Table 1 Notation for the MILP model... | Emerald Publishing

Table 1

Notation for the MILP model

Indices and sets	Description
$A = {A_{1}, A_{2}, \dots, A_{w}}$ ⁠:	Set of w available advisors, indexed by a
$M = {M_{1}, M_{2}, \dots, M_{x}}$ ⁠:	Set of x students’ majors, indexed by m
$S = {S_{1}, S_{2}, \dots, S_{y}}$ ⁠:	Set of y students, indexed by s
$C = {C_{1}, C_{2}, \dots, C_{z}}$ ⁠:	Set of z students’ classes, indexed by c

Indices and sets	Description
$A = {A_{1}, A_{2}, \dots, A_{w}}$ :	Set of w available advisors, indexed by a
$M = {M_{1}, M_{2}, \dots, M_{x}}$ :	Set of x students’ majors, indexed by m
$S = {S_{1}, S_{2}, \dots, S_{y}}$ :	Set of y students, indexed by s
$C = {C_{1}, C_{2}, \dots, C_{z}}$ :	Set of z students’ classes, indexed by c

Parameters	Description
${S M}_{s m}$ ⁠:	Binary student-major allocation matrix, where ${S M}_{s m}$ = 1if student s belongs to major m, otherwise 0
${S C}_{s c}$ ⁠:	Binary student-class allocation matrix, where ${S C}_{s c}$ = 1 if student s possesses class c, otherwise 0
$P_{a m}$ ⁠:	Advisor a’s preference ranking for major m, with lower values indicating higher preference
${A T L}_{a}$ ⁠:	Average total number of students per advisor a
${A L C}_{a c}$ ⁠:	Average number of students with class c per advisor a

Parameters	Description
${S M}_{s m}$ :	Binary student-major allocation matrix, where ${S M}_{s m}$ = 1if student s belongs to major m, otherwise 0
${S C}_{s c}$ :	Binary student-class allocation matrix, where ${S C}_{s c}$ = 1 if student s possesses class c, otherwise 0
$P_{a m}$ :	Advisor a’s preference ranking for major m, with lower values indicating higher preference
${A T L}_{a}$ :	Average total number of students per advisor a
${A L C}_{a c}$ :	Average number of students with class c per advisor a

Decision variables	Description
${S A}_{s a}$ ⁠:	Binary variable where ${S A}_{s a}$ = 1 if student s is assigned to advisor a, otherwise 0
${M A}_{m a}$ ⁠:	Binary variable where ${M A}_{m a}$ = 1 if major m is assigned to advisor a, otherwise 0
$α_{a}^{T L +}$ , $α_{a}^{T L -}$ ⁠:	Positive continuous variables measuring deviations from the average total caseload per advisor
$α_{a c}^{C L +}$ , $α_{a c}^{C L -}$ ⁠:	Positive continuous variables measuring deviations from the average number of students per advisor within each risk- and class-category

Decision variables	Description
${S A}_{s a}$ :	Binary variable where ${S A}_{s a}$ = 1 if student s is assigned to advisor a, otherwise 0
${M A}_{m a}$ :	Binary variable where ${M A}_{m a}$ = 1 if major m is assigned to advisor a, otherwise 0
$α_{a}^{T L +}$ , $α_{a}^{T L -}$ :	Positive continuous variables measuring deviations from the average total caseload per advisor
$α_{a c}^{C L +}$ , $α_{a c}^{C L -}$ :	Positive continuous variables measuring deviations from the average number of students per advisor within each risk- and class-category