Music Festival Schedule Optimizer
Music Festival Schedule Optimizer creates an optimal schedule for a music festival by assigning bands to stages and time slots to maximize attendee satisfaction based on band popularity and stage capacity, with a detailed breakdown.
Formulas Used in Music Festival Schedule Optimizer
The calculator uses the following formulas to optimize the festival schedule:
Satisfaction Score for Assignment:
\\[ S_{i,j,k} = P_i \cdot C_j \\]Total Satisfaction:
\\[ S_{\text{total}} = \sum_{i,j,k} S_{i,j,k} \cdot x_{i,j,k} \\]Constraints:
- Each band plays at most once: \\( \sum_{j,k} x_{i,j,k} \leq 1 \ \forall i \\)
- Each stage-time slot has at most one band: \\( \sum_i x_{i,j,k} \leq 1 \ \forall j,k \\)
- Band availability: \\( x_{i,j,k} = 0 \\) if band \\( i \\) unavailable at slot \\( k \\)
Where:
- \\( S_{i,j,k} \\): Satisfaction score for band \\( i \\) on stage \\( j \\) at time slot \\( k \\)
- \\( P_i \\): Popularity score of band \\( i \\) (0 to 100)
- \\( C_j \\): Capacity of stage \\( j \\) (attendees)
- \\( x_{i,j,k} \\): Binary variable (1 if band \\( i \\) is assigned to stage \\( j \\) at slot \\( k \\), 0 otherwise)
- \\( S_{\text{total}} \\): Total satisfaction score
Example Calculations
Example 1: Small Festival
Input: Bands = [BandA,80,1-2,BandB,60,1-2,BandC,40,2], Stages = [MainStage,1000,SmallStage,500], Time Slots = 2
Sort bands by popularity: BandA (80), BandB (60), BandC (40)
Assign BandA to MainStage, slot 1: \\( S = 80 \cdot 1000 = 80,000 \\)
Assign BandB to SmallStage, slot 1: \\( S = 60 \cdot 500 = 30,000 \\)
Assign BandC to MainStage, slot 2: \\( S = 40 \cdot 1000 = 40,000 \\)
\\[ S_{\text{total}} = 80000 + 30000 + 40000 = 150,000 \\]Result: Schedule = [BandA,MainStage,1; BandB,SmallStage,1; BandC,MainStage,2], Total Satisfaction = 150,000
Example 2: Medium Festival
Input: Bands = [BandA,90,1-3,BandB,70,2-3,BandC,65,1-2,BandD,50,1-3,BandE,30,3], Stages = [MainStage,2000,MediumStage,1000,SmallStage,300], Time Slots = 3
Sort bands: BandA (90), BandB (70), BandC (65), BandD (50), BandE (30)
Assign BandA to MainStage, slot 1: \\( S = 90 \cdot 2000 = 180,000 \\)
Assign BandB to MainStage, slot 2: \\( S = 70 \cdot 2000 = 140,000 \\)
Assign BandC to MediumStage, slot 1: \\( S = 65 \cdot 1000 = 65,000 \\)
Assign BandD to SmallStage, slot 1: \\( S = 50 \cdot 300 = 15,000 \\)
Assign BandE to MainStage, slot 3: \\( S = 30 \cdot 2000 = 60,000 \\)
\\[ S_{\text{total}} = 180000 + 140000 + 65000 + 15000 + 60000 = 460,000 \\]Result: Schedule = [BandA,MainStage,1; BandB,MainStage,2; BandC,MediumStage,1; BandD,SmallStage,1; BandE,MainStage,3], Total Satisfaction = 460,000
Example 3: Large Festival
Input: Bands = [BandA,95,1-5,BandB,85,2-4,…,BandJ,20,4-5], Stages = [MainStage,5000,Stage2,3000,Stage3,1500,SmallStage,500], Time Slots = 5
Sort bands: BandA (95), BandB (85), …, BandJ (20)
Assign BandA to MainStage, slot 1: \\( S = 95 \cdot 5000 = 475,000 \\)
Assign BandB to MainStage, slot 2: \\( S = 85 \cdot 5000 = 425,000 \\)
…
Assign BandJ to SmallStage, slot 4: \\( S = 20 \cdot 500 = 10,000 \\)
\\[ S_{\text{total}} \approx 1,900,000 \\]Result: Total Satisfaction ≈ 1,900,000 (full schedule in output)