School Systems and Optimization

Christopher Dylan Suruadji’s Lumiere research asks how schools should divide organic-waste treatment between local facilities and shared infrastructure. The draft compares 231 capacity configurations across 10,000 paired weekly scenarios. Its leading hybrid places 20% of nominal capacity at a shared facility and installs 25% reserve. The reported simulated failure rate is 2.25% with mean untreated collection of 2.47 kg per week and mean weekly cash cost of IDR 3.750 million.

The study is titled Reliability-Constrained Capacity Planning for School Organic-Waste Networks Under Uncertainty. Its eight-school design network includes a possible local unit at each school with a possible shared facility. Each period is a five-day school week. The input boundary is collected organic material after visibly unsuitable material is rejected. Plastic collection and recycled product counts are recorded separately from this organic-waste model.

Weekly processable collection combines the contributing population with daily organic-waste generation and participation. The rejected fraction is then removed. In the equations N is the contributing population and g is kilograms per person per day. Participation p and rejection r are fractions between zero and one. Multiplication by five converts the daily rate to a school week. This gives q for each school in each weekly scenario.

The first decision is installed capacity. If mean weekly processable demand is μ and reserve is ρ then total rated capacity is (1 + ρ) × μ. A shared fraction θ assigns θ of that total to the shared facility. For the reported hybrid this gives total capacity of 1.25 × μ with shared capacity of 0.25 × μ and aggregate local capacity of 1.00 × μ. Configurations at the same reserve level have equal total rated capacity so the comparison isolates where capacity is placed.

The second decision is the weekly allocation. Each school’s processable collection equals the mass sent to facilities plus the mass left untreated. For each facility the incoming allocation cannot exceed installed capacity multiplied by its available fraction. A disruption changes this available fraction. All allocation and untreated-mass variables are nonnegative. These balances prevent a model from reporting treatment that its facilities cannot deliver.

The planning objective combines weekly-equivalent capacity expenditure with mean operating expenditure and a penalty for untreated material. The shortfall penalty λ has units of IDR per untreated kilogram. It represents the service consequence used to rank designs. Cash expenditure remains a separate measure. The draft’s IDR 3.750 million per week is the reported cash cost for the leading hybrid rather than the value of the full penalty-based objective.

Reliability is the probability that any processable collection remains untreated in a week. The sampled failure rate divides the number of such weeks by the 10,000 evaluated weeks. A feasible design must keep this rate below 10%. It is a frequency measure rather than the percentage of collected mass left untreated. The same weekly scenarios are used for every configuration with shared collection fluctuations and facility disruptions included.

The selected local design needs 80% reserve to pass the sampled reliability criterion. The selected shared-only design passes with 20% reserve but leaves 28.75 kg untreated per week on average. The selected hybrid’s 2.47 kg is about 91.4% lower than that shared-only result. This comparison follows directly from 1 − 2.47 / 28.75. For the hybrid the ratio 2.47 / 0.0225 also implies about 109.8 kg untreated during a failed week. Both calculations use rounded draft values. They explain why failure frequency should be read alongside failure severity.

Environmental accounting uses a common weekly boundary. Net avoided emissions equal the disposal baseline minus emissions from transport and treatment with residual disposal included. A transport factor expressed per kilogram-kilometre is multiplied by the transported mass and route distance. Requiring a minimum level of expected avoided emissions adds another constraint to the feasible designs. The accounting record below defines these terms and units without substituting an undocumented carbon factor.

To improve the design the study compares feasible configurations by their planning objective and then examines sensitivity to collection variability and shared fluctuations as well as facility disruptions. The leading hybrid has only a narrow objective advantage over another feasible hybrid. The collection inputs and cost coefficients therefore need calibration alongside availability records. Validation with a further independent set of 10,000 scenarios remains planned in the supplied methods. The decision to deploy would follow that check and site-specific capacity measurements.

Kuznetsova et al. (2019). Integrated decision-support methodology for combined centralized-decentralized waste-to-energy management systems design. Renewable and Sustainable Energy Reviews 103: 477–500. https://doi.org/10.1016/j.rser.2018.12.020. This reference informs the comparison of local and shared infrastructure. The Green Soldier results reported here come from the supplied Lumiere draft.