An Optimization Model to Help Cruise Companies to Evaluate their

Offer in a Basin

Daniela Ambrosino and Veronica Asta

Department of Economics and business studies, University of Genova, Via Vivaldi 5, 16126, Genoa, Italy

Keywords:

Cruise Offer Decision Process, Evaluation of Cruise Offer, Optimization Model.

Abstract:

This work focuses on the problem of evaluating and improving a current offer, when the market changes due

to either new customers demands or new actions of competitors. A model for evaluating the current offer of

cruise itineraries is proposed. A case study related to the Mediterranean sea cruise offer is presented. Offers

have been compared in terms of demand satisfaction, revenue, costs, accessibility and appealing values that are

important information that can help the decision maker to choose the best offer in accordance with the trend

of the demand, the future business development and the future companys strategies. The current situation due

to COVID-19 pandemic represents an extreme case that poses new decision problems and requires different

analysis due to very high level of uncertainty. The present paper can furnish useful insights for facing some of

the emerging decision problems but it is dedicated to help decision makers in evaluating the cruise offer when

changes occur in a single market or in a limited area.

1 INTRODUCTION

The worldwide cruise ship tourism account for about

2 percent of the world tourism markets revenue, about

1.22 trillion (Statista, 2018). Over a ten-year period

(from 2007 to 2017), the world demand for cruising

has increased of about 69 percent passing from 15.9

million passengers to 26.8 million, as stressed in the

Cruise Lines International Association report (CLIA,

2018), and the capacity deployed by the cruise indus-

try has followed a similar growth, with 19 new ships

in 2020. In the last decades, cruise ship tourism has

represented the most dynamic segment of the tourism

involving many groups of stakeholders: from the de-

mand side customers and tourists, from the supply

side travel agencies, carriers and providers of tourist

services, and ﬁnally, tourist destinations and regula-

tory systems (Chen et al., 2016).

The health emergency due to COVID-19 has

changed these trends and forecasts for 2020 and 2021.

The health emergency forced cruise companies to

stop their ships and to re-organise their offer.

Since the production of the cruise industry output

has a great impact (also in terms of new jobs and in-

comes) on the global economy, it is really important

a rapid re-start of the cruise sector. Companies have

deﬁned health and safety measures protocols for be-

ing able to offer their cruises on the market. New

operative procedures derived by international health

authorities have been adopted and must be contin-

uously modiﬁed in accordance with new authorities

guidelines. As a consequence it is required to re-

organize cruises, to analyse constantly new distribu-

tion of the cruise demand from the world markets and

to re-evaluate the cruise offer.

The deﬁnition of the cruise itineraries offer is a

long process involving three planning levels: a long,

a medium and a day by day plan.

Given the planning horizon, usually ten years, and

the global long term strategy deﬁned by the company,

the main decisions of the long term plan consist in

the assignment of the available ships belonging to the

ﬂeet to the different basins of the world in which the

company offers its services. Seasons, specialties of

the different geographical areas, dry docks related to

the ordinary and no-ordinary maintenance of the ships

may be considered at this level, together with past re-

sults in terms of operative margin and customer satis-

faction degree, competitive analysis and business de-

velopment.

The medium level (at basin level) focuses on each

basin and a planning horizon of generally less than

one year (i.e. a season). For each ship assigned to

the basin are deﬁned the duration and the homeport

of its itineraries. These decisions are again guided by

the demand forecasting for the markets linked to the

Ambrosino, D. and Asta, V.

An Optimization Model to Help Cruise Companies to Evaluate their Offer in a Basin.

DOI: 10.5220/0010350203750383

In Proceedings of the 10th International Conference on Operations Research and Enterprise Systems (ICORES 2021), pages 375-383

ISBN: 978-989-758-485-5

375

basin.

Finally, there is the day by day planning (at

itinerary level). At this level each itinerary of each

ship of a basin is detailed, starting from the duration

and the homeport determined at the previous level.

Each itinerary is characterized by a schedule, which

is the arrival time at each port and the departure time.

Note that the schedule has an impact on the activities

offered and sold to customers when the ship arrives at

ports, but also on the activities offered on board dur-

ing the dock at ports and during navigation.

Each itinerary is deﬁned in such a way to grant

guest safety, to maximize the customer satisfaction

and the revenue, and minimize total costs.

At the end of this three level decision process the

cruise offer is deﬁned. This decision process is rolling

and each year is updated to include a new year.

Generally, cruise companies have two main objec-

tives: to gain new clients among those that usually

do not choose a cruise and to offer attractive and de-

sirable itineraries for maintaining repeater clients. In

fact, the cruise customers are usually loyal/repeater

clients, and the company has to propose them new

and different destinations, new and unique experi-

ences. For doing that, new itineraries must be sug-

gested and the cruise offer must constantly updated.

On the other hand, for reaching new market segments,

the cruise industry has to offer different cruise prod-

ucts. In (Ward, 2005) a classiﬁcation of ocean cruises

into ten different categories is presented, together

with a lifestyle classiﬁcation that distinguishes stan-

dard, premium, luxury cruises (Barron and Green-

wood, 2006). A detailed analysis on cruise tourism

motivation, preference, intention and competitiveness

is reported in (Chen et al., 2016).

A constant market analysis is required in such a

way to immediately notice changes in the market de-

mand; a change in the customers demand can be due

to particular events in some countries, to actions real-

ized by competitors and so on. The company has to

verify if its current offer is able to face the new market

demand.

Summarizing for the cruise company is really im-

portant to plan optimal space-time itineraries in such

a way to maximize occupancy and expected revenue

(Sun et al., 2011). Even if few papers deal with the

optimal deﬁnition of an itinerary, the optimal plan

space time itineraries is not at all discussed in the

literature (at least for the authors knowledge). This

work is a ﬁrst attempt of both describing the deci-

sion process followed by cruise industries to deﬁne

their cruise offer and deﬁning a model to evaluate

and, in case, improve the current cruise itineraries of-

fer in a given basin (i.e. deﬁning optimal space-time

itineraries). Note that, this decision problem can be

considered between the day by day planning and the

cruise by cruise one. In fact, itineraries are the inputs

data and the output is a set of itineraries to offer in a

basin in a planning horizon as for example a season

or 6 months.

The Covid-19 pandemic at the beginning of 2020

is a global event that has temporally and partially

changed the decision process described above and the

main objectives: companies have to attract clients and

reassure them on safety in taking a cruise, and their

main aim is to reduce the risks connected to the epi-

demic. Companies have to act at different levels: i) at

itinerary level to grant safety, to dock available ports

and to respect new rules emerging with the health

emergency (in fact, new decision problems related to

the deﬁnition of new reduced capacity of the ships,

to the reorganization of activities on board are emerg-

ing); ii) at basin level for adapting the itineraries of-

fer to the new demand; iii) at deployment level since

global distribution of passenger will not remain the

same in next few years.

The current situation due to COVID-19 pandemic

represents an extreme case that poses new decision

problems and requires different analysis due to very

high level of uncertainty. The present paper can fur-

nish useful insights for facing some of the emerging

decision problems but it is dedicated to help decision

makers in evaluating the cruise offer when changes

occur in a single market or in a limited area. The pan-

demic is having its effects on the world market. The

model here proposed, related to the cruise offer in a

given basin, should be extended to include more than

one basin for addressing some aspects and some new

emerging problems.

The paper is organized as follows. Section 2 is

devoted to the literature review, while Section 3 de-

scribes the problem under investigation and the pro-

posed mathematical model. Results are discussed in

Section 4 and conclusions outlined in the last section.

2 LITERATURE REVIEW

Even if studies about the cruise shipping are lim-

ited, recently some works are emerging in this ﬁeld,

in particular in the economic literature. (Sun et al.,

2011) propose a concise review of the past research

on cruise industry. They also discuss the importance

of applying revenue management to cruise industry.

It is clear that good revenue management deci-

sions are strongly dependent on accurate forecasting.

Interesting forecasting methods are presented in (Sun

et al., 2010). (Petrick, 2005) segments cruise pas-

ICORES 2021 - 10th International Conference on Operations Research and Enterprise Systems

376

sengers on the bases of their price sensitivity. In the

cruise industry, each passenger should be priced and

managed separately (Biehn, 2006). The cruise com-

pany has to plan optimal space-time itineraries in such

a way to maximize occupancy and expected revenue

(Sun et al., 2011).

Only few papers deal with itinerary de-

sign/optimization, optimal market segmentation,

and demand inﬁltration (see for example, (Wang

and Qu, 2016), (Ambrosino et al., 2018), (Mancini

and Stecca, 2018)). The itinerary design, recently

included by (Cusano et al., 2017) in the class of

cruise supply, is a problem that received few atten-

tion, even if it has been recognized that it represents

an important task having an impact on consumers

satisfaction.

The importance of itinerary design is underlined

by (Lee and Ramdeen, 2013) which performed a lin-

ear regression analysis to investigate the interaction of

cruise ship itinerary on cruise ship occupancy rates.

The regression model explained a signiﬁcant propor-

tion (23 %) of the variance in occupancy rates. (Chen

and Nijkamp, 2018) presents a guide for ports market-

ing policies and cruise companies decisional process

for ports selection and destinations. Tourists lengths

of stay at destination is investigated being an impor-

tant variable for estimating tourist consumption (Chen

et al., 2019). Moreover, port locations and port net-

works affect the overall spending at port destinations

and onboard services and experiences (Satta et al.,

2015). Finally, the occupancy rates are inﬂuenced by

the ports geography, the destinations and costs. (Sun

et al., 2011) suggest the integration of the itinerary

design and the revenue management, being a cruise

a combination of transportation and accommodation.

Integrating these two components, in fact, the cruise

line companies can not only enhance revenue but in-

crease customers satisfaction.

(Cusano et al., 2017) review works published in

the last two decades. Moreover, the authors analyze

the organization of cruise itineraries in the Mediter-

ranean Sea and highlight the dual role of excursions

used by cruise companies to differentiate services and

by the port cities to promote themselves. In (Ro-

drigue and Notteboom, 2013) is stressed the role of

the itineraries in the appeal of a cruise service. (Wang

and Qu, 2016) deal with a Cruise Service Planning

(CSP) Problem, which consists in determining cruise

transport services, i.e. the assignment of some prede-

ﬁned sequences of ports to a set of ships, in order to

maximize total proﬁt, while considering berth avail-

ability and the effect of decreasing marginal proﬁt.

The main point of a cruise service design is the abil-

ity to offer to the customer a various set of itineraries

including different kind of destinations.

In (Ambrosino et al., 2018) a mathematical for-

mulation for determining a new itinerary maximiz-

ing revenue, customers satisfaction, while minimiz-

ing operative costs has been proposed. The customer

satisfaction is one of the main issue to consider. It

depends on different aspects, for example the accessi-

bility and the appealing of the destinations achievable

from the port. The (Wang et al., 2014) analysis shows

that the category tourism attractions is the most con-

siderable issue taken in consideration when a cruise

ship is selecting a port of call location. In their re-

sults the category connectivity and agility ranks sec-

ond. The aim of itinerary design is to determine when

to depart and return, what duration, which destina-

tions and what fare structure to adopt.

(Mancini and Stecca, 2018) face the tour planning

problem deﬁning a ﬁxed number of tours (a tour for

each available vessel) that must be repeated in a given

planning horizon in such a way to minimize ﬁxed and

variable costs related to the ports and to fuel con-

sumption. The authors propose a model for solving

the tour planning problem that is a rich vehicle routing

problem and propose a Large Neighborhood Search

based matheuristic for solving it. The problem un-

der investigation is similar to the CSP introduced in

(Wang and Qu, 2016) and differs from that studied

in (Mancini and Stecca, 2018) for the fact that, each

vessel is not obliged to repeat the same tour during

the planning horizon and for the objective function

considered when deﬁning the tours (itineraries) to of-

fer. In this paper, the offer is deﬁned by selecting a

number of itineraries among a set of potential ones,

each one with a given set of characteristics as better

explained in the following section.

3 THE CRUISE ITINERARY

OFFER

As already introduced, this work aims at evaluating

a cruise offer and improving it by choosing what

itineraries offer in a given basin during a planning

horizon, for example a season. We suppose that all

itineraries have the same duration, thus the planning

horizon under investigation can be split into a certain

number of time periods each one having length equal

to the itinerary duration (i.e. 7 days = a week, that

is the most common, as reported in (CLIA, 2018)).

Given a basin with its ships and a set of markets with

a positive cruise demand for each period of the plan-

ning horizon, given a set of itineraries designed to sat-

isfy the cruise demand of the markets of the basin, the

problem consists in selecting the itineraries to offer in

An Optimization Model to Help Cruise Companies to Evaluate their Offer in a Basin

377

each period of the planning horizon in such a way to

maximize the revenue, the customers satisfaction, the

accessibility and minimize the operative costs, while

satisfying some requirements.

The itineraries among which to choose for deﬁn-

ing the offer are characterized by a sequence of visited

ports, a cost, a revenue, an appealing and an accessi-

bility value. Moreover, each itinerary is able to satisfy

a given amount of the demand of the markets of the

basin.

When deﬁning the cruise offer, the requirements

to take into consideration may be different for the

cruise companies but are generally related to:

• the demand to satisfy: the chosen itineraries must

satisfy the cruise demand of each market involved

in the basin under consideration and of each time

period;

• the maximum number of itineraries that can be of-

fered in the whole planning horizon, that is lim-

ited:

- by the number of ships deployed in the basin;

- for commercial and organizational reasons;

• the maximum number of itineraries that can be of-

fered in each time period of the planning horizon,

that is limited:

- by the number of ships deployed in the basin and

available in each time period;

• the repeatability of the itineraries in the whole

planning horizon, due to commercial and organi-

zational reasons; when an itinerary is chosen:

- it must be offered for a certain number of con-

secutively period of times;

- it can be offered again, but there is a limitation

to the number of times the same itinerary can be

re-offered;

• the maximum number of times a port can be

present in the itineraries offered in each time pe-

riod.

For what concerns the limitation for ports, it is de-

ﬁned by the cruise company differently depending on

each port: the company assigns to each port an ap-

pealing class and thus, in accordance with the appeal-

ing class of the ports, deﬁnes the limitation.

Finally, the number of ships available in each time

period can be less than the number of ships assigned

to the basin due to, for example, planned dry docks.

3.1 The Optimization Model

The mixed integer 0/1 linear programming model for

solving Cruise Itinerary Offer Problem (CIOP), to-

gether with the useful notation, are here below intro-

duced. Let be:

• T the set of periods of time in which is divided the

planning horizon;

• M the set of markets;

• I the set of available itineraries that can be se-

lected for the offer;

• P the set of ports belonging to the different

itineraries of set I;

• Q the set of appealing classes of the ports of set P;

• d

demand to satisfy in market m, in time period

t, ∀m ∈ M, ∀t ∈ T ;

• o

demand of market m, satisﬁed by itinerary

i, ∀m ∈ M, ∀i ∈ I ;

• r

revenue of itinerary i, ∀i ∈ I;

• c

costs of itinerary i, ∀i ∈ I;

• ap

appealing value of itinerary i,∀i ∈ I;

• ac

accessibility value of itinerary i, ∀i ∈ I;

• b

= 1 if port p belongs to itinerary i, ∀p ∈ P, ∀i ∈

• s

max

maximum number of itineraries that can be

offered in time period t, ∀t ∈ T ;

• i

max

maximum number of itineraries that can be

offered during the whole planning horizon;

• n

maximum number of time the itinerary i can be

offered during the planning horizon, ∀i ∈ I;

• µ maximum number of time an itinerary can be

re-planned in the cruise offer during the planning

horizon;

• r

maximum number of time port p, having ap-

pealing belonging to the appealing class q, can be

offered in each time period, ∀p ∈ P, ∀q ∈ Q;

• g

= 1 if appealing value of port p belongs to the

appealing class q, ∀p ∈ P, ∀q ∈ Q;

• α, β weights used in the objective function.

The decision variables are the following:

∈ {0, 1} ∀i ∈ I,y

= 1 if itinerary i is selected;

i,t

∈ {0, 1} ∀i ∈ I, ∀t ∈ T , x

i,t

= 1 if itinerary i is

selected for being offered in time period t;

i,t

∈ {0, 1} ∀i ∈ I, ∀t ∈ T , j

i,t

= 1 if itinerary i is

offered starting from time period t.

MIN

∑

t∈T

∑

i∈I

−c

+α

∑

t∈T

∑

i∈I

+β

∑

t∈T

∑

i∈I

(1)

subject to

∑

t∈T

≤ |T |y

∀i ∈ I (2)

ICORES 2021 - 10th International Conference on Operations Research and Enterprise Systems

378

∑

i∈I

≥ r

∀m ∈ M, ∀t ∈ T (3)

∑

i∈I

≤ i

max

(4)

∑

i∈I

≤ s

max

∀t ∈ T (5)

− x

it−1

≤ j

∀i ∈ I, ∀t ∈ T − {t

} (6)

≤ j

∀i ∈ I, ∀t ∈ T : t = t

(7)

∑

t∈T

≤ µy

∀i ∈ I (8)

it+1

it+2

it+3

≥ 4 j

∀i ∈ I, ∀t ∈ T : t < |T |−3

(9)

∑

i∈I

≤ m

+M(1 −g

) ∀i ∈ I, ∀p ∈ P, ∀q ∈ Q

(10)

Equation (1) represents the objective function that

is the maximization of weight sum of operative mar-

gin, appealing and accessibility. Constraints (2) de-

ﬁne variables y

, indicating if itinerary i is offered in

some periods of the planning horizon.

Equations (3) are the demand constraints: in each

time period t the demand of each market m must be

covered by the selected itineraries. Equation (4) lim-

its the number of itineraries to offer during the consid-

ered planning horizon, while the maximum number of

itineraries that can be offered in each time period t is

veriﬁed thanks to equations (5). Equations (6) and (7)

deﬁne the variable j

as the ﬁrst time period in which

the itinerary i is offered. During the planning horizon

each selected itinerary can not be re-offered more than

µ times as imposed by (8), but it must be offered for

at least four consecutive periods, as required by (9).

Constraints (10) impose the number of time a port p

can be visited in each time period t; this limit depends

on the appealing class of port p.

4 A CASE STUDY

The proposed model has been used to analyse the

offer of a cruise company operating in the West

Mediterranean basin. The model has been solved

ﬁrstly for determining which itineraries to add to two

itineraries already offered in the basin (Partially Fixed

Offer - PFO), and secondly, for deﬁning a Completely

New Offer (CNO). The offer must be deﬁned for a

planning horizon of 12 periods (12 weeks). The max-

imum number of ships available during each week

is equal to four, except for weeks 5 and 6 in which

only three ships are available because of the dry dock

planned for the fourth ship. The maximum number

of itineraries to offer during the planning horizon is

ﬁxed equal to 6.

The set I of itineraries used to deﬁne the cruise

offer has been obtained as the union of the set of

itineraries already offered by the company and a set of

new itineraries obtained by using the model proposed

in (Ambrosino et al., 2018) for the cruise itinerary de-

sign problem. The ports situated in the West Mediter-

ranean area are Savona, Ajaccio, Toulon, Marseille,

Barcelona, Mahon, Palma, Ibiza, Valencia, Valletta,

Palermo, Catania, Cagliari, Naples, Civitavecchia,

Livorno, La Spezia. All the itineraries are character-

ized by homeport Savona, duration 7 nights, one day

at sea, port stop of half day (i.e. the afternoon) in few

cases, while generally is the whole day (morning and

afternoon).

Figure 1: Example of two itineraries schedule.

Figure 1 sketches two itineraries of set I, showing

the sequence of ports visited and the stop duration at

ports.

The model has been implemented in Mathematical

Programming Language (MPL, 2020) and solved by

the commercial solver Gurobi 7.0.2.(Gurobi, 2020)

on a PC Intel Core i3, 2.00 G Hz; 4 G RAM. The

optimal solutions has been obtained within few sec-

onds. The solved models have 200 variables and 770

constraints.

Figure 2 shows the two offers (PFO and CNO)

deﬁned when solving CIOP. Note that the two offers

are equals: the itineraries already offered by the com-

pany have been chosen also in the CNO. Two other

itineraries are then chosen for satisfying the demand

of the the three markets here considered for the basin

under investigation, i.e. the Italian, the French and

the Spanish ones. Tables below Figure 2 report the

percentages of the markets demand satisﬁed by each

itinerary offered in the PFO and CNO (weeks of the

time horizon are grouped depending on the itineraries

selected, i.e. T1-T4, T5-T6 and T7-T12).

Moreover, for the above-deﬁned groups of weeks,

Figure 3 shows the comparison between the markets

offer and the demand to satisfy. This comparison

regards again the three markets under investigation.

Note that imposing a minimum of demand to satisfy

but no an upper bound, for each market the supply

of every complete offer overcomes the minimum de-

An Optimization Model to Help Cruise Companies to Evaluate their Offer in a Basin

379

Figure 2: Market’s offer of PFO and CNO.

Figure 3: Market’s offer and demand to satisfy.

mand to satisfy.

All the selected itineraries contribute equally to

cover the markets demand. From Figure 3 we can

note that the oversupply is lower in weeks 5 and 6

than in the other periods because of the lack of one

of the four ship during this period. This kind of anal-

ysis is useful to enable the marketing department to

adopt some pricing tools in such a way to increase the

demand (for example for the French market). On the

other hand, if it should be necessary to move a ship

from a basin to another, this analysis could help to

take the more appropriate decisions by evaluating the

impact of the change on the markets.

4.1 Determining the Offers by using

Different Criteria

In this subsection, we present a comparison of the

cruise itineraries offers obtained by solving the CIOP

by modifying the objective functions used in model

(1)-(10), i.e. the criteria for the selection of the

itineraries. In particular, the four cases have been con-

sidered: a) maximization of the appealing; b) maxi-

mization of the accessibility; c) maximization of the

revenue; d) maximization of the operative margin.

Figure 4 shows the offer changes in accordance with

the objective function used (i.e. cases a)-d)), report-

ing both PFO and CNO. When using the maximiza-

tion of the appealing as the criteria for selecting the

itineraries to offer, the CNO is identical to the ob-

tained PFO. This means that the itineraries already

offered by the company perform very well in terms

of appealing. When considering the other objective

functions (i.e. b)-d)) the obtained offers are differ-

ent. The reader can also note that when comparing the

PFO obtained in the four cases, the offer determined

by maximizing the accessibility and the revenue are

equals (this fact is true also for the CNOs).

Figure 4: A comparison of PFO and CNO when varying the

objective function.

A deeply analysis related to the offers depicted

in Figure 4 is reported in the following graphs. The

CNOs permit to obtain better results in terms of ac-

cessibility, revenue and operative margin. When max-

imizing the accessibility, the CNO permits to obtain

higher accessibility, but also higher revenue and op-

erative margin, while there is a small reduction in the

appealing level, as shown in the graph of Figure 5 .

When maximizing the revenue, the CNO permits

to obtain again higher revenue, and also higher acces-

sibility and operative margin, while there is a small

ICORES 2021 - 10th International Conference on Operations Research and Enterprise Systems

380

Figure 5: A graph comparing PFO and CNO when maxi-

mizing the accessibility.

reduction in the appealing level, as shown in the graph

of Figure 6. The same situation arises when maximiz-

ing the operative margin, as showed in Figure 7.

Figure 6: A graph comparing PFO and CNO when maxi-

mizing the revenue.

Figure 7: A graph comparing PFO and CNO when maxi-

mizing the operative margin.

4.2 Determining the Offers Maximizing

the Revenue While Granting

Certain Appealing Levels

The model has been used for deﬁning the optimal of-

fer in terms of revenue maximization, controlling the

appealing level by a constraint.

If the company wants to maximize the revenue

while granting offers characterized by a certain level

of appealing, the proposed modal can be easily modi-

ﬁed and solved.

In the following we report the results obtained in

three cases: no constraints for the appealing level,

and imposing two different levels (i.e. named A1, A2

and in ascending order). The comparison among the

planned itineraries is reported in Figure 8 . Asking for

higher values of appealing, the obtained solutions are

characterized by a higher variability in the itinerary

offered: the number of itineraries offered during the

planning horizon increases from four to ﬁve. This

is an important aspect characterizing the offer. The

itinerary management department is not indifferent to

the number of itineraries to manage. Moreover, also

to move a ship from an itinerary to another one is not

a preferred solution (i.e. this happen in PFO with ap-

pealing constraint ≥ A2 in correspondence of week 5

and 6).

Figure 8: PFO and CNO Itineraries planned maximizing

revenue while imposing different levels of appealing.

Comparing the appealing, accessibility and rev-

enue values of the solutions reported in Figure 8, we

noted that when the level of appealing is forced to in-

crease, the other values decrease or remain almost sta-

ble for both PFO and CNO (see Figure 9). Moreover,

The effect on the accessibility and revenue values is

greater in case of partially ﬁxed offer; this fact could

evidence the necessity of modifying the current offer

of the company for obtaining better results in terms of

accessibility and revenue.

Figure 9: PFO and CNO solutions maximizing the revenue

while imposing different levels of appealing.

4.3 The Analysis on the Markets Offer

and the Demand to Satisfy

Let us conclude with an analysis on the solutions in

such a way to furnish important information to the

An Optimization Model to Help Cruise Companies to Evaluate their Offer in a Basin

381

cruise company. We compare the markets offer (de-

termined for PFO and CNO ) with the demand to sat-

isfy, when the company aim is maximizing the rev-

enue.

Figure 10: Markets offer and demand to satisfy.

This comparison realized for three types of offers

(without the constraint for imposing a given appeal-

ing level, and imposing two different appealing lev-

els A1 and A2 as explained before) has been done

for each period of the time horizon characterized by

the same set of itineraries to sell. Figure 10 shows

the obtained results (PFO and CNO) for three periods

(T1-T4, T5-T6 and T7-T12). The graphs show the

comparison between the offer and the demand for the

Italian, the French and the Spanish markets. Having a

minimum demand to satisfy without an upper bound,

for each market the supply overcomes the demand.

The only indirect limitation of the markets offer is the

maximum number of itineraries that can be offered

for each period of time (i.e. each week). Note that the

three offers are equals in weeks 5 and 6 in which the

number of ships is limited for the dry docks. In weeks

7-12 the change in the market offer is derived when

imposing an appealing level of A1, while in weeks

1-4 the change is evident when imposing the higher

level of appealing. This different impact of the ap-

pealing level on the markets offer seems due to the ra-

tio between the demand to satisfy and the global offer

capacity. These graphs permit the company to choose

the best offer taking into account also the trend of the

markets demand.

The information related to the differences between

the demand and the offer for each market can be used

in order to adopt new marketing activities and pric-

ing policies in such a way to increase the revenue and

also to face market variations due to both competitors

activities and customers behavior changes.

5 CONCLUSIONS

The mathematical formulation proposed in this paper

permits to evaluate the current cruise offer in such a

way to modify it, if necessary. It furnishes applicable

solutions and represents a support during the cruise

itinerary planning decision process. This approach to

ﬁnd and analyze different solutions can be used for

deciding how to reply to market changes and also to

some operative problems related to ships or ports tem-

porally unavailable.

In this ﬁrst attempt to face the cruise offer prob-

lem, some simplifying assumptions have been used.

For example, the duration of the itineraries used for

deﬁning the cruise offer is considered constant and

equal to seven days. In practice, it is possible to have

itineraries characterized by different duration. The

proposed model can be extended to admit itineraries

of different length. Moreover it should be also modi-

ﬁed for deﬁning the offer in more than one basin.

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