Abstract

Ocean transportation is the workhorse for logistics in global chemical supply chains. Often, logistics cost can be as high as 20% of the purchasing cost. Efficient routing and scheduling of multi-parcel chemical tankers to reduce logistics expenditure is important for both chemical and shipping industry. We consider the maximum-profit scheduling of a fleet of multi-parcel tankers engaged in shipping bulk liquid chemicals. For this, we present a mixed-integer linear programming (MILP) formulation using variable-length slots and propose a heuristic decomposition algorithm that obtains the fleet schedule by repeatedly solving the base formulation for a single ship. The formulation is generally applicable to all kinds of carriers engaged in the transportation of multiple commodities, and to transportation systems where frequent schedule updates or a short-term planning horizon is required. We illustrate our approach on a real industrial case study involving 10 tankers, 36 ports and 79 cargos. Our approach showed an increase of 32.7% in profit as compared to the plan actually used by a major chemical shipping company.

Author Keywords: Dynamic scheduling; Routing; Chemical shipping; Maritime transportation; Multi-commodity; Transshipment

Nomenclature

A_s

set of cargos that are permanently assigned to ship s

L_s

Set of cargos on-board ship s at time zero

U

set of new cargos that require service in the planning horizon

D_ii′

distance (Nautical miles) between ports i and i′

DP_j

discharge port for cargo j

DR_j

discharge rate (pump capacity) of cargo j (tonnes/day)

EPT_j

earliest time for pickup of cargo j

FC_s

cost of fuel per unit distance for ship s

K_s

number of sailing legs for ship s in the multi-ship formulation

LPT_j

latest time for pickup of cargo j

LR_j

loading rate (pump capacity) of cargo j (tonnes/day)

M

some large number

P

number of ports

PC_is

port cost for ship s at port i

PP_j

loading port for cargo j

SR_j

shipping rate or revenue for cargo j (US$)

T_adm

time for inspections, customs and surveys for each port visit

TCC_s

time-charter cost per unit time for ship s

v_s

sailing speed of ship s (nm/day)

V_j

volume of cargo j (tonnes)

VMAX_s

total carrying capacity of ship s in tonnes or volume or number of compartments

W_j

capacity of the tank compartment where cargo j is stowed (tonnes)

T_ks

time at which leg k ends and ship s arrives at a port

TT_ks

time required by ship s to travel during leg (k+1)

X_iks

1 if ship s arrives at port i at the end of leg k

XD_jks

1 if ship s unloads cargo j at the end of leg k

XP_jks

1 if ship s loads cargo j at the end of leg k

Y_jks

1 if ship s carries cargo j on-board during leg k

Y_js

1 if ship s serves cargo j

Z_ii′k

1 if ship s moves from port i to i′ during leg (k+1)

i

ports, i = 0 means dummy port

j

cargos

k

sailing legs

s

ships or carriers or tankers

Article Outline

Nomenclature

1. Introduction

1.1. Previous work

1.2. Problem complexity

2. One-ship problem

2.1. MILP formulation

2.2. Example

3. Multi-ship problem

3.1. Example

4. Decomposition algorithm

4.1. Heuristic H1

4.1.1. Example

4.2. Heuristic H2

5. Conclusion

Acknowledgements

References

Corresponding author. Tel.: +65-687-42186; fax: +65-677-91936.