Question

# A retailer purchases a certain type of chemical from a supplier on the following quantity discount...

A retailer purchases a certain type of chemical from a supplier on the following quantity discount schedule: • If the order amount is less than 100 kg.s, the supplier charges \$30 per kg. • If the order amount is at least 100 kg.s and less than 500 kg.s, the supplier applies an incremental discount where the ﬁrst 100 kg. costs \$30 per kg. and the remaining amount costs \$28 per kg. • If the order amount is at least 500 kg.s, the supplier applies an all-units discount and charges \$28 per kg. for all units. The ordering cost is \$100 per order and the retail owner assumes an annual holding cost based on the annual inﬂation rate which is 25%. The annual demand of this chemical to retailer is 800 kg.s and the demand rate stays constant in the planning horizon. Back-ordering is disallowed and both the retailer and the supplier works for 365 days in a year. Find the economic order quantity and the order cycle time (in days) that minimizes the total inventory cost. Calculate the minimum total annual inventory cost. Carry out the whole analysis and show all of your calculations. **how is the total cost calculated?**

1. EOQ = [ 2 * Annual demand * Ordering cost / Cost of holding one unit per year]^(1/2)

EOQ = [ 2 * 800 * 100 / (0.25*30)]^(1/2) = 146

2. For 146 Units, Total Cost = 100 * 30 + 46 * 28 = \$4288

Cost per Unit = Total Cost / EOQ = 4288 / 146 = \$29.36

New EOQ with Cost per unit of \$29..36 = [ 2 * Annual demand * Ordering cost / Cost of holding one unit per year]^(1/2)

New EOQ with Cost per unit of \$29..36 = [ 2 * 800 * 100 / 0.25 * 29.36]^(1/2)

New EOQ with Cost per unit of \$29..36 = 148 Units

2. Order Cycle in Days = 365 Days * EOQ / Annual Demand = 365 * 148 / 800 = 67.525

3. cost of inventory = holding cost + ordering cost = (EOQ /2) * 29.36 * 0.25 + 100 * (800/148) = 540.54 + 543.16 = \$1084

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