380. Silver-Meal
A lot-sizing heuristic for time-varying demand (Silver & Meal, 1973). Chooses order intervals to minimize average cost per period covered.
Easier than Wagner-Whitin (which is DP-optimal) and often close in quality.
380.1. Setup
Demand over periods. Setup cost per order, holding cost per unit per period.
380.2. Algorithm
Start with a candidate order in period covering periods of demand. Average cost per period:
(Setup once + holding cost for demand carried periods.)
Extend as long as decreases. Stop at first where . Place an order in to cover periods. Start a new order in . Repeat until all periods are covered.
380.3. Worked example
Demand: , , .
Start at period 1:
- ← tied
- ← rose, stop. Order in period 1 covers 2 periods (160 units).
Start at period 3:
- ← decreasing
- ← rose. Order in period 3 covers 2 periods (130 units).
Start at period 5:
- ← decreasing
- ( doesn’t exist, ). Order in period 5 covers 2 periods (110 units).
Three orders: period 1 (160), period 3 (130), period 5 (110). Total cost computable.
380.4. Compared to alternatives
| Heuristic | Quality vs WW optimum | Computational cost |
|---|---|---|
| Lot-for-lot | worst; high setup cost | trivial |
| POQ / fixed-quantity (EOQ) | moderate; ignores demand variation | trivial |
| Least Unit Cost | usually within 5-10% | |
| Silver-Meal | usually within 3-5% | |
| Part-Period Balancing | usually within 5% | |
| Wagner-Whitin | optimal | DP |
Silver-Meal is fast and good. Wagner-Whitin is exact and not much slower; usually preferred when implementable.
380.5. Limitations
- Greedy — no lookahead beyond current order
- Can miss good solutions by stopping too early
- Failure mode: when demand has long-running upticks, Silver-Meal may stop short of the truly optimal order span
380.6. See also
- Least Unit Cost
- Part-Period Balancing
- Wagner-Whitin — DP-optimal
- MRP — where lot-sizing fits