timing and frequency conﬁguration ying both these balances. We can succinctly write this misation problem as the following nonlinear integer am: maximise X F( X , C , s, r, d) subject to Â xi2 X xi N, X ✓ ZS + . ( 3 . 6 ) The broadcast scheduling problem as a nonlinear integer program. orm of the program reveals that it is an instance of onlinear knapsack problem1. Our speciﬁc objective 1 Kurt M Bretthauer and Bala Shetty. The nonlinear knapsack problem– algorithms and applications. European Journal of Operational Research, 2002 ion is non-separable: it cannot be decomposed into a r combination of functions gi(xi), separate for each nsion. Additionally, it is nonconcave in general over Nonlinear Knapsack Problem (Bretthauer, European Journal of Operational Research, ’02) The objective is non-separable, non-concave, non- quasiconcave. Our Approach An Optimisation Problem ptimal schedule maximises attention potential by ng the perfect post timing and frequency conﬁguration ying both these balances. We can succinctly write this misation problem as the following nonlinear integer am: maximise X F( X , C , s, r, d) subject to Â xi2 X xi N, X ✓ ZS + . ( 3 . 6 ) The broadcast scheduling problem as a nonlinear integer program. orm of the program reveals that it is an instance of onlinear knapsack problem1. Our speciﬁc objective 1 Kurt M Bretthauer and Bala Shetty. The nonlinear knapsack problem– algorithms and applications. European Journal of Operational Research, 2002 ion is non-separable: it cannot be decomposed into a r combination of functions gi(xi), separate for each nsion. Additionally, it is nonconcave in general over Essentially greedy hill-climbing, can be combined with random restarts. The form of the program reveals that it is an instance of the nonlinear knapsack problem1. Our speciﬁc objective 1 Kurt M Bretthauer and The nonlinear knapsack algorithms and applicati Journal of Operational Res function is non-separable: it cannot be decomposed into a linear combination of functions gi(xi), separate for each dimension. Additionally, it is nonconcave in general over the reals. This places the problem outside the realm for which efﬁcient general algorithms have been devised. Greedily exploring the discrete state space is a common local optimisation strategy. For constrained integer pro- grams, greedy algorithms are typically applications of the method of marginal allocation. When adapted to our prob- lem, this corresponds to the following algorithm: Algorithm 1 : Marginal Allocation Input : Constraint N, initial solution X 0 2 ZS + begin Y X 0 D 0 repeat i argmaxk F( Y + e k) F( Y ) Y prev Y Y Y + e i D Y Y prev until D 0 or Ây2 Y y > N return Y prev end e k 2 ZS + is the kth unit v In each iteration, the al a single post to the slot w the maximum increase in function value. It termin adding a post to any slo the total intended posts does not improve the ob value. Essentially, this is a hil algorithm starting from solution and is guarante at an optimum, which m