A large scale pharmaceutical manufacturing company estimates, based on a shippin

Question

A large scale pharmaceutical manufacturing company estimates, based on a shipping fee of $1000 per order, that they can optimally balance inventory holding costs and shipping costs for one of their frequently used chemicals if they receive shipments of this chemical at an average rate of 4.5 times per year. The annual demand is 6500 tons. Suppose that they wish to instead receive shipments every month in order to reduce the working capital requirements of holding inventory.
(a) What shipping fee should they negotiate with the supplier?
(b) Based on this new shipping fee, what would be the reduction in annual holding cost as compared to their prior situation? Assume that they operate optimally.

Explanation / Answer

Solution:

Given,

A = Annual demand = 6500 Tonnes

S = Cost per order = $1000 per order

Number of orders per year = N = 4.5 times

Here, determine optimal order quantity and holding cost for current ordering policy.

First obtain optimal order quantity (Q*)

Considering the optimal ordering policy,

Optimal number of orders = N* = (A/Q*)

Q* is optimal order quantity, = A/N* = 6500/4.5 = 1444.44 Tonnes

Obtain holding cost (H)

Economic order quantity (EOQ) is calculated as follows:

By rearranging elements of equation:

H = (2 × A × S) / Q2

H = (2 × 6500 × 1000) / 1444.442

H = $6.23 per tonne per year

Annual Holding cost (HC) = Average inventory level × Holding cost (H)

AHC = (Q*/2) × H = (1444.44/2) × 6.23 = $4500

Now, for new ordering policy,

N1* = 12 times per order

H = $6.23

A = 6500 tonnes

Q1* = (A/ N1*) 6500/12 = 541.67 tonnes

Economic order quantity (EOQ) is calculated as follows:

By rearranging elements of equation:

S = (Q2 × H)/ (2 × A)

S = (541.672 × 6.23)/ (2 × 6500)

S = $140.6 per order

For new ordering policy, company should negotiate for shipping cost of $140.6 with supplier

Revised Annual Holding Cost,

AHC1 = (541.67/2) x 6.23 = $1687.29

Reduction in annual holding cost = 4500 – 1687.29 = $2812.71

By changing ordering policy the company can reduce annual holding cost by $2812.71.

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