## 1. Decision **FULL COVERAGE** Recommended approval draft: - Candidate A — Y/MAIN: **4 units** - Candidate B — MILK/MAIN: **2 units** - Total purchase cost: **USD 8.00** - Shared budget: **USD 10.00** - Budget remaining: **USD 2.00** - Search: **Exhaustive** - Affordable combinations checked: **8 of 8** - Total combinations generated: **8** - Optimal quantity vector by candidate ID `(A, B)`: **(4, 2)** Ranking tuple: `(total lost units, total target shortfall, total expired units, total purchase cost, total closing units, order vector)` Selected plan: `(0, 0, 4, 800 cents, 0, (4,2))` The 4 expired units are existing Y1 inventory that expires after D1. Candidate A cannot prevent this because it arrives on D2. All affordable combinations: | A qty | B qty | Cost | Lost | Target shortfall | Expired | Closing | Rank-relevant result | |---:|---:|---:|---:|---:|---:|---:|---| | 0 | 0 | $0.00 | 6 | 0 | 4 | 0 | Baseline | | 0 | 2 | $4.00 | 4 | 0 | 4 | 0 | MILK covered only | | 2 | 0 | $2.00 | 4 | 0 | 4 | 0 | Partial Y | | 2 | 2 | $6.00 | 2 | 0 | 4 | 0 | Y shortage remains | | 4 | 0 | $4.00 | 2 | 0 | 4 | 0 | MILK shortage remains | | **4** | **2** | **$8.00** | **0** | **0** | **4** | **0** | **Selected** | | 6 | 0 | $6.00 | 2 | 0 | 6 | 0 | Excess Y expires | | 6 | 2 | $10.00 | 0 | 0 | 6 | 0 | Full coverage, but 2 unnecessary expiries | ## 2. Purchase table | Candidate | Lane | Quantity | Cases | Arrival | Extended cost | |---|---|---:|---:|---|---:| | A | Y/MAIN | **4** | **2** | D2 | **$4.00** | | B | MILK/MAIN | **2** | **1** | D2 | **$4.00** | | **Total** | | **6** | **3** | | **$8.00** | Zero was evaluated as a valid choice for both A and B but was not selected. Candidate rules checked: - A: case 2; allowed quantities `0, 2, 4, 6` - B: case 2; allowed quantities `0, 2` - A4 cost = `4 × $1.00 = $4.00` - B2 cost = `2 × $2.00 = $4.00` - Fixed charges = `$0.00` - Total = `$8.00` ## 3. Baseline versus plan | Lane | Scenario | Lost units | First shortage | Expired units | Final stock | Target | Target shortfall | |---|---|---:|---|---:|---:|---:|---:| | Y/MAIN | Baseline | 4 | D2 | 4 | 0 | 0 | 0 | | Y/MAIN | Plan | **0** | None | 4 | 0 | 0 | 0 | | MILK/MAIN | Baseline | 2 | D2 | 0 | 0 | 0 | 0 | | MILK/MAIN | Plan | **0** | None | 0 | 0 | 0 | 0 | | **Total** | Baseline | **6** | D2 | **4** | **0** | 0 | **0** | | **Total** | Plan | **0** | None | **4** | **0** | 0 | **0** | The plan eliminates all **6 baseline lost units** while avoiding incremental expiry. ## 4. Daily ledgers ### Baseline — Y/MAIN Opening lot: Y1 = 6 units, last sell day D1. | Day | Arrivals | Demand | Sold | Lost | Expired by lot | Closing | |---|---|---:|---:|---:|---|---:| | D1 | — | 2 | 2 | 0 | Y1: 4 | 0 | | D2 | — | 2 | 0 | 2 | — | 0 | | D3 | — | 2 | 0 | 2 | — | 0 | | **Total** | **0** | **6** | **2** | **4** | **4** | **0** | Reconciliation: `Opening 6 + receipts 0 = sold 2 + expired 4 + closing 0 = 6` ### Plan — Y/MAIN Candidate A supplies 4 units on D2, last sell day D3. | Day | Arrivals | Demand | Sold | Lost | Expired by lot | Closing | |---|---|---:|---:|---:|---|---:| | D1 | — | 2 | 2 | 0 | Y1: 4 | 0 | | D2 | A: 4 | 2 | 2 | 0 | — | 2 | | D3 | — | 2 | 2 | 0 | — | 0 | | **Total** | **4** | **6** | **6** | **0** | **4** | **0** | Reconciliation: `Opening 6 + receipts 4 = sold 6 + expired 4 + closing 0 = 10` ### Baseline — MILK/MAIN Opening lot: M1 = 1 unit, last sell day D1. | Day | Arrivals | Demand | Sold | Lost | Expired by lot | Closing | |---|---|---:|---:|---:|---|---:| | D1 | — | 1 | 1 | 0 | — | 0 | | D2 | — | 1 | 0 | 1 | — | 0 | | D3 | — | 1 | 0 | 1 | — | 0 | | **Total** | **0** | **3** | **1** | **2** | **0** | **0** | Reconciliation: `Opening 1 + receipts 0 = sold 1 + expired 0 + closing 0 = 1` ### Plan — MILK/MAIN Candidate B supplies 2 units on D2, last sell day D3. | Day | Arrivals | Demand | Sold | Lost | Expired by lot | Closing | |---|---|---:|---:|---:|---|---:| | D1 | — | 1 | 1 | 0 | — | 0 | | D2 | B: 2 | 1 | 1 | 0 | — | 1 | | D3 | — | 1 | 1 | 0 | — | 0 | | **Total** | **2** | **3** | **3** | **0** | **0** | **0** | Reconciliation: `Opening 1 + receipts 2 = sold 3 + expired 0 + closing 0 = 3` ## 5. Binding constraints and next actions There is **no pre-arrival lost demand** on D1. Y/MAIN has enough Y1 stock to satisfy its D1 demand of 2, and MILK/MAIN has exactly 1 unit for its D1 demand of 1. However, **4 remaining Y1 units must expire after D1** because D1 is their stated last sell day. The D2 candidate arrival cannot legally extend or recover those units. The key constraints are expiry and timing rather than the USD 10.00 budget. Candidate A at **4 units** exactly covers Y/MAIN demand on D2-D3. Buying its 6-unit maximum would spend another $2.00 and cause another 2 units to expire on D3. Candidate B is capped at 2 units, which exactly covers MILK/MAIN's D2-D3 requirement. Next actions: 1. **Approve for consideration A = 4 units for Y/MAIN and B = 2 units for MILK/MAIN**, total proposed spend $8.00. 2. For **Y/MAIN**, investigate whether future replenishment can arrive before D2 if reducing unavoidable D1 expiry is operationally possible; this draft does not assume such a lead-time change. 3. Keep the remaining **$2.00 unspent** rather than increasing A to 6, because the additional 2 units provide no service benefit and would expire by the end of D3. This is an **approval draft only**. No purchase order, stock reservation, supplier commitment, or system update is implied.