Please solve the following task:
The following data is given for planning the ordering policy of a material type in an industrial company:
Planning period: 180 days
Total requirement: 30,000 ME
Cost price: 30 GE/MU
Order cost rate: 200 GE
Storage cost rate: 1.50 GE/ME (related to the planning period)
Interest rate: 5% (related to the planning period)
Determine the optimal order quantity, the optimal order frequency and storage range as well as the costs resulting from the optimal ordering policy as the sum of order costs and storage costs (including capital commitment costs).*
ChatGPT result:
The optimal order quantity, order frequency, and storage range can be determined using the Economic Order Quantity (EOQ) model. The EOQ model balances the trade-off between ordering costs and holding costs.
Ordering costs are the costs incurred each time an order is placed, and holding costs are the costs associated with holding inventory in stock over the planning period.
The EOQ model is calculated using the following formula:
EOQ = √(2DS/H)
Where:
D = Total requirement (30,000 ME)
S = Order cost rate (200 GE)
H = Holding cost rate (1.5 GE/ME)
Plugging in the values:
EOQ = √(2 * 30,000 * 200 / 1.5) = √(12,000,000) = 3464.16 ME
The optimal order quantity is approximately 3464.16 ME.
The order frequency can be calculated as the total requirement divided by the EOQ:
Order frequency = Total requirement / EOQ = 30,000 / 3464.16 = 8.68 orders
The optimal order frequency is approximately 8.68 orders.
The storage range can be calculated as the EOQ divided by 2:
Storage range = EOQ / 2 = 3464.16 / 2 = 1732.08 ME
The optimal storage range is approximately 1732.08 ME.
The costs resulting from the optimal ordering policy can be calculated as the sum of the order costs and holding costs.
Order costs = Order frequency * Order cost rate = 8.68 * 200 = 1736 GE
持有成本=（EOQ/2）*持有成本率*计划期=（3464.16/2）*1.5*180=126601.76通用电气
资本承诺成本=（EOQ/2）*利率*成本价格=（3464.16/2）*0.05*30=523.25GE
总成本=订单成本+持有成本+资本承诺成本=1736+126601.76+523.25=127861.01通用电气
The costs resulting from the optimal ordering policy are approximately 127,861.01 GE.
