Optimization: Capacity

Purpose

This calculator allocates limited resource capacity against required demand, minimizing allocation cost plus shortage penalty.

It helps you answer a hard but common question: when you can't fully cover every requirement, which shortfalls should you accept, and how should the capacity you do have be allocated to keep total cost as low as possible?

Background

Problem Domain

Capacity optimization is useful when resources may be insufficient and you need the least-cost allocation/shortage tradeoff. It formalizes a decision many teams make instinctively under pressure — which shortfalls are cheapest to accept — by putting an explicit price on unmet demand instead of leaving it as an unplanned surprise.

Real-World Uses

• Production capacity planning: Peak demand can exceed available machine or line capacity. Use the model to allocate capacity at least cost and quantify unavoidable shortfalls.
• Staffing across departments: Staff-hours are limited and service requests compete for the same pool. Use the model to allocate effort and measure shortfalls with penalty impact.
• Utility/resource allocation: Finite supply (power, water, bandwidth) must cover required loads. Use the model to create a cost-minimizing dispatch with explicit unmet-demand quantities.
• Service commitment planning: Committed workloads across resources may not all be fully fulfillable. Use the model to prioritize allocations using cost and shortage-penalty tradeoffs.

Inputs

• capacity_object: Input table with columns Resource, Available, Required, and Unit Cost. Available and Required must use the same quantity units, and Unit Cost is interpreted per one quantity unit.
• capacity_qty_type: Allocation/shortage quantity type. Use continuous for fractional quantities or integer for whole numbers.
• shortage_penalty: Penalty cost applied per unit of shortage in the same quantity basis as Required.
• show_zero: Controls output display. Turn on to include rows with zero allocation/shortage; turn off to focus on active rows.

Results

• Summary: Aggregate fulfillment outcome with required, allocated, shortage, and Fulfillment %. This quickly shows whether you can meet demand or must accept shortfalls.
• Decision Table: Resource-level allocation details (Required, Available, Allocated, Shortage, Unit Cost) to guide operational adjustments.
• Constraint Slack: Slack on availability and requirement-balance constraints, highlighting where capacity pressure is limiting service levels.

Understanding the Calculation

Objective:

• Minimize $\sum_r (\text{UnitCost}_r\,\text{Alloc}_r + \text{Penalty}\,\text{Short}_r)$.

Constraints:

• $\text{Alloc}_r \le \text{Available}_r$
• $\text{Alloc}_r + \text{Short}_r = \text{Required}_r$
• Non-negativity (and integer if selected).

Example

Default run returns Optimal with objective 1060, Total Shortage = 0, and Fulfillment % = 100%.

Interpretation: available capacity is sufficient, so all requirements are met without shortage penalties. Try lowering Available on one resource and re-running — you'll see exactly how much shortage the model accepts before it becomes cheaper than paying for more capacity.

Important Assumptions and Limitations

• Independent resources (no substitution logic between resources).
• Linear costs and penalties.
• No minimum-run, setup, or temporal constraints.