Consider the case of a garment textile company: ABC sells a large number of white dress shirts. The shirts cost $8 each and sell for $15 each. The cost of processing an order and receiving new goods amounts to $80, and it takes three weeks to receive a shipment. Monthly demand is approximately normally distributed with mean 120 and standard deviation 32. Assume a 2% monthly interest rate for computing the holding cost. The system applies the shortage policy which means that the customer will go elsewhere to find the supply if the stockout occurs, and the associated loss - of - goodwill costs are estimated to be about $10 per unit a. Find the order quantity reorder point (Q,s) policy by sequential determination of s and Q (10pts) b. Find the order quantity reorder point (Q,s) policy by iterative determination of s and Q (compute three iterations only: iteration 0, iteration 1 and iteration 2) (10pts) c. Compare the two approaches in part (a) and (b) based on their total cost (including holding cost, ordering cost, purchasing cost and shortage cost). (10pts) d. Find the formula for order quantity Q that the total cost TC(Q) is minimized. Assume that the total cost includes holding cost, ordering cost, purchasing cost and shortage cost. The shortage cost is calculated by using the formular below: (10pts) Given that the shortage cost per year is: Byvo Gu(k)D Q Where: v: unit cost ($ per unit) o: demand standard deviation (unit) D: mean demand Q: order quantity Byv is the cost per unit short (B2 is the fractional charge per unit short and is assumed to be constant) OG, (k) is the expected shortages per replenishment cycle (ESPRC) Pis the number of cycles per year Question (3a). Demand during lead time is assumed to be normally distributed Consider the case of a garment textile company: ABC sells a large number of white dress shirts. The shirts cost $8 each and sell for $15 each. The cost of processing an order and receiving new goods amounts to $80, and it takes three weeks to receive a shipment. Monthly demand is approximately normally distributed with mean 120 and standard deviation 32. Assume a 2% monthly interest rate for computing the holding cost. The system applies the shortage policy which means that the customer will go elsewhere to find the supply if the stockout occurs, and the associated loss - of - goodwill costs are estimated to be about $10 per unit a. Find the order quantity reorder point (Q,s) policy by sequential determination of s and Q (10pts) b. Find the order quantity reorder point (Q,s) policy by iterative determination of s and Q (compute three iterations only: iteration 0, iteration 1 and iteration 2) (10pts) c. Compare the two approaches in part (a) and (b) based on their total cost (including holding cost, ordering cost, purchasing cost and shortage cost). (10pts) d. Find the formula for order quantity Q that the total cost TC(Q) is minimized. Assume that the total cost includes holding cost, ordering cost, purchasing cost and shortage cost. The shortage cost is calculated by using the formular below: (10pts) Given that the shortage cost per year is: Byvo Gu(k)D Q Where: v: unit cost ($ per unit) o: demand standard deviation (unit) D: mean demand Q: order quantity Byv is the cost per unit short (B2 is the fractional charge per unit short and is assumed to be constant) OG, (k) is the expected shortages per replenishment cycle (ESPRC) Pis the number of cycles per year Question (3a). Demand during lead time is assumed to be normally distributed
