Concept

MOQ vs EOQ

Direct answer

EOQ is the buyer-optimal order quantity given costs. MOQ (minimum order quantity) is the supplier-imposed floor. They are distinct: EOQ tells you what you should order; MOQ tells you what you’re allowed to order. When MOQ > Wilson Q*, MOQ binds and the carrying-cost penalty becomes the cost of doing business with that supplier^[1].

Concept

MOQ vs EOQ

Supplier-imposed minimum vs buyer-optimal quantity.

actual_Q = max(MOQ, Q_Wilson)

When it matters: In the MOQ-binding case, EOQ tells you the cost of the binding constraint. That number is the negotiation lever: 'you cost us $X/year by setting MOQ at Y; drop MOQ to Y/2 and we share Z.'

Three cases

MOQ < Q_Wilson: MOQ is non-binding. Order Q* per Wilson. Note MOQ on the PO; ignore it for sizing.
MOQ approx Q_Wilson: the case-pack rounding case. Round up to the next case multiple. Cost penalty is a small Taylor approximation, typically < 1 percent of TC.
MOQ > Q_Wilson: MOQ binds. Quantify the over-order cost: H * (MOQ - Q*)/2 + reduced ordering frequency saving. The net is usually a cost in dollars per year; that number is your negotiation lever.

Documenting the override on a PO

On a PO that overrides EOQ to satisfy MOQ, add a line in the buyer notes: "MOQ-bound: Wilson Q* = X; MOQ = Y; over-order penalty = $Z/year computed at H = $K, S = $L." This protects the buyer in audit and gives the procurement lead a defensible number when negotiating MOQ down at next contract review.

MOQ negotiation logic

Suppliers set MOQ to amortise their own setup cost (S from the supplier’s perspective). A buyer absorbing high MOQ is paying for the supplier’s changeover. The negotiation framing: "your MOQ costs us $X carrying penalty annually; we’ll split that with you in exchange for a MOQ at half" tends to land because the supplier’s setup cost is usually well below the buyer’s carrying penalty.

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