A Survey on Reviewer Assignment Problem 723 from the corresponding category, and matching degrees are acquired by a computa- tion mechanism set by organizer [20]. The above computation methods are raised as increasing matching degree, which is appropriate to the optimizations of maximizing utility. In fact, the smaller value for higher preference, with the evaluation on the converse way, so as to be adapted for minimum optimization. With the"matching degree"matrix C, a binary variable xi, whose value is I if manuscript i is assigned to reviewer j and 0 otherwise, is brought to present the integer programming(IP) formulation of the RAP(here we take the increasing match ing degree as example) max x ∑号=a1 x≤b x 0 or 1 Note that constraint (4) along with(5)force that reviewer would not be assigned to a manuscript whenever ci is smaller than the given threshold T.However, some conference chairs just require that at least one assigned reviewer is exactly expert for that manuscript, constraint(6) instead of(4), is brought into the mathematical model to ensure that at least one reviewer whose matching degree for manuscript i is greater than or equal to T[20 max{cnxn}≥T In case the above model does not have a feasible solution or takes too much run ing-time, the formulation will be reformed as a multi-objective(7) by relaxing con- strains(2)and (3). The parameter a>0 is the penalty weight for missing reviewers (a=0.5 in the work of [23]), and B20 is for reviewers'over-workload(B is set to be o when the over-workload problem is not taken into consideration). These two free control parameters enable us to freely shape the solution structure. Once an opti- mal/feasible solution is found, the assignment procedure comes to the end, otherwiseA Survey on Reviewer Assignment Problem 723 from the corresponding category, and matching degrees are acquired by a computa￾tion mechanism set by organizer [20]. The above computation methods are raised as increasing matching degree, which is appropriate to the optimizations of maximizing assignment utility. In fact, the matching degree ij c can easily be transformed as smaller value for higher preference, with the evaluation on the converse way, so as to be adapted for minimum optimization. With the “matching degree” matrix C , a binary variable ij x , whose value is 1 if manuscript i is assigned to reviewer j and 0 otherwise, is brought to present the integer programming (IP) formulation of the RAP (here we take the increasing match￾ing degree as example): 1 1 max p r ij ij i j c x = = ∑∑ (1) Subject to 1 r ij i j x a = ∑ = (2) 1 p ij j i x b = ∑ ≤ (3) ij ij c x T ⎢ ⎥ ≤ ⎢ ⎥ ⎣ ⎦ (4) 0 1 ij x or = (5) Note that constraint (4) along with (5) force that reviewer would not be assigned to a manuscript whenever ij c is smaller than the given threshold T . However, some conference chairs just require that at least one assigned reviewer is exactly expert for that manuscript, constraint (6) instead of (4), is brought into the mathematical model to ensure that at least one reviewer whose matching degree for manuscript i is greater than or equal to T [20]. { } 1 max ij ij j r cx T ≤ ≤ ≥ (6) In case the above model does not have a feasible solution or takes too much run￾ning-time, the formulation will be reformed as a multi-objective (7) by relaxing con￾strains (2) and (3). The parameter α > 0 is the penalty weight for missing reviewers ( 5 α = 0. in the work of [23]), and β ≥ 0 is for reviewers’ over-workload ( β is set to be 0 when the over-workload problem is not taken into consideration). These two free control parameters enable us to freely shape the solution structure. Once an opti￾mal/feasible solution is found, the assignment procedure comes to the end, otherwise