perf(staffing): replace day-by-day capacity loop with range arithmetic

Eliminates O(resource × allocation × days) iteration in findCapacityWindows
by pre-computing vacation date sets and using direct range overlap math.
Adds performance regression test (50 resources × 20 allocs × 365 days < 500ms).

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

packages/staffing/src/__tests__/capacity-analyzer-perf.test.ts

@@ -0,0 +1,97 @@
+import { AllocationStatus } from "@capakraken/shared";
+import { describe, expect, it } from "vitest";
+import { findCapacityWindows, analyzeUtilization } from "../capacity-analyzer.js";
+import type { CapacityAnalysisInput } from "../capacity-analyzer.js";
+
+const standardAvailability = {
+  sunday: 0,
+  monday: 8,
+  tuesday: 8,
+  wednesday: 8,
+  thursday: 8,
+  friday: 8,
+  saturday: 0,
+};
+
+/**
+ * Performance regression test.
+ * 50 resources × 20 allocations × 365 days must complete in under 500 ms.
+ */
+describe("capacity-analyzer performance", () => {
+  it("analyzeUtilization: 50 resources × 20 allocations × 365 days < 500 ms", () => {
+    const analysisStart = new Date("2026-01-01");
+    const analysisEnd = new Date("2026-12-31");
+    const periodMs = analysisEnd.getTime() - analysisStart.getTime();
+
+    const resources: CapacityAnalysisInput[] = Array.from({ length: 50 }, (_, ri) => {
+      const allocations = Array.from({ length: 20 }, (_, ai) => {
+        // Distribute allocations pseudo-randomly across the year
+        const offset = Math.floor(((ri * 20 + ai) / 1000) * periodMs);
+        const start = new Date(analysisStart.getTime() + offset);
+        const end = new Date(start.getTime() + 30 * 24 * 60 * 60 * 1000); // 30-day blocks
+        return {
+          startDate: start > analysisEnd ? analysisStart : start,
+          endDate: end > analysisEnd ? analysisEnd : end,
+          hoursPerDay: 4,
+          status: AllocationStatus.CONFIRMED,
+          projectName: `Project-${ri}-${ai}`,
+          isChargeable: ai % 2 === 0,
+        };
+      });
+
+      return {
+        resource: {
+          id: `res-${ri}`,
+          displayName: `Resource ${ri}`,
+          chargeabilityTarget: 80,
+          availability: standardAvailability,
+        },
+        allocations,
+        analysisStart,
+        analysisEnd,
+      };
+    });
+
+    const t0 = performance.now();
+    for (const input of resources) {
+      analyzeUtilization(input);
+    }
+    const elapsed = performance.now() - t0;
+
+    expect(elapsed).toBeLessThan(500);
+  });
+
+  it("findCapacityWindows: 50 resources × 20 allocations × 365 days < 500 ms", () => {
+    const searchStart = new Date("2026-01-01");
+    const searchEnd = new Date("2026-12-31");
+    const periodMs = searchEnd.getTime() - searchStart.getTime();
+
+    const simpleResource = {
+      id: "res-perf",
+      displayName: "Perf Resource",
+      availability: standardAvailability,
+    };
+
+    const t0 = performance.now();
+
+    for (let ri = 0; ri < 50; ri++) {
+      const allocations = Array.from({ length: 20 }, (_, ai) => {
+        const offset = Math.floor(((ri * 20 + ai) / 1000) * periodMs);
+        const start = new Date(searchStart.getTime() + offset);
+        const end = new Date(start.getTime() + 30 * 24 * 60 * 60 * 1000);
+        return {
+          startDate: start > searchEnd ? searchStart : start,
+          endDate: end > searchEnd ? searchEnd : end,
+          hoursPerDay: 4,
+          status: AllocationStatus.CONFIRMED,
+        };
+      });
+
+      findCapacityWindows(simpleResource, allocations, searchStart, searchEnd);
+    }
+
+    const elapsed = performance.now() - t0;
+
+    expect(elapsed).toBeLessThan(500);
+  });
+});