381. Least Unit Cost

A lot-sizing heuristic similar to Silver-Meal, but minimizing cost per unit produced instead of cost per period covered.

381.1. Algorithm

For an order starting in period covering periods:

Numerator: total setup + holding cost. Denominator: total units in the order.

Extend while decreases. Stop when it increases. Order covers periods.

381.2. Compared to Silver-Meal

• Silver-Meal: minimize cost per time period
• LUC: minimize cost per unit

When demand is uniform, the two give similar / identical answers. When demand varies, they diverge:

• Spiky demand peaks: LUC tends to order bigger batches (drives down per-unit cost via fixed-cost amortization)
• Smoother demand: Silver-Meal tends to order more frequently

Neither is strictly better. Both are heuristics, both within  5% of Wagner-Whitin optimum on typical instances.

381.3. Worked example

Same data as Silver-Meal: , , .

Start period 1:

• ← decreasing
• ← rose, stop. Order 1 covers 2 periods.

(Same answer as Silver-Meal in this case.)

381.4. When LUC favors larger orders

If subsequent demand is high (say ), Silver-Meal’s per-period cost increases fast (high holding cost on big inventory), but LUC’s per-unit cost may still drop (fixed cost spread over more units).

So LUC tends to bundle into larger orders when downstream demand is high.

381.5. See also

• Silver-Meal — sister heuristic
• Part-Period Balancing
• Wagner-Whitin — optimal
• EOQ — stationary-demand analog