Mand place to its nearest chosen port, as shown in Figure four. every single island is explicUnder this alternative disaggregated scheme, the total GTC for It might be shown that any effective option is equivalent toallocationassignment scheme that all inhabitants may perhaps itly computed determined by the actual a greedy with the demands to the chosen ports. The adhere to. Note that this figure presents an example of a part to a comprehensive feasible solution proposed model contains more variables compared of the prior Approximated (ground transportation element). representation. Model but delivers a superior problemFigure 4. Instance of demand location COTI-2 MDM-2/p53 assignments towards the chosen ports inside the islands. Figure four. of demand place assignments towards the chosen ports inside the islands.Under this Formulation considers thescheme, theof theGTC for just about every island is explicThe Precise option disaggregated definition total following additional parameitly computed based on the actual allocation on the demands for the selected ports. The ters and choice variables: proposed model Birinapant manufacturer consists of added variables every single islandto the previous Approximated Mh: Set of demand places belonging to compared h; Modelil: Distance among port i and demand place l; d but delivers a superior issue representation. The Precise Formulation considers the definition of your following extra parameters ql: Demand of place l; and choice variables: indicating if demand location l is allocated to node i. il: Binary variable Mh : Set thedemand locations belonging toinformation h; each particular demand locaDue to of absence of freight generation each island for dil : Distance in between port i and demand place l; tion, it is actually assumed that the total demand of an island is homogeneously split among all ql : Demand of place l; demand areas, as ql = Qh/|Mh|, hH, lMh. Notice that this assumption will not il : Binary variable indicating if demand location l is allocated to node i. Because of the absence of freight generation info for each certain demand place, it can be assumed that the total demand of an island is homogeneously split among all demand locations, as ql = Qh /|Mh |, h H, l Mh . Notice that this assumption does not have an effect on the structure of the Exact Formulation, given that ql is only a parameter on the model that may be computed following any other info or assumption. Consequently, the novel Exact Formulation with the BO-InTSP is as (14) to (27). Expressions (14) and (15) correspond to the MTC and GTC objective functions, respectively. MTC could be the very same as the Approximated Model, whereas GTC corresponds to a brand new Exact Formulation determined by demand location assignment choices. Constraints (16)18) are new constraints that allow for computing GTC in an exact manner. Constraints (16) ensure that at the very least 1 port is chosen for every island. Constraints (17) assure that each and every demand place is assigned to a single port, and restrictions (18) let for assignment decisions (ij)Mathematics 2021, 9,8 ofonly involving chosen ports (Zi = 1). Expressions (19)24) are routing-related constraints, and are equivalent to Equations (six)11). Ultimately, Constraints (25)27) are of domain. Mini,j N0 ,j =iMCij Yij(14)Minh H i h l Mhdil ql il(15)i hsubject to : Zi0 = 1 Zi 1 il =h H(16) (17) (18) (19) (20) (21)i hh H, l Mh h H, l Mh , i hil Zij N:i = jYij = Zi Yji = Zii N i Nj N:j =ij NFi0 j = Zjj N j N0 /i = jj N0 /i = jFij =Fji Zii N(22) (23) (24) (25) (26) (27)j NFji0 =i, j.