Question

Inventory: You own a toy company and you are producing wooden rocking horses. Assume you have 18,000 units of demand per year. Your ordering cost would be $10 per order. Your unit cost would be $3 and your dollar carrying cost would be 8%.

1. Basic EOQ: If your policy were to order Q=800 units when R= 0, what would your total cost be? (assume 360 days)

2. Basic EOQ: If your policy were to order Q= 1000 unites when R=0, what would your total cost be?

3. Basic EOQ: With the above information, what would your optimal solution be? Tell me what n, Q* ,and TC* would be. (round to the nearest tenth)

4. Basic EOQ with Lead Time: If you needed a lead time of 3 days with your optimal solution, what would your reorder point be? Tell me your new policy in terms of Q* and R.

5. Basic EOQ with a Discount: Suppose there were a discount of 4% on the unit cost on order of Q>= 2500. Would you take the discount or not? Show me all of the potential options and advise which is the best. Option 1 would use your optimal solution and not take the discount, option 2 would assess the discount, option 3 would assess greater than the discount quantity. (Make sure you revise all variables that are affected by the discount and include unit cost to get the grand total cost.)

Answer 1

Q = 800

Annual ordering cost = (D/Q)*K = (18000/800)*10 = $225
Annula carrying cost = (Q/2)*i*C = (800/2)*8%*3 = $96

So, TC (excluding the cost of purchase) = 225 + 96 = $321

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Q = 1000

Annual ordering cost = (D/Q)*K = (18000/1000)*10 = $180
Annula carrying cost = (Q/2)*i*C = (1000/2)*8%*3 = $120

So, TC (excluding the cost of purchase) = 180 + 120 = $300

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Q* = (2.D.K / i.C)^1/2 = SQRT(2*18000*10/(8%*3)) = 1225 units

n = D/Q* = 18000/1225 = 14.7

TC = (D/Q*).K + (Q*/2).i.C = (18000/1225)*10 + (1225/2)*8%*3 = $293.9

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Q* = 1225 units

R = Lead time * Daily demand = 3 days * (18000/360) per day = 150 units

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Option-1:

Total cost (including the purchae cost) = $293.9 + 18000*$3 = $54,293.9

Option-2:

Q = 2500

TC without purchase cost = (D/Q).K + (Q/2).i.C = (18000/2500)*10 + (2500/2)*8%*3*96% = $360

TC with the purchase cost = 360 + 18000*3*96% = $52,200

Option-3:

Any qyantity higher than Q = 2500 will not give any better result. We can test it for Q = 2501

TC without purchase cost = (D/Q).K + (Q/2).i.C = (18000/2501)*10 + (2501/2)*8%*3*96% = $360.086

TC with the purchase cost = 360.086 + 18000*3*96% = $52,200.086

So, comparing the 3 options, the cheapest is the Option-2. So, the optimal order quantity is Q = 2,500 and the Grand total cost is $52,200.