Advanced : Quantity discount s and calculation of EOQ Wagtail Ltd uses the 'optimal batch size' model (see below) to determine optimal levels of raw materials. Material B is consumed at a steady, known rate over the company's planning horizon of one year; the current usage is 4000 units per annum. The costs of ordering B are invariant with respect to order size; clerical costs of ordering have been calculated at £30 per order. Each order is checked by an employee engaged in using B in production who earns £5 per hour irrespective of his output. The employee generates a contribution of £4 per hour when not involved in materials checks and the stock check takes five hours. Holding costs amount to £15 per unit per annum.

The supplier of material B has very recently offered Wagtail a quantity discount of 24p a unit on the current price of £24, for all orders of 400 or more units of B.

You are required to:

(a) calculate the optimal order level of material B, ignoring the quantity discount; (3 marks)

(b) evaluate whether the quantity discount offered should be taken up by Wagtail; (5 marks)

(c) explain how uncertainties in materials usage and lead time may be incorporated into the analysis.

Note: Ignore taxation Optimal batch size

where xis the optimal batch size. fis fixed costs per batch, sis expected sales volume per annum, hIS the cost of holding a unit in stock for one year.

Transcribed Image Text:

2fs x= h