Homework- Chapter 15 – Solutions
1. Assumptions of the EOQ model
 Demand for the product is constant and uniform throughout the period
 Lead time is constant
 There is a fixed cost of ordering
 Price per unit of product is constant
 Inventory holding cost is based on average inventory
 All demand will be satisfied (no backorders are allowed)
 Multiple periods
2. Assumptions of newsvendor model
 Single period
 Uncertain demand
 We know the distribution of demand
 There is a unit cost of underage/overage
3. We know that :
Annual Demand (D)= 3,000 units
Daily Demand (Dd)= 3000/365
Fixed ordering cost (S)=$ 75
Cost per unit (C)= $ 30
Holding cost/year/unit(H)= 0.5*30= $15
Lead Time (L)= 14 days
a) Qopt= (2DS/H)1/2=(2*3000*75/15)1/2=173 units (after rounding). Since the number of
orders over the year is D/Qopt =3000/ 173 = 17 times, we need to order every 365/17= 21
days
b) The reorder point is R= DdL=(3,000/365) 14=115 units
4.
Annual Demand (D)= 520 units
Fixed ordering cost (S)=$ 1000
Holding cost/unit/year(H)= $1200
a) Qopt= (2DS/H)1/2=(2*520*1000/1200)1/2= 29 units (after rounding)
b) Number of orders over the year is D/Qopt =520 / 29 = 18
c ) We need to order every 365/18= 21.4 days
d) The total annual cost is TC= (D/Q)S +(Q/2)H = (520/29)1000+ (29/2) 1200= $ 35331
5. For L= 3 weeks, the reorder point is R= DwL=(520/52) 3= 30 units.
For weekly σ=2 and service level = 95% we have:
σL2= 22 + 22 +22 =12 so σL= 3.46
z = 1. 64 (for 95%) and thus R= DwL+z σL= 30 + 5.6744 = 35.6744 units
6. ML= 0.49-0.29 = $0.2 and MP= 0.69-0.49 = $0.2 , so Pc=ML/ ML+MP= 0.5, and 1Pc = 0.5, which means that z=0 and thus, Q= μ + z*σ = 2400 dozen cookies