The EOQ model can easily show the effects of set-up cost reduction on total set-up and holding costs, total holding costs and total set-up costs.

Equation (1) shows that decreasing the set-up costs, S, will reduce the total cost per period, C.If the amount of set-up cost reduction is R, the total cost is reduced by [square root of]R.

All previous discussions of ZI are descriptive, but set-up cost reduction is viewed as an important factor.

Zangwill presents an example that is a non-stationary reduction of set-up cost. His example shows that cutting set-up cost need not reduce inventories and total cost.

Since the set-up costs during the day are higher than they are at night, the engineering department significantly reduces the set-up cost, which becomes [S.sub.1] = [S.sub.3] = 1, [S.sub.2] = [S.sub.4] = 4.

In practice, a major factor of set-up cost reduction is set-up time reduction.

Adopting the above notations, let us discuss the case of stationary reduction of set-up costs. Let R be the amount of set-up cost reduction for each period.

Suppose the amount of the set-up cost reduction is [R.sub.i] in each period i, then as [R.sub.i] increases the total cost should be decreased.

The total cost should be reduced by set-up cost reduction [R.sub.i], i = 1, ..., t.

What is the new total holding costs when set-up cost is stationarily cut by R.

(1) the relation of the reduction between the total cost and the set-up cost with normal distribution and 100 runs of simulation;