The “Traveling Musician” Problem
As Semester 1 draws to a close at Parvis School of Economics and Music, the distinctions between the Department of Economics and the Conservatory continue to blur. This week, the capstone presentation for the “ECON305: Logistics & Operations Research” module offered a fascinating case study in why mathematical efficiency does not always equal artistic success.
The assignment was deceptively simple: Design a mathematically optimal 12-city national tour for a 65-piece symphony orchestra, minimising travel costs and venue hire fees while maximising ticket revenue. The dataset included real-world constraints from New Zealand’s geography, including the notoriously variable Cook Strait ferry schedules and regional flight capacities.
The MILP Model: Efficiency at a Cost
The winning student team, “Vector Harmony,” utilised a Mixed-Integer Linear Programming (MILP) model run on the Gurobi optimiser to solve this variation of the classic “Traveling Salesman Problem.”
Their proposed itinerary was a triumph of computational logic. By routing the tour through non-linear zig-zags between Napier, Palmerston North, and Wellington, and utilising off-peak travel windows (often between 11:00 PM and 5:00 AM), the model slashed the theoretical budget by an impressive 18% compared to the standard touring schedule used by national bodies.
“The math was irrefutable,” remarked Dr. Percival Thorne, Head of Economics. “On paper, they saved the hypothetical arts council nearly fifty thousand dollars in fuel and accommodation.”
The Biological Constraint
However, the project faced a brutal critique from the Music Faculty panel. While the economists had solved the financial equation, they had neglected the physiological equation.
Dr. Elara Vance pointed out that the model’s reliance on “red-eye” travel and back-to-back performances violated the fundamental limits of human endurance, specifically “embouchure fatigue”—the breakdown of facial muscles in brass and woodwind players.
“You have scheduled a performance of Wagner’s Die Walküre in Dunedin exactly four hours after a bus ride from Christchurch,” Dr. Vance noted during the defence. “While geographically possible, the French Horn section would be physically unable to hit a high C. You have optimised the budget, but you have destroyed the product.”
The “Double Bass” Variable
Furthermore, the model exposed a critical lack of practical knowledge regarding instrumentation. The algorithm had booked regional turbo-prop flights to reduce travel time to Nelson. However, the students failed to account for the cargo hold dimensions of the Bombardier Q300 aircraft used on these routes.
“An algorithm does not know that a double bass in a flight case is simply too wide for the cargo door of a regional plane,” explained Arts Management lecturer Hamish McDuff. “The model stranded the entire rhythm section on the tarmac in Wellington while the rest of the orchestra flew to Nelson. In logistics, geometry is just as important as algebra.”
The Pareto Efficient Compromise
Forced to revisit their code, the student team introduced a new variable: the “Fatigue Coefficient.” They assigned a negative utility value to any travel occurring before 9:00 AM and added hard constraints regarding instrument cargo dimensions.
The revised model, presented yesterday, was 12% more expensive than their initial attempt but was deemed “artistically viable.” It replaced the risky flights with a chartered ferry crossing and added mandatory rest days following heavy repertoire.
Conclusion: The Human Factor
The ECON305 project serves as a microcosm of the Parvis philosophy. It demonstrated that while data science can drive decision-making, it cannot replace domain-specific expertise.
“We learned that an orchestra is not a package to be delivered,” concluded the student team leader in their final report. “It is a biological organism that requires sleep, hydration, and oversized luggage allowances.”
The revised itinerary has been open-sourced and offered to local arts organisations as a template for sustainable tour planning in a post-recession economy.
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