Efficient Resource Planning of Intermodal Terminals under Uncertainty

15th IFAC Symposium on Control in Transportation Systems JuneIFAC 6-8, 2018. Savona,on Italy Symposium Control in Transportation Systems 15th 15th IFAC Symposium on Control Systems Available online at www.sciencedirect.com 15th IFAC Symposium on Control in in Transportation Transportation Systems June 6-8, 2018. Savona, Italy JuneIFAC 6-8, 2018. 2018. Savona,on Italy 15th Symposium Control in Transportation Systems June 6-8, Savona, Italy June 6-8, 2018. Savona, Italy

ScienceDirect

IFAC PapersOnLine 51-9 (2018) 398–403

Efficient Resource Planning of Intermodal Terminals under Uncertainty Efficient Resource Planning of Intermodal Terminals under Uncertainty Efficient of Intermodal Terminals under Efficient Resource Resource Planning Planning ofCavone*. Intermodal Terminals under Uncertainty Uncertainty Graziana Mariagrazia Dotoli*. under Uncertainty Efficient Resource Planning of Intermodal Terminals Graziana Dotoli*. NicolaCavone*. Epicoco*.Mariagrazia Carla Seatzu** Graziana Cavone*. Mariagrazia Dotoli*. Graziana Cavone*. Mariagrazia Dotoli*. Nicola Epicoco*. Carla Seatzu** Graziana Cavone*. Mariagrazia Dotoli*. Nicola Epicoco*. Epicoco*. Carla Carla Seatzu** Seatzu** Nicola *Department of Electrical Nicola and Information Politecnico di Bari, Bari, Italy Epicoco*.Engineering, Carla Seatzu** *Department of Electrical and Information Engineering, Politecnico di Bari, Bari, Italy (e-mail: [email protected], [email protected], [email protected]) *Department of and Engineering, Politecnico di Bari, Bari, Italy *Department of Electrical Electrical and Information Information Engineering, Politecnico di Bari, Bari,Cagliari, Italy (e-mail: [email protected], [email protected], [email protected]) *Department of Electrical and Electronic Engineering, Università degli Studi di Cagliari, Italy *Department of Electrical and Information Engineering, Politecnico di Bari, Bari, Italy (e-mail: [email protected], [email protected], [email protected]) (e-mail: [email protected], [email protected], [email protected]) *Department of Electrical and Electronic Engineering, Università degli Studi di Cagliari, Cagliari, (e-mail: [email protected]) (e-mail: [email protected], [email protected], [email protected]) *Department of of Electrical Electrical and and Electronic Electronic Engineering, Engineering, Università Università degli degli Studi Studi di di Cagliari, Cagliari, Cagliari, Cagliari, Italy Italy *Department Italy (e-mail: [email protected]) *Department of Electrical and Electronic Engineering, Università degli Studi di Cagliari, Cagliari, Italy (e-mail: [email protected]) [email protected]) (e-mail: (e-mail: [email protected]) Abstract: This paper presents a decision support tool for the efficient resource planning and management Abstract: This paper decision tool efficient and management of intermodal underaa uncertainty, allowing to the address the resource planning planning issue under or Abstract: Thisterminals paper presents presents decision support support tool for for the efficient resource planning and imprecise management Abstract: This paper a uncertainty, decision support tool for the efficient resource planning and management of intermodal terminals under allowing to address the planning issue under imprecise or uncertain data (e.g., presents estimates on flows, resource utilization, operating conditions). The procedure Abstract: This paper presents a decision support tool for the efficient resource planning and management of intermodal terminals under uncertainty, allowing to address the planning issue under imprecise or of intermodal terminals uncertainty, allowing to Net address issue2)under imprecise or uncertain (e.g., on flows, resource utilization, operating conditions). procedure consists ofdata three steps:estimates 1)under the definition of a Timed Petri modelthe of planning the terminal; the The computation of of intermodal terminals under uncertainty, allowing to address the planning issue under imprecise or uncertain data (e.g., estimates on flows, resource utilization, operating conditions). The procedure uncertain data (e.g., estimates on flows, resource utilization, operating conditions). The procedure consists of three steps: 1) the definition of aa Timed Net model of the terminal; the computation of suitable performance indices to evaluate whether thePetri current configuration is conditions). able to2) cope with aprocedure foreseen uncertain data (e.g., estimates on flows, resource utilization, operating The consists of three steps: 1) the definition of Timed Petri Net model of the terminal; 2) the computation of consists performance of steps:indices 1) the to definition ofwhether a Timed Petri Net configuration model of of the terminal; 2)cope computation of suitable current is able to aa foreseen increase in three the freight flows; 3)evaluate in the case of notthe satisfactory values indices atthe thewith previous step, consists of three steps:indices 1) the to definition ofwhether a Timed Petri Net configuration model of thethe terminal; 2)cope the computation of suitable performance evaluate the current is able to with foreseen suitable performance indices to evaluate whether the current configuration is able to cope with a foreseen increase in the freight flows; 3) in the case of not satisfactory values of the indices at the previous step, the simulation of alternative planning solutions and the detection of the most efficient one via a crosssuitable performance indices to evaluate whether the current configuration is able to cope with a foreseen increase in the freight flows; 3) in the case of not satisfactory values of the indices at the previous step, increase infuzzy the freight flows; planning 3) in the case oftechnique. not satisfactory values ofitsthe indices at the step, the simulation alternative solutions and the detection most efficient one via aa crossefficiency Data Envelopment Analysis In order to of testthe effectiveness, theprevious procedure is increase in the of freight flows; planning 3) in the case of not satisfactory values of the indices at the previous step, the simulation of alternative solutions and the detection of the most efficient one via crossthe simulation of alternative planning solutions and the detection of the most efficient one via a crossefficiency fuzzy Data Envelopment Analysis technique. In order to test its effectiveness, the procedure is applied to a real case study. the simulation of alternative planning solutions and the detection of the most efficient one via a crossefficiency fuzzy fuzzy Data Data Envelopment Envelopment Analysis Analysis technique. technique. In In order order to to test test its its effectiveness, effectiveness, the the procedure procedure is is efficiency applied to aafuzzy real case efficiency Datastudy. Envelopment Analysis technique. In order to test its effectiveness, the procedure is applied to real case study. applied to a real case study. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: intermodal terminals, performance evaluation, resource planning, Petri Nets, fuzzy theory, applied to a real case study. Keywords: intermodal terminals, performance evaluation, resource planning, Petri Nets, fuzzy theory, Data Envelopment Analysis, efficiency, uncertainty. Keywords: intermodal terminals, performance evaluation, Keywords: intermodal terminals, performance evaluation, resource resource planning, planning, Petri Petri Nets, Nets, fuzzy fuzzy theory, theory, Data Envelopment Analysis, efficiency, uncertainty. Keywords: intermodal terminals, performance evaluation, resource planning, Petri Nets, fuzzy theory, Data Envelopment Analysis, efficiency, uncertainty. Data Envelopment Analysis, efficiency, uncertainty. Data Envelopment Analysis, efficiency, uncertainty. hybrid PNs are used to optimize the terminal performance, 1. INTRODUCTION hybrid PNs are used to Shinoda optimize(2017) the terminal performance, and finally Hangga and where PNs are used hybrid PNs are used terminal performance, 1. INTRODUCTION hybrid PNsthe areunder/overutilization used to to optimize optimize the the terminal performance, 1. to evaluate of straddle carriers the and finally Hangga and Shinoda (2017) where PNs 1. INTRODUCTION INTRODUCTION Intermodal transportation involves the transport of freight hybrid PNs are used to optimize the terminal performance, and finally finally Hangga Hangga and and Shinoda Shinoda (2017) (2017) where where PNs PNs are areinused used and are used 1. INTRODUCTION to evaluate the under/overutilization of straddle carriers in terminal. The above contributions simply propose modelling Intermodal transportation involves the transport of freight stored in Intermodal Transport Units (ITUs) and combining and finally Hangga and Shinoda (2017) where PNs are used to evaluate evaluate the the under/overutilization under/overutilization of of straddle straddle carriers carriers in in the the Intermodal transportation involves the transport of freight to the Intermodal transportation involves the transport of freight terminal. The above contributions simply propose modelling approaches for intermodal terminals, but lack of automated stored Intermodal Transport Units (ITUs) combining at leastin two transportation modes, tothe offer a and more reliable, to evaluateThe theabove under/overutilization of straddle carriers in the terminal. contributions simply propose modelling Intermodal transportation involves transport of freight stored in Intermodal Transport Units (ITUs) and combining terminal. The above contributions simply propose modelling stored intwo Intermodal Transport Units (ITUs) and combining for intermodal terminals, but lack of automated guidelines/procedures for their resource planning. This topic at least transportation modes, to offer aaservice more reliable, flexible, profitable, and sustainable transport than the approaches terminal. The contributions simply propose modelling approaches for intermodal terminals, but lack of automated stored intwo Intermodal Transport Units (ITUs) and combining at least transportation modes, to offer more reliable, approaches forabove intermodal terminals, but lack of and automated at least two transportation modes, to offer a more reliable, guidelines/procedures for their resource planning. This topic is preliminarily addressed in Cavone et al. (2017) further flexible, profitable, and the single (SteadieSeifi et al.,transport However, for intermodal terminals, butplanning. lack of automated guidelines/procedures for their resource This topic at least mode two transportation modes, to 2014). offer aservice more than reliable, flexible, profitable, and sustainable sustainable transport service than the approaches guidelines/procedures for their resource planning. Thisfurther topic flexible, profitable, and sustainable transport service than the is preliminarily addressed in Cavone et al. (2017) and discussed in this paper. In particular, here we combine TPNs single mode (SteadieSeifi et al., 2014). However, the integration of different transportation modes and of several guidelines/procedures for their resource planning. This topic is preliminarily addressed in Cavone et al. (2017) and further flexible, profitable, and sustainable transport service than the single mode mode (SteadieSeifi (SteadieSeifi et et al., al., 2014). 2014). However, However, the with is preliminarily addressed in Cavone et al. (2017) and further single a cross-efficiency fuzzy Data et Envelopment Analysis discussed in this paper. In particular, here we combine TPNs integration of different transportation modes and of several actors is non-trivial. As a consequence, intermodal terminals is preliminarily addressed in Cavone al. (2017) and further discussed in this paper. In particular, here we combine TPNs single mode (SteadieSeifi et al., 2014). However, the integration of of different different transportation transportation modes modes and and of of several several discussed in this paper. In particular, here we combine TPNs integration to model the terminal, determine theAnalysis impact with aa technique cross-efficiency Data Envelopment actors non-trivial. As aa consequence, intermodal need tois be ofproperly managed to be modes an efficient interface discussed in this paper. Infuzzy particular, we combine TPNs with cross-efficiency fuzzy Data here Envelopment Analysis integration different transportation and ofterminals several (DEA) actors is non-trivial. As consequence, intermodal terminals with a technique cross-efficiency fuzzy Data Envelopment Analysis actors is non-trivial. As a consequence, intermodal terminals (DEA) to model the terminal, determine the impact of planning alternatives on suitable Key Performance between freight forwarders and conveyors and ensure a high with a cross-efficiency fuzzy Data Envelopment Analysis need to be properly managed to be an efficient interface (DEA) technique technique to to model model the the terminal, terminal, determine determine the the impact impact actors non-trivial. As a consequence, intermodal terminals need to be managed to efficient interface (DEA) need tois freight be properly properly to be be an an efficient interface alternatives on suitable Key Performance Indicators (KPIs), detect the mostdetermine efficient planning between forwarders and conveyors and ensure aa high competitiveness of themanaged whole transportation chain (Caris et of (DEA) technique to and model the the impact of planning planning alternatives on terminal, suitable Key Performance need to be properly managed to be an efficient interface between freight forwarders and conveyors and ensure high of planning alternatives on suitable Key Performance between freight forwarders and conveyors and ensure a high Indicators (KPIs), and detect the most efficient planning options under uncertain data and in a multi-criteria competitiveness of the whole transportation chain (Caris et al., 2013; SteadieSeifi et al., 2014; Li et al., 2015). of planning alternatives on suitable Key Performance Indicators (KPIs), and detect the most efficient planning between freight forwarders andtransportation conveyors andchain ensure a high competitiveness of (Caris et (KPIs), and detect theprocedure mostin efficient planning competitiveness of the theetwhole whole transportation chain (Caris et Indicators options under uncertain data aais intended multi-criteria perspective. In fact, the presented as a al., 2013; SteadieSeifi al., 2014; Li et al., 2015). Indicators (KPIs), and detect theand mostin efficient planning options under uncertain data and multi-criteria competitiveness of the whole transportation chain (Caris et al., 2013; SteadieSeifi et al., 2014; Li et al., 2015). options under uncertain data and in a multi-criteria al., 2013; SteadieSeifi al., 2014; al., 2015). Several approaches areetavailable in Li theetliterature to ensure the perspective. In fact, the presented procedure is intended as a strategic support tool for the proper long/medium-term options under uncertain data procedure and in ais multi-criteria perspective. In fact, the intended as al., 2013; SteadieSeifi et al., 2014; Li et al., 2015). perspective. Inintermodal fact, the presented presented procedure isthe intended as aa Several approaches are available in the literature to ensure efficient functioning of intermodal terminals (see, e.g., the strategic support tool for the proper long/medium-term planning of terminals. Due to dynamical In fact,tool the presented procedure is intended as a Several approaches approaches are are available available in in the the literature literature to to ensure ensure the the perspective. strategic support for long/medium-term Several strategic tool for the the proper proper long/medium-term efficient functioning intermodal terminals (see, e.g., review SteadieSeifi al. (2014)). Inliterature particular, to the features ofsupport theintermodal terminal activities, such evaluations are based of terminals. Due to the dynamical Several approaches areof available in the to due ensure the planning strategic support tool for the proper long/medium-term efficientin functioning ofet intermodal terminals (see, e.g., planning of intermodal terminals. Due to efficient functioning of intermodal terminals (see, e.g., the planning of intermodal terminals. Due to the the dynamical dynamical review in SteadieSeifi et al. (2014)). In particular, due to the features of such terminals, Discrete Event System (DES) on preliminary estimates of the system parameters which are features of the terminal activities, such evaluations are based efficient functioning of intermodal terminals (see, e.g., the planning of intermodal terminals. Due to the dynamical review in in SteadieSeifi SteadieSeifi et et al. al. (2014)). (2014)). In In particular, particular, due due to to the features of activities, such evaluations are review features of the the terminal terminal activities, such evaluations are based based models are suitable toetrepresent andInanalyse themdue (Cartenì features of such terminals, Discrete Event System (DES) clearly affected by uncertainty and cannot be managed in on preliminary estimates of the system parameters which review in SteadieSeifi al. (2014)). particular, to the features of the terminal activities, such evaluations are based features of such terminals, Discrete Event System (DES) on preliminary preliminary estimates estimates of of the the system system parameters parameters which which are area features of such terminals, Event System (DES) are and de Luca, 2012; Cavone etDiscrete al.,and 2016; Di Febbraro et al., on models are suitable to represent analyse them (Cartenì clearly affected by uncertainty and cannot be managed in deterministic way. features of such terminals, Discrete Event System (DES) on preliminary estimates of the system parameters which models are suitable to represent and analyse them (Cartenì clearly affected affected by by uncertainty uncertainty and and cannot cannot be be managed managed in inareaaa models are suitable to represent and analyse them (Cartenì clearly and de Luca, 2012; Cavone et al., 2016; Di Febbraro et al., 2016; Dotoli et al., 2016). Among the DES models, Petri deterministic way. models are suitable to represent analyse them (Cartenì affected by uncertainty and cannot be managed in a and de Luca, 2012; Cavone et al., 2016; Di et al., deterministic way. and Luca, 2012; Cavone et al.,and 2016; Di Febbraro Febbraro etPetri al., clearly deterministic way. To support intermodal managers in the decision making, the 2016; Dotoli et al., 2016). Among the DES models, Netsde (PNs) allow to systematically represent terminal and de Luca, 2012; Cavone et al., 2016; Di Febbraro et al., deterministic way. 2016; Dotoli et al., 2016). Among the DES models, Petri 2016; Dotoli et al., 2016). Among the DES models, Petri To support intermodal managers the decision making, proposed procedure takes into in account uncertainty inthe a Nets (PNs) allow to systematically represent terminal activities, shared synchronized ormodels, parallelized support intermodal managers in the making, the 2016; Dotoli et al.,resources, 2016). Among the DES Petri To Nets (PNs) allow to systematically represent terminal To support intermodal managers inaccount the decision decision making, thea Nets (PNs) allow to systematically represent terminal proposed procedure takes into uncertainty in twofold manner: 1) by using stochastic transitions in the processes, and malfunctioning (Maione etrepresent al.,or Hangga proposed To supportprocedure intermodaltakes managers inaccount the decision making,in theaa activities, shared resources, synchronized parallelized into uncertainty Nets (PNs) allow to systematically terminal activities, shared resources, synchronized or2016; parallelized proposed procedure takes intostochastic account uncertainty inthe activities, shared resources, synchronized or parallelized twofold manner: 1) by using in terminal modelling and performing Monte transitions Carlo simulations processes, and malfunctioning (Maione et al., 2016; Hangga and Shinoda, 2017). proposed procedure takes into account uncertainty in twofold manner: 1) by using stochastic transitions in the activities, shared resources, synchronized or parallelized processes, and and malfunctioning malfunctioning (Maione (Maione et et al., al., 2016; 2016; Hangga Hangga twofold manner: 1)and byperforming using transitions in thea processes, terminal modelling Monte Carlo simulations of the terminal dynamics; 2) bystochastic applying a fuzzy decision and Shinoda, 2017). twofold manner: 1) by using stochastic transitions in the terminal modelling and performing Monte Carlo simulations processes, and malfunctioning (Maione et al., 2016; Hangga and Shinoda, 2017). modelling and performing Monte simulations and Shinoda, 2017). Among the most recent contributions using PNs we recall terminal of the terminal dynamics; 2) by applying aa the fuzzy decision making approach to compare and rankCarlo alternative terminal modelling and performing Monte Carlo simulations of the terminal dynamics; 2) by applying fuzzy decision and Shinoda, 2017). the terminal dynamics; 2) by and applying a because fuzzyalternative decision Among the recent contributions using PNs we recall here Silva et most al. (2015) where PNs with predicates are used to of making approach to rank resource planning configurations. Moreover, of the of the terminal dynamics; 2) by and applying fuzzyalternative decision Among the most recent contributions using PNs we recall making approach to compare compare and rank a the the alternative Among theetevaluate most recent contributions using PNsare we recall making approach to compare rank the here Silva al. (2015) where PNs with predicates used to model and the performance of a seaport terminal, resource planning configurations. Moreover, because large amount of conflicting objectives to be pursued in the Among the most recent contributions using PNs we recall making approach to compare and rank the alternative here Silva et al. (2015) where PNs with predicates are used to resource planning planning configurations. configurations. Moreover, Moreover, because because of of the here Silva etevaluate al. (2015) where PNs withofpredicates areterminal, used to resource of model and the performance a seaport Maione et al. (2016) where stochastic PNs are used to large amount of conflicting objectives to be pursued in thea terminal resource planning, alternatives are evaluated viathe here Silva etevaluate al. (2015) where PNs withof predicates areterminal, used to resource planning configurations. Moreover, because of the model and the performance aa seaport large amount of conflicting objectives to be pursued in model and evaluate the performance of seaport terminal, large amount of conflicting objectives to be pursued in the Maione et al. (2016) where stochastic PNs are used to coordinate human activities in intermodal terminals, Dotoli et multi-criteria optimization technique. As a result, theaa terminal resource planning, alternatives are evaluated via model and evaluate the where performance of aPNs seaport terminal, large amount of conflicting objectives toare be evaluated pursued invia the Maione et al. (2016) stochastic are used to terminal resource planning, alternatives Maione et al. (2016) where stochastic PNs are used to terminal resource planning, alternatives are evaluated via a al. (2016) where a TPN based modular approach is presented coordinate human activities in intermodal terminals, Dotoli et multi-criteria optimization technique. As a result, proposed approach is useful to evaluate the terminal Maione et human al. (2016) where stochastic terminals, PNs are Dotoli used to terminal resource planning, alternatives are evaluated viathe a coordinate activities in intermodal et multi-criteria optimization technique. As aa result, the coordinate human activities in intermodal terminals, Dotoli et multi-criteria optimization technique. As result, the al. (2016) aa activities TPN based modular approach presented to describe intermodal and identify theiris proposed approach useful to evaluate the terminal performance, performis what-if analyses, and efficiently coordinate human in intermodal terminals, Dotoli et multi-criteria optimization technique. As a result, the al. (2016) where where TPNterminals based modular approach iscriticalities presented proposed approach is useful to evaluate the terminal al. (2016) where a TPN based modular approach is presented proposed approach is what-if useful to evaluateandtheefficiently terminal to intermodal identify their and bottlenecks, et modular al.and where first-order perform analyses, al. (2016) where a Cavone TPNterminals based approach presented performance, proposed approach useful to evaluateand terminal to describe describe intermodal terminals and(2016) identify theiriscriticalities criticalities performance, perform analyses, to describe intermodal terminals and identify their criticalities performance, performis what-if what-if analyses, andtheefficiently efficiently and bottlenecks, Cavone et al. (2016) where first-order to intermodal terminals identifywhere their criticalities anddescribe bottlenecks, Cavone et al. al.and(2016) (2016) where first-order performance, perform what-if analyses, and efficiently and bottlenecks, Cavone et first-order and bottlenecks, Cavone et al. Federation (2016) where first-order Copyright © 2018, 2018 IFAC 398Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International of Automatic Control) Peer review©under of International Federation of Automatic 2018 responsibility IFAC 398Control. Copyright Copyright © 2018 2018 IFAC IFAC 398 10.1016/j.ifacol.2018.07.065 Copyright © 398 Copyright © 2018 IFAC 398

2018 IFAC CTS June 6-8, 2018. Savona, Italy

Graziana Cavone et al. / IFAC PapersOnLine 51-9 (2018) 398–403

399

this is not the case, the third step determines the possible alternative planning solutions by varying the terminal parameters in the TPN model, computes the updated KPIs, and applies the cross-efficiency fuzzy DEA technique to identify the most efficient planning configuration. More in detail, the considered TPN framework of the first step is based on the modular modelling approach proposed in Dotoli et al. (2016) to simulate the terminal dynamics. In the second and third steps of the procedure, the TPN formalism is used to simulate the terminal behavior in case of increases in the commercial flows and determine the specific actions to overcome congestion. To this aim, the TPN formalism is combined with a cross-efficiency fuzzy DEA approach to automatically compare and rank a set of alternatives with heterogeneous operating characteristics under multiple conflicting criteria and under uncertain data. Several Multi-Criteria Decision Making (MCDM) approaches can be used to evaluate different and conflicting alternative resource planning solutions (see, e.g., the reviews by Velasquez and Hester (2013) and by Aruldoss et al. (2013)). In this paper we select the DEA approach since it acknowledges between its advantages its ease of use, robustness, and ability to quantify results, which simplify the analysis (Dotoli et al., 2015). Furthermore, DEA does not require normalized data and is applicable in case of missing data (due to the relevant relations within the variables influencing the terminal behavior) (Dotoli et al., 2015). The choice of DEA also overcomes the typical drawbacks of other MCDM techniques: high subjectivity in the evaluations, high effort required to pre-process and analyse information, and inability to handle missing data (Velasquez and Hester, 2013). Nonetheless, the classical DEA technique has two main weaknesses (Dotoli et al., 2015): 1) it only discriminates between inefficient and efficient alternatives, without further distinguishing among the latter, and 2) it is unable to handle uncertain data. We overcome such limitations by combining the DEA with a cross-efficiency evaluation - to increase the discriminative power - and with fuzzy set theory - to deal with uncertainty without requiring historical data on the terminal performance and without assuming that what happened in the past will occur in future, allowing to get interval solutions, and considering the risk attitude of decision makers.

Fig. 1. Pseudo-code summarizing the proposed procedure. address the resource planning and management of intermodal terminals. The technique is tested on a real intermodal terminal located in Southern Italy that was preliminarily considered in Cavone et al. (2017), where the problem of determining an optimal resource planning is solved using a procedure that is related to that considered in this paper. In particular, in our previous contribution the classical DEA approach is applied instead of the fuzzy version of it. This does not allow to cope with uncertainties in the input data of the simulations used to rank the possible alternatives.

Since the use of the TPN modelling framework for intermodal terminals is not new, we refer the interested reader to the contributions by Dotoli et al. (2016) and Cavone et al. (2017) for details. In the sequel we illustrate the crossefficiency fuzzy DEA approach.

The remainder of the paper is organized as follows: Section 2 describes the proposed approach, Section 3 presents the real case study and discusses the outcomes, Section 4 summarizes the conclusions and proposes possible future developments. The reference list closes the paper.

2.1 The cross-efficiency fuzzy DEA approach Assume there are F alternatives (i.e., terminal plannings) to be evaluated according to n conflicting criteria (i.e., the terminal KPIs), divided into H criteria whose performance index is to be minimized and K criteria whose performance index is to be maximized (H+K=n). Let xh,i be the value of the h-th KPI to be minimized, e.g., the average yard occupation (h=1,…,H), and yk,i the value of the k-th KPI to be maximized, e.g., the average resource utilization (k=1,…,K), both referred to the i-th alternative planning (i=1,...,F). The

2. THE PROPOSED APPROACH The proposed procedure for the efficient resource planning of intermodal terminals is based on three steps (see Fig. 1). First, TPNs are used to model the terminal in its nominal operating conditions. In case of an estimated increase in the commercial flows, the second step allows evaluating whether the available resources are sufficient to avoid congestion. If 399

2018 IFAC CTS 400 June 6-8, 2018. Savona, Italy

Graziana Cavone et al. / IFAC PapersOnLine 51-9 (2018) 398–403

aim of DEA is to maximize the efficiency of each planning alternative (defined as the ratio between the weighted sum of the values of the KPIs to be maximized and that of the KPIs to be minimized) by appropriately determining non-negative weight coefficients of performance indices (uk,i and vh,i), and imposing that the efficiency does not overcome the unitary value (Charnes et al., 1978). However, as already recalled, such a formulation presents some weaknesses. In fact, it allows identifying efficient alternatives among the F available options, but without properly distinguishing among them. The cross-efficiency evaluation allows overcoming such a drawback. In this way, each i-th alternative planning configuration is measured via F relative efficiency values (each one determined with respect to one of the others, including itself). The resulting crossefficiency of the alternative is the mean value of these F relative efficiencies. Hence, a cross-efficiency matrix CE = { Ei0 ,i } ∈ ( ℜ + )FxF is determined, whose generic element

Fig. 2. Graphical meaning of the PIS. estimates on the commercial flows. To overcome such a limitation, uncertain data can be modelled by triangular fuzzy numbers, leading to a cross-efficiency fuzzy DEA approach (Dotoli et al., 2015). Hence, instead of using a single deterministic value xh,i (yk,i) associated with the generic h-th (k-th) KPI and the generic i-th alternative resource planning, a triangular fuzzy number is defined as a triple xɶh ,i = ( xho,i , xhm,i , xhp,i ) ∈ ℜ 3 ( yɶ k ,i = ( ykp,i , ykm,i , yko,i ) ∈ ℜ 3 ) , whose

Ei0 ,i

represents the efficiency of the i0-th alternative calculated with the most favourable weights of the i-th competing alternative planning solution (obtained solving the classical DEA optimization problem), namely: H  K  Ei0 ,i =   uk ,i ⋅ yk ,i0 vh,i ⋅ xh,i0  (1)  h =1  k =1  The efficiency optimization problem, suitably modified to linearize it and guarantee a unique solution, may be expressed as follows (Dotoli et al., 2015): K  F  max  uk ,i ⋅   yk ,i0  (2)   k =1  i0 =1,i0 ≠ i  s.t.: H

v h =1

h,i

K

u k =1

k =1

i

pessimistic value CEip and the modal one, and (c) the maximization of the distance between the optimistic value CEio and the modal one. Note that these goals aim at maximizing the most probable value while increasing the possibility of getting better results (see Fig. 2). Also note that, because of the efficiency definition, each alternative is still evaluated according to all the n conflicting criteria, that is, the terminal KPIs. Therefore, for each planning alternative i, a Positive Ideal Solution (PIS) is defined as the ideal PIS PIS PIS solution (CE1,i , CE2,i , CE3,i ) that simultaneously satisfies these goals, i.e., such that:

(3)

H

k ,i

⋅ yk ,i − Ei  vh ,i ⋅ xh ,i = 0

k ,i

⋅ yk ,i0 −  vh ,i ⋅ xh ,i0 ≤ 0, i0 = 1,.., F (i0 ≠ i )

K

u

 F  ⋅   xh,i0  = 1  i0 =1,i0 ≠i 

values represent the most optimistic, modal, and most pessimistic estimate of the i-th alternative under the h-th (kth) indicator. Such triples can assume different real values with a degree of possibility in the [0,1] range, following suitable membership functions (see Dotoli et al., 2015). Hence, for each i-th alternative planning we determine a fuzzy cross-efficiency CEɶ = (CEip , CEim , CEio ) , i.e., a fuzzy triple whose values are obtained as a trade-off between three conflicting goals: (a) the maximization of the modal value CEim , (b) the minimization of the distance between the

(4)

h =1

H

(5)

h =1

uk ,i , vh ,i ≥ 0, k = 1,..., K , h = 1,..., H .

(6)

m FaPIS ,i = max CEi  PIS m p Fb,i = min[CEi − CEi ]  PIS o m Fc,i = max[CEi − CEi ]

In particular, (2) is the output-oriented linearized form of the maximization of (1), (3) assures that the weighted sum of inputs is equal to 1, constraint (4) imposes the efficiency definition (according to (1)), (5) means that each efficiency value has not to overcome 1, and (6) imposes that the weights assume non-negative values. Solving (2)-(6) for each i-th alternative, variables uk,i and vh,i are determined, so that the corresponding cross-efficiency is computed as: CEi =

1 F

Hence, the PIS cross-efficiencies are obtained as: PIS CEip, PIS = FaPIS ,i − Fb,i  m, PIS = FaPIS CEi ,i  o, PIS PIS = Fa,i + FcPIS CEi ,i

F

E i0 =1

i0 , i

.

(8)

(7)

(9)

The PIS ideal planning alternative is determined solving three problems similar to (2)-(6), where the objective functions are in turn the three equations in (8), and constraints are obtained by appropriately modifying (3)-(6) to cope with the fuzzy character of the terminal’s KPIs (see Dotoli et al. (2015) for details). Since in practice goals (a)-(c) can never be reached

Having determined the cross-efficiency values of all the F alternatives, they can be ranked to determine the most efficient resolution action to be implemented. The above formulation is deterministic, and as such it is not able to cope with uncertain data, which usually arise from 400

2018 IFAC CTS June 6-8, 2018. Savona, Italy

Graziana Cavone et al. / IFAC PapersOnLine 51-9 (2018) 398–403

401

simultaneously by the same weight set, from the PIS of the ith alternative planning a compromise fuzzy cross-efficiency value (CEip , CEim , CEio ) is determined by solving a fuzzy multi-objective linear programming problem as described in Dotoli et al. (2015). The obtained triple is finally defuzzified for each alternative i by determining the center of the area of the corresponding triangular distribution: CEip + CEim + CEio (10) . 3 The F crisp cross-efficiencies are then used to rank the related planning alternatives, i.e., to evaluate under uncertain data and in a multi-objective perspective which planning solution is the most efficient one according to the KPIs. DCEi =

Fig. 3. General scheme of the GTS terminal. due for instance to new contracts. The TPN model is used to evaluate the KPIs in the new scenario (called S100). The results obtained with the current resource planning are reported in Table I (last row), showing a strong reduction in the average free capacity of the yard (the modal value of index FYS drops from 221.70 to 0.95 ITUs), that the yard subareas dedicated to ITUs on the Bologna and Piacenza lines tend to saturate (indices OYB and OYP strongly increase), and that the current resource configuration is unable to cope with the estimated increased flows (the optimistic value of the time before a congestion within the terminal is only TM=506 hours≈21 days). As a consequence, the decision maker is required to analyze the performance of a set of alternative plannings and to identify the most suitable one, in a multicriteria setting (i.e., under conflicting KPIs) and while taking into account the uncertainty that afflicts the estimates.

3. A REAL CASE STUDY In this section we illustrate and test the proposed approach on a real case study. We first introduce the considered intermodal terminal, then we describe the application of the technique to such a terminal and discuss the outcomes. 3.1 The considered intermodal terminal The proposed approach is tested on a real case study, at the General Transport Service S.p.A. (GTS), an intermodal railroad terminal in Bari (Southern Italy). GTS owns about 2,000 ITUs of different types, a fleet of 20 trucks for road transport, 2 cranes, and 280 train wagons. The company has about 700 clients, a yearly turnover of about 85 M€ and a compound annual growth rate of about 40% (GTS, 2016). The terminal description and its TPN model are provided in Cavone et al. (2017), to which we refer interested readers. We just recall here that (see Fig. 3) trucks and trains can enter and exit the terminal via dedicated access roads and railway lines that connect Bari with Bologna or Piacenza (with different service times and timetables) and that the yard is partitioned into five sub-areas: full ITUs from/to Bologna, Piacenza, empty ITUs for all the destinations, final customers, and seaport.

Hence, we apply the third step of the proposed tool. First, the possible planning alternatives are created by progressively increasing the number of resources in use within the terminal. In the GTS terminal the possible actions consist in increasing either the number of cranes, or the frequency of trains, or the number of wagons for each train, or in suitably combining such actions. Clearly, some of these actions are unfeasible (e.g., the number of trains or wagons cannot be increased beyond a certain value) or useless (some actions may not be able to avoid a congestion in less than 90 days), hence all these solutions are not considered. Given a 100% increase of input flows by road, four alternative planning configurations are evaluated (note that this number may be greatly increased by taking more finely granulated choices and all options may be investigated, we avoid this for the sake of brevity):

3.2 Application of the proposed technique The above terminal is modeled using TPNs in Cavone et al. (2017) (the model is not reported here for sake of brevity), proving that, when the terminal operates in nominal conditions (scenario AS-IS), no congestion occurs, i.e., the terminal is well planned. Table I shows the considered KPIs (computed over 100 replications), together with their physical meaning, relative to the nominal operating conditions. For instance, OYB, OYP, OYE, OYFC, and OYPO represent the yard occupation of each sub-area constituting the yard. Such KPIs are selected with the GTS managers as they are the most useful to understand the terminal dynamics (see also Silva et al. (2015)). Note that, since the TPN model is stochastic (see Cavone et al. (2017)), together with the modal values of the KPIs over the 100 replications, also the corresponding pessimistic and optimistic values are reported.

- i=1: the number of cranes is increased from 2 to 5; - i=2: the number of cranes is increased to 3 and the weekly frequency of Bologna trains is increased from 3 to 4; - i=3: the number of cranes is increased to 3 and the number of wagons of each train from/to Bologna is increased from 20 to 25; - i=4: the number of cranes is 3 and the number of wagons of each train from/to Piacenza is increased from 34 to 40. Then, the TPN model is used to simulate the planning alternatives and determine the corresponding KPIs. Evidently, such indices are estimates, hence they are represented as fuzzy triples indicating the most optimistic, the

We assume that a 100% increase in the commercial flows by road is foreseen for a duration of 90 days (i.e., 2,160 hours), 401

2018 IFAC CTS 402 June 6-8, 2018. Savona, Italy

Graziana Cavone et al. / IFAC PapersOnLine 51-9 (2018) 398–403

Table I Most pessimistic, modal, and most optimistic values of the evaluated KPIs under scenarios AS-IS and S100 (over 100 replications). OYB [ITUs]

OYP [ITUs]

Bologna

Piacenza

36.19 20.85 7.80 78.43 64.68 51.63

4.71 3.91 3.41 201.31 183.81 169.73

Alt.

AS-IS

S100

OYE [ITUs]

OYFC [ITUs]

OYPO [ITUs]

empty ITUs

final customers

seaport

1.65 1.33 1.14 1.01 0.53 0.14

1.35 1.28 1.13 0.03 0.02 0.01

1.09 0.93 0.75 0.01 0.01 0.01

yard occupation

Pessimistic Modal Optimistic Pessimistic Modal Optimistic

FYS [ITUs]

min FYS [ITUs]

yard free minimum available space value of FYS

213.81 221.70 228.02 0.48 0.95 1.50

173.56 179.64 184.35 0.00 0.00 0.00

UC [ITUs]

TH [ITUs/h]

TM [h]

cranes utilization

railway outflows

time before congestion

1.12 1.15 1.20 1.29 1.99 2.80

0.17 0.18 0.19 0.13 0.18 0.24

8,322 8,760 9,636 437 460 506

Table II.A Most optimistic, modal, and most pessimistic values of the KPIs to be minimized (h=1,…,7) under alternative resource plannings (i=1,…4). Alt. i=1 i=2 i=3 i=4

OYB [ITUs] xh=1,i (110.35; 118.71; 124.36) (89.11; 100.00; 111.29) (57.53; 61.75; 65.27) (108.26; 110.66; 113.99)

OYP [ITUs] xh=2,i (3.55; 4.56; 5.56) (4.98; 6.15; 8.36) (7.63; 9.77; 11.44) (4.07; 5.11; 6.32)

OYE [ITUs] xh=3,i (2.32; 3.65; 5.76) (2.86; 4.17; 5.13) (4.00; 4.30; 4.65) (3.07; 3.82; 4.82)

OYFC [ITUs] xh=4,i (1.00; 1.13; 1.32) (0.54; 0.64; 0.72) (0.64; 0.71; 0.79) (0.64; 0.67; 0.81)

OYPO [ITUs] xh=5,i (0.37; 0.46; 0.52) (0.35; 0.40; 0.45) (0.33; 0.37; 0.39) (0.08; 0.14; 0.15)

Cost CO2-eq [k€] [t-CO2-eq] xh=6,i xh=7,i (135.59; 150.66; 158.19) (6.91; 8.64; 9.94) (97.44; 108.27; 113.68) (25.44; 31.80; 36.57) (104.76; 116.40; 122.22) (20.74; 25.92; 29.81) (230.27; 244.75; 256.99) (52.85; 59.76; 68.72)

Table II.B Most pessimistic, modal, and most optimistic values of the KPIs to be maximized (k=1,…,6) under alternative resource plannings (i=1,…4). FYS [ITUs] yk=1,i (105.75; 121.48; 141.31) (111.43; 138.62; 168.46) (158.75; 173.10; 197.10) (118.12; 129.40; 144.83)

Alt. i=1 i=2 i=3 i=4

min FYS [ITUs] yk=2,i (6.60; 10.00; 18.33) (12.00; 18.00; 33.60) (86.63; 113.00; 232.78) (3.50; 5.00; 10.00)

UC [ITUs] yk=3,i (2.67; 3.01; 3.44) (1.19; 1.29; 1.41) (1.24; 1.29; 1.35) (1.13; 1.31; 1.44)

Table III Cross-efficiency values and rank for the alternative plannings in Table II. Alt. CEɶ = (CE , CE , CE ) (·10 ) DCEi (∙10 ) p

i

i=1 i=2 i=3 i=4

i

m

o

i

i

(47.85, 65.56, 86.49) (32.75, 49.23, 76.43) (42.58, 65.73, 122.05) (25.70, 31.87, 46.85)

2

2

(1.16; 1.37; 1.63) (1.21; 1.42; 1.71) (1.32; 1.46; 1.67) (1.15; 1.39; 1.61)

TM [h] yk=5,i (2,170; 2,510; 2,515) (2,800; 3,432; 4,200) (2,380; 3,270; 3,812) (2,150; 2,222; 2,500)

Δ [%] yk=6,i (102; 108; 119) (123; 130; 143) (118; 125; 138) (100; 109; 120)

rail), 2) CO2-eq (the increase of greenhouse gases released into the atmosphere due to the additional resources, estimated according to the values in (Ecotransit)), and 3) Δ (the maximum increase in commercial flows that the solution is able to cope with, evaluated thanks to the TPN model). Overall, in the considered case study there are F=4 alternative actions to be evaluated according to n=13 KPIs. Table II.A shows the H=7 KPIs to be minimized (e.g., the yard occupation) and Table II.B reports the K=6 indices to be maximized (e.g., the free available space in the yard).

rank

66.64 52.80 76.79 34.81

TH [ITUs/h] yk=4,i

2 3 1 4

Because of the many conflicting indices to take into account, a comparison of the possible alternative planning solutions by simply simulating the terminal functioning via the TPN model is not trivial (as can be seen by analyzing the values of the KPIs in Tables II.A and II.B). Hence, the cross-efficiency fuzzy DEA approach is applied to compare and rank the planning alternatives and identify the most appropriate action among the multiple available ones. Table III shows the obtained DCEi values and the final ranking for the considered alternative planning solutions. These results are also graphically depicted in Fig. 4. The planning configuration i=3 results to be the most efficient alternative, providing the best compromise between the conflicting objectives of the KPIs. In fact, this planning solution not only avoids congestion within the terminal for more than 90 days (TM=2,380 hours≈99 days in the pessimistic estimate), but it also provides, with respect to the other scenarios, the highest value of FYS (i.e., the highest average free available space in the yard storage area), as well as the highest value of the min FYS parameter, meaning that,

Fig. 4. Fuzzy cross-efficiencies of the alternatives modal, and the most pessimistic value among those obtained via 100 replications. In addition, in accordance with the GTS managers, three further indices are estimated together with the original KPIs, since they affect the evaluation of the best resource planning: 1) Cost (the additional cost for the corresponding investment in new resources, obtained considering the average rental cost for cranes and the salary of a crane operator, or the contract for carriage of goods by 402

2018 IFAC CTS June 6-8, 2018. Savona, Italy

Graziana Cavone et al. / IFAC PapersOnLine 51-9 (2018) 398–403

under such scenario, the yard storage area is never saturated for the estimated duration of the flows increase. Furthermore, scenario i=3 also presents good values for the Cost and the CO2-eq KPIs, and is able to cope with even stronger increases in the foreseen commercial flows (Δ∈[118, 138] in the last column of Table II.B).

403

Future work will consider the use of high-level Petri nets for more compact and intuitive models and of the reinforcement learning to rapidly identify the best planning action. REFERENCES Aruldoss, M., Miranda Lakshmi, T., Prasanna Venkatesan, V. (2013). A survey on Multi Criteria Decision Making Methods and its applications, Am J Inf Sys, 1(1): 31-43. Caris, A., Macharis, C., Janssens, G.K. (2013). Decision support in intermodal transport: A new research agenda, Comput Ind, 64(2): 105-112. Cartenì A. and de Luca S. (2012). Tactical and strategic planning for a container terminal: Modeling issues within a discrete event simulation approach, Simulat Model Pract Theor, 21: 23-45. Cavone, G., Dotoli, M., Seatzu, C. (2016). Management of intermodal freight terminals by First-Order Hybrid Petri Nets, Rob Aut Lett, 1(1): 2-9. Cavone, G., Dotoli, M., Epicoco, N., Seatzu, C. (2017). Intermodal terminal planning by Petri Nets and Data Envelopment Analysis, Control Eng Prac, 69: 9-22. Charnes, A., Cooper, W.W., Rhodes, E. (1978). Measuring the efficiency of Decision Making Units, Eur J Oper Res, 2: 429-444. Di Febbraro, A., Sacco, N., Saeednia, M. (2016). An agentbased framework for cooperative planning of intermodal freight transport chains, Transp Res C, 64: 72-85. Dotoli, M., Epicoco, N., Falagario, M., Sciancalepore, F. (2015). A cross-efficiency fuzzy Data Envelopment Analysis technique for performance evaluation of decision making units under uncertainty, Comput Ind Eng, 79: 103-114. Dotoli, M., Epicoco, N., Falagario, M., Cavone, G. (2016). A Timed Petri Nets model for performance evaluation of intermodal freight transport terminals, IEEE Trans Autom Sci Eng, 13(2): 842-857. Ecotransit, at http://www.ecotransit.org/calculation.en.html. GTS, at http://www.gtslogistic.com/en/integratedreport2016. Hangga, P. and Shinoda, T. (2017). A Petri Net model and its simulation for straddle carrier direct-system operation in a container terminal, Appl Mech Mater, 862: 202-207. Li, L., Negenborn, R.R., De Schutter, B. (2015). Intermodal freight transport planning - A receding horizon control approach. Transp Res C, 60: 77-95. Maione, G., Mangini, A.M., Ottomanelli, M. (2016). A generalized stochastic Petri Net approach for modeling activities of human operators in intermodal container terminals, IEEE Trans Autom Sci Eng, 13(4): 1504-1516. Silva, C.A., Guedes Soares, C., Signoret, J.P. (2015). Intermodal terminal cargo handling simulation using Petri Nets with predicates, J Eng Marit Env, 229(4): 323339. SteadieSeifi, M., Dellaert, N.P., Nuijten, W., Van Woensel, T., Raoufi, R. (2014). Multimodal freight transportation planning: A literature review, Eur J Oper Res, 233: 1-15. Velasquez, M. and Hester, P.T. (2013). An analysis of MultiCriteria Decision Making methods, Int J Oper Res, 10(2): 56-66.

The above results demonstrate the effectiveness of the presented approach in supporting the planning decision making process of intermodal terminals. In particular, the procedure allows to take into account possible errors in the preliminary estimates, and therefore the most efficient planning configuration is also robust to possible data imprecisions. In fact, the obtained interval solutions are wide and the defuzzified values of the cross-efficiencies are far away from the bounds of the corresponding intervals (i.e., small changes in the evaluation parameters would not lead to relevant changes in the final assessment). It is also important to remark that, although the value of the DCE3 is 76.79, thanks to the PIS formulation in eq. (8), there is a high possibility of getting better results (see Fig. 4). In fact the pessimistic value is CE =42.58, while the optimistic value is CE =122.05. In addition, since the adopted formulation provides interval solutions, the outcomes reflect the inherent uncertainty of the decision making process. Therefore, the presented procedure directly considers the decision maker’s judgments and takes into account his specific risk attitude and the adopted policy. In fact, since interval numbers have more information than crisp numbers, the proposed method allows to make wiser and more logical decision when planning the resource investments in intermodal terminals. p

i

o

i

We conclude this section remarking that the comparison and ranking of the planning alternatives just requires about 8 seconds (on a PC with an Intel Core 2 Duo-2.80 GHz processor and 4 Gb RAM, using the GLPK optimizer in the MATLAB environment) once all TPN simulations are performed (the computation time of each replication is 80 seconds in the worst case). Therefore, the approach also allows to rapidly perform what-if analyses, and represents a useful tool to help decision makers gain insights into the interactions among the various functioning conditions and resources availability in the terminal and the corresponding obtained performance, as well as between investments cost and risk of inefficiencies. 4. CONCLUSIONS AND FUTURE DEVELOPMENTS This paper proposes a technique for the optimal management and planning of intermodal terminals under uncertainty. The approach combines the timed Petri net formalism and the cross-efficiency fuzzy Data Envelopment Analysis technique, allowing decision makers to: 1) model the terminal’s behavior, 2) analyze its performance in the nominal operating conditions, 3) identify possible bottlenecks and waste sources, 4) perform what-if analyses and cost-benefit evaluations to identify the most efficient resolution actions to such critical situations. All these investigations are carried out in a multi-objective perspective while taking into account the uncertainty in estimates. The effectiveness of the approach is shown by a real case study analysis. 403