA= 1500 + 500 LOCATION= LOADING=(SAMSUN) LOADING =(AMBARLI ) (TARIFF OF SAMSUN (DANGEROUS CONTAINER)= 110 SAMSUN HOURBOUR) TERMINAL= 42 (LIVESTOCK)= 1.5 WAREHOUSING CHARGE (FIRST TERMINAL= 0 15 DAYS)= 3.6 WAREHOUSING CHARGE (FIRST 15 DAYS)= 0 CHARGES OF THE PORT WHICH CHARGES OF THE PORT WHICH THE THE LOADING IS PERFORMED= LOADING IS PERFORMED= (OTHER (OTHER CARGO VESSEL) CARGO VESSEL) - PILOTAGE= 350 - PILOTAGE= 350 - TUG BOAT= 303 - TUG BOAT= 303 - WARP= 65 - WARP= 65 - SHELTERING= 40 - SHELTERING= 40 - DUMPING OF WASTE - DUMPING OF WASTE (SOLID-LIQUID)(BY LAND)= (SOLID-LIQUID)(BY LAND)= 20+30 20+30 - FRESH WATER= (BY VALVE)= 5 - FRESH WATER= (BY VALVE)= 5 UNLOADING= (BANDIRMA) LIVESTOCK= 1.5 UNLOADING=(MERSIN) TERMINAL= 0 (DANGEROUS CONTAINER)= 114 WAREHOUSING CHARGE (FIRST 15 DAYS) = 0 TERMINAL= 42 CHARGES OF THE PORT WHICH THE WAREHOUSING CHARGE UNLOADING IS PERFORMED= (OTHER (FIRST 15 DAYS)= 4.8 CARGO VESSEL) - PILOTAGE= 350 CHARGES OF THE PORT WHICH - TUG BOAT= 303 THE UNLOADING IS PERFORMED= - WARP= 65 (OTHER CARGO VESSEL) - SHELTERING= 40 - PILOTAGE= 380 - DUMPING OF WASTE - TUG BOAT= 336 (SOLID-LIQUID)(FROM SEA BEING - WARP= 75 AT ANCHOR)= 20+30 - SHELTERING= 40 - FRESH WATER= (BY VALVE)= 5 - DUMPING OF WASTE
COSTS ACCORDING TO THE 3. SCHEDULE ($)
(SOLID-LIQUID)(FROM SEA GRATUITY TO PILOT= 1000 BEING AT ANCHOR)= 20+30 - FRESH WATER= (BY VALVE)= 6 GRATUITY TO PILOT= 1000
SHIP NAME OF THE NO SHIP/TANKER 2
TOTAL= $ 6016.4 COSTS ACCORDING TO THE 1. SCHEDULE ($)
TOTAL= $ 5647.5 COSTS ACCORDING TO THE 2. SCHEDULE ($)
COSTS ACCORDING TO THE 4. SCHEDULE ($)
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FUEL COSTS =BANDIRMA-SAMSUNMERSIN= 1700+ 4000 LOADING= ( SAMSUN ) (DANGEROUS CONTAINER)= 110 TERMINAL= 12 WAREHOUSING CHARGE (FIRST 15 DAYS)= 3.6 CHARGES OF THE PORT WHICH THE LOADING IS PERFORMED= (OTHER CARGO VESSEL) - PILOTAGE= 740 - TUG BOAT= 591 - WARP= 153 - SHELTERING= 100 - DUMPING OF WASTE (SOLID-LIQUID)(BY LAND)= 30+45 - FRESH WATER= (BY VALVE)= 5 UNLOADING=(MERSIN) DANGEROUS CONTAINER= 114 UNLOADING= (ISKENDERUN) TERMINAL= 42 WAREHOUSING CHARGE (FIRST 15 (BULK FREIGHT (LIQUID))= 0 DAYS)= 4.8 TERMINAL= 2 WAREHOUSING CHARGE CHARGES OF THE PORT WHICH THE UNLOADING IS PERFORMED= (OTHER (FIRST 15 DAYS)= 2 CARGO VESSEL) CHARGES OF THE PORT WHICH - PILOTAGE= 800 THE UNLOADING IS PERFORMED= - TUG BOAT= 654 (OTHER CARGO VESSEL) - WARP= 165 - PILOTAGE= 800 - SHELTERING= 100
ATMACA 2 (9200 GT) FUEL COSTS= BANDIRMA-IZMIRISKENDERUN= 700+4000 LOCATION= LOADING= (IZMIR ) BANDIRMA (BULK FREIGHT (LIQUID)) TERMINAL= 4 WAREHOUSING CHARGE (FIRST 15 DAYS)= 4.5 CHARGES OF THE PORT WHICH THE LOADING IS PERFORMED= (OTHER CARGO VESSEL) - PILOTAGE= 740 - TUG BOAT= 591 - WARP= 153 - SHELTERING= 100 - DUMPING OF WASTE (SOLID-LIQUID)(BY LAND)= 30+45 - FRESH WATER= (BY VALVE)= 5
COSTS ACCORDING TO THE 3. SCHEDULE ($)
3
- DUMPING OF WASTE (SOLID-LIQUID)(FROM SEA BEING AT ANCHOR)= 30+45 - FRESH WATER= (FROM SEA)= 6
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GRATUITY TO PILOT = 1000+1000+1000 TOTAL= $ 12450.4 FUEL COSTS =GEMLIK-BANDIRMAIZMIT-HAYDARPASA= 700+ 700 + 700 LOADING =( GEMLIK + BANDIRMA ) TARIFF OF BANDIRMA HOURBOUR (BULK FREIGHT (LIQUID))= 4 TERMINAL= 1.5 WAREHOUSING CHARGE (FIRST 15 DAYS)= 0.15 CHARGES OF THE PORT WHICH THE CHARGES OF THE PORT WHICH LOADING IS PERFORMED= (OTHER THE LOADING IS PERFORMED= CARGO VESSEL) (OTHER CARGO VESSEL) - PILOTAGE= 675 - PILOTAGE= 675 - TUG BOAT= 543 - TUGBOAT= 543 - WARP= 139 - WARP= 139 - SHELTERING= 90 - SHELTERING= 90 - DUMPING OF WASTE (SOLID- DUMPING OF WASTE LIQUID)(BY LAND)= 30+45 (SOLID-LIQUID)(BY LAND)= - FRESH WATER= (BY VALVE)= 5 30+45 TARIFF OF GEMLIK PORT= 6004 - FRESH WATER= (BY VALVE)= 5 UNLOADING= (IZMIT + HAYDARPAŞA) UNLOADING=(BANDIRMA) CHARGES FOR IZMIT HOURBOUR= 11363 (LIVESTOCK)= 1.5 CHARGES FOR HAYDARPASA TERMINAL= 0 HOURBOUR= WAREHOUSING CHARGE (FIRST 15 DAYS)= 0 (BULK FREIGHT(SOLID))= 4 CHARGES OF THE PORT WHICH TERMINAL= 1.5 THE UNLOADING IS PERFORMED= WAREHOUSING CHARGE (FIRST 15 (OTHER CARGO VESSEL) DAYS)= 3 - PILOTAGE= 675 CHARGES OF THE PORT WHICH THE - TUGBOAT= 543 UNLOADING IS PERFORMED= (OTHER - WARP= 139 CARGO VESSEL)
Tanker scheduling by using optimization techniques and a case study
- TUG BOAT= 654 - WARP= 165 - SHELTERING= 100 - DUMPING OF WASTE (SOLID-LIQUID)(BY LAND)= 30+45 - FRESH WATER= (FROM SEA)= 5 GRATUITY TO PILOT= 1000 TOTAL= $ 9275.5 TRITON (8500 GT) FUEL COSTS= GEMLIK-AMBARLIBANDIRMA= 700 + 700 LOCATION= LOADING= ( AMBARLI ) (TARIFF GEMLIK OF SAMSUN PORT) (LIVESTOCK)= 1.5 TERMINAL= 0 WAREHOUSING CHARGE (FIRST 15 DAYS)= 0
- SHELTERING= 90 - DUMPING OF WASTE (SOLID-LIQUID)(FROM SEA BEING AT ANCHOR)= 30+45 - FRESH WATER= (FROM SEA)= 5 TOTAL= $ 4457 SHIP NAME OF THE NO SHIP/TANKER 4
COSTS ACCORDING TO THE 1. SCHEDULE ($)
- PILOTAGE= 675 - TUG BOAT= 543 - WARP= 139 - SHELTERING= 90 - DUMPING OF WASTE (SOLID-LIQUID)(FROM SEA BEING AT ANCHOR)= 30+45 - FRESH WATER= (FROM SEA)= 5 TOTAL= $22535.15 COSTS ACCORDING TO THE 2. SCHEDULE ($)
COSTS ACCORDING TO THE 4. SCHEDULE ($)
FUEL COSTS= AMBARLIBANDIRMA-HAYDARPASA= 700+700 LOADING= ( BANDIRMA ) BULK FREIGHT(LIQUID)= 4 TERMINAL= 1.5 WAREHOUSING CHARGE (FIRST 15 DAYS)= 0.15
FUEL COSTS= AMBARLIGEMLIK-IZMIT= 700+700 LOADING=( GEMLIK ) (BULK FREIGHT (SOLID) CHARGES FOR GEMLIK PORT= 6004 UNLOADING= (IZMIT) BULK FREIGHT(SOLID) CHARGES FOR IZMIT PORT= 11363
CHARGES OF THE PORT WHICH THE LOADING IS PERFORMED= (OTHER CARGO VESSEL) - PILOTAGE= 610 - TUG BOAT= 495 - WARP= 125 - SHELTERING= 80 - DUMPING OF WASTE (SOLID-LIQUID)(BY LAND)= 30+45 - FRESH WATER= (BY VALVE)= 5 UNLOADING= (HAYDARPASA) (BULK FREIGHT (SOLID)= 4 TERMINAL= 1.5 WAREHOUSING CHARGE (FIRST 15 DAYS)= 0.15
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AKINCI (7100 GT) FUEL COSTS= AMBARLIFUEL COSTS =AMBARLI-GEMLIKLOCATION= BANDIRMA= 700 BANDIRMA- IZMITAMBARLI LOADING= (AMBARLI) (SAMSUN HAYDARPASA= PORT TARIFF) 700+700+700+700 (LIVESTOCK)= 1.5 LOADING= ( GEMLIK+BANDIRMA ) TERMINAL= 0 CHARGES FOR GEMLIK PORT= 6004 WAREHOUSING CHARGE (FIRST CHARGES FOR BANDIRMA PORT= 15 DAYS)= 0 (BULK FREIGHT (SOLID))= 4 TERMINAL= 1.5 CHARGES OF THE PORT WHICH WAREHOUSING CHARGE (FIRST 15 THE LOADING IS PERFORMED= DAYS)= 0.15 (OTHER CARGO VESSEL) CHARGES OF THE PORT WHICH THE - PILOTAGE= 610 LOADING IS PERFORMED= (OTHER - TUG BOAT= 495 CARGO VESSEL) - PILOTAGE= 610 - WARP= 125 - SHELTERING= 80 - TUG BOAT= 495 - DUMPING OF WASTE - WARP= 125 (SOLID-LIQUID)(BY LAND)= - SHELTERING= 80 30+45 - DUMPING OF WASTE - FRESH WATER= (BY VALVE)= 5 (SOLID-LIQUID)(BY LAND)= 30+45 UNLOADING= (BANDIRMA) - FRESH WATER= (BY VALVE)= 5 UNLOADING=(IZMIT+HAYDARPASA) LIVESTOCK= 1.5 TERMINAL= 0 CHARGES FOR IZMIT PORT= 11363 CHARGES FOR HAYDARPASA PORT= WAREHOUSING CHARGE (FIRST 15 DAYS)= 0 (BULK FREIGHT (SOLID))= 4 TERMINAL= 1.5 CHARGES OF THE PORT WHICH WAREHOUSING CHARGE (FIRST 15 THE UNLOADING IS PERFORMED=
COSTS ACCORDING TO THE 3. SCHEDULE ($)
CHARGES OF THE PORT WHICH THE UNLOADING IS PERFORMED= (OTHER CARGO VESSEL) - PILOTAGE= 610 - TUG BOAT= 495 - PLAMAR= 125 - SHELTERING= 80 - DUMPING OF WASTE (SOLID-LIQUID)(FROM SEA TOTAL= $ 18767 BEING AT ANCHOR)= 30+45 - FRESH WATER= (BYVALVE) = 10
TOTAL= $ 3483 TOTAL= $4196.3
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Table 6. Income SHIP NO NAME OF THE SHIP/TANKER INCOME ACCORDING TO THE 1. SCHEDULE($) 1 ATMACA 1 10000 2 ATMACA 2 10000 3 TRITON 6000 4 AKINCI 6000
INCOME ACCORDING TO THE 2. SCHEDULE($) 6000 12000 20000 20000
INCOME ACCORDING TO THE 3. SCHEDULE($) 10000
INCOME ACCORDING TO THE 4. SCHEDULE($) 20000
Table 7. Profit SHIP NO NAME OF THE SHIP/TANKER PROFIT ACCORDING TO THE 1. SCHEDULE($) 1 ATMACA 1 3983.6 2 ATMACA 2 724.5 3 TRITON 1543 4 AKINCI 2517
PROFIT ACCORDING TO THE 2. SCHEDULE($) 352.5 -450.4 -2535.15 -2963.3
PROFIT ACCORDING TO THE 3. SCHEDULE($) 5803.7
PROFIT ACCORDING TO THE 4. SCHEDULE($) 1233
Tanker scheduling by using optimization techniques and a case study
(OTHER CARGO VESSEL) DAYS)= 0.15 - PILOTAGE= 610 CHARGES OF THE PORT WHICH THE - TUGBOAT= 495 UNLOADING IS PERFORMED= (OTHER - WARP= 125 CARGO VESSEL) - SHELTERING= 80 - PILOTAGE= 610 - DUMPING OF WASTE - TUG BOAT= 495 (SOLID-LIQUID)(FROM SEA - WARP= 125 BEING AT ANCHOR)= 30+45 - SHELTERING= 80 - FRESH WATER= (BY VALVE)= 5 - DUMPING OF WASTE (SOLID-LIQUID)(FROM SEA BEING AT ANCHOR)= 30+45 - FRESH WATER= (BY VALVE)= 10 TOTAL= $ 22963.3
A. D. Karaoğlan
Distance
Table 8. Fuel consumption assumptions for the ships according to their deadweights Fuel Consumption($) DEADWEIGHT 0-5000 GT 10000-15000 500 1000 SHORT 1500 2000 MIDDLE 3000 5000 LONG
3. Results and discussion Xij= i. Ship/Tanker, j. Schedule (i=1,2,3,4) (j=1,2,3,4) Max P= 3983.6X11+352.5X12+724.5X21-450.4X22+1543X31-2535.15X32+2517X412963.3X42+5803.7X43+1233X44 s.t. X11+X22 ≤1 Constraint related to the 1. cargo X12+X31+X41 ≤1 Constraint related to the 2. cargo X32+X42+X43 ≤1 Constraint related to the 3. cargo X21 ≤1 Constraint related to the 4. cargo X21 ≤1 Constraint related to the 5. cargo X32+X42+X44 ≤1 Constraint related to the 6. cargo X11+X12 ≤1 X21+X22 ≤1 X31+X32 ≤1 X41+X42+X43+ X44 ≤1
Constraint related to the ship no:1 Constraint related to the ship no:2 Constraint related to the ship no:3 Constraint related to the ship no:4
Xij=0,1 (i=1,2,3,4) (j=1,2,3,4) The notation of model according to LINDO package programme which is used in computing the solutions and the solution report are given below: Max 983.6X11+352.5X12+724.5X21-450.4X22+1543X31-2535.15X32+2517X412963.3X42 +5803.7X43+1233X44 subject to X11+X22
