Question

only a and b

3. The warehouse store in Problem #2 has a lot of market power. It has convinced its supplier to build a warehouse nearby and to provide vendor-managed-inventory (VMI) services - including delivery-- for free, with inventory being delivered on consignment. Under a vendor-managed inventory system, the warehouse store no longer sends orders to the supplier. Instead the supplier is responsible for managing the inventory according to some rules that are mutually agreed upon by the buyer and supplier. Under a consignment system, the buyer does not pay the supplier for the goods until the buyer has sold the product. Thus, the supplier owns the inventory and incurs the financial cost of holding it until it is sold. It costs approximately $50 for the supplier to make a delivery, and $6.00 for the supplier to manufacture a package of paper towels. The supplier uses an annual inventory holding cost rate of 80%. The supplier plans to (electronically) check the inventory status at the warehouse store at the end of each day, and expects to be able to make a delivery by the end of the following day. The warehouse store has asked for a 98% probability of no stockout during the order cycle, but the supplier also recognizes that each shortage will result in a lost sale, and it will therefore lose its profit if a shortage occurs. For simplicity, you may assume that a year has 50 weeks, and each week has 7 working days. (That is, deliveries can be made on any day of the week.) (a) How often should the supplier send a truck to the warehouse store? (b) Use the Newsvendor model to estimate the economically optimal probability of no stockout during the order cycle.

pt 2 for reference

newsvendor model

Answer 1

Ordering costs	50
C	6
i	80%
H	4.8
Demand	300
Standard deviation	60
Days	350
Probability	98%
Z	2.06
Selling price	10
Lead time	1 days
EOQ	1479
The said quantity will able to suffice demand for
	=EoQ/re-order level
	=1479/423.6
	3.49 days
	The order shall be place every 3.5 days
Re-order level	=(daily demand*lead time)+safety stock
	=(300*1)+123.6
	=423.6
Safety stock	Square root N *Standard deviation * Z model of non-stockput probability
	Square root 1* 60 * 2.06
	123.6
Newsvendor model
The cost of not having enough	=Price-cost
	=10-6
Cu	=4
The cost of having excess	=cost-salvage
	=6-1.2
Co	=4.8
Average daily demand	300
Variance	=standardeviation^2
	=60^2
Criticality ratio	Cu/(Co+Cu)
CR	=4/(4.8+4)
	0.45