12 Inventory Management Homework; 3, 22, 28ab, 31, Add1, Add2, Add3

Chapter 12, Additional Homework 1 Yellow Press Inc. buys slick paper in rolls for textbook printing. Annual demand is 2500 rolls. The cost per roll is $800, and the annual holding cost is 15 percent of the cost. Each order costs $50. Yellow Press uses a fixed quantity ordering model. a.How many rolls should be ordered at a time? b.What is the time between orders (assuming 250 working days in a year)?

Chapter 12, Additional Homework 2 Sam’s Cat Hotel operates 52 weeks per year, 6 days per week, and uses a fixed quantity ordering model. It purchases kitty litter for $11.70 per bag. Current on-hand inventory is 320 bags, with no open orders or backorders. Demand = 90 bags / week, varies via a normal distribution Order cost = $54 / order Annual holding cost = 27% of cost Desired service level = 80% Lead time = 3 weeks (18 working days), constant Standard deviation of weekly demand = 15 bags a.What is the EOQ? What is the average time between orders in weeks? b.What is the ROP? c.An inventory withdrawal of 10 bags was just made. Is it time to reorder? d.The store currently uses a lot size of 500 bags (i.e. Q=500). What is the annual holding cost of this policy? Annual ordering cost? Without calculating the EOQ, how could you conclude from these two calculations that the current lot size is too large? e.What would be the annual cost saved by shifting from the 500-bag lot size to the EOQ?

Chapter 12, Additional Homework 3 Petromax Enterprises uses a fixed quantity ordering system for one of its inventory items. The firm operates 50 weeks in a year. Demand = 50,000 units per year Ordering cost = $35 per order Holding cost = $2 per unit per year Lead time is 3 weeks fixed Standard deviation of weekly demand = 125 units a.What is the EOQ? b.If Petromax wants to provide a 90% service level, what should be the safety stock and reorder point?

Outline, Two Major Models Fixed Quantity Model Order a fixed amount Order cycle (time between orders) varies EOQ, Q 0, TC (holding and ordering costs) ROP - Constant demand, constant lead time - Variable demand~N, constant lead time Fixed Interval Model Order various amounts Order cycle is fixed or constant

Inventory Management  Inventory is a stock of anything held to meet some future demand. It is created when the rate of receipts exceeds the rate of disbursements.  A stock or store of goods.  Inventory Turns (Turnover) COGS/Avg. Inventory Investment

ABC Analysis Percentage of items Percentage of dollar value 100 — 90 — 80 — 70 — 60 — 50 — 40 — 30 — 20 — 10 — 0 — Class C Class A Class B

Fixed Quantity Model Constant demand, constant lead time. On-hand inventory (units) Time Average cycle inventory QQ—2QQ—2 1 cycle Receive order Inventory depletion (demand rate)

Fixed Quantity Model – Formulas Constant demand, constant lead time. Q 0 =Economic Order Quantity Q=Order Quantity D=Annual demand S=Order cost per order H=Annual holding cost per unit TC=Total annual costs TBO=Time between orders, order cycle time ROP=Reorder Point, used when LT>0 d=demand rate LT=Lead time Constant means fixed or non-fluctuating.

Fixed Quantity Model – Total Costs Constant demand, constant lead time.

Ex: Find Q 0, TBO, and make cost comparisons Constant demand, constant lead time, LT=0. Suppose that you are reviewing the inventory policies on an item stocked at a hardware store. The current policy is to replenish inventory by ordering in lots of 360 units. Additional information given: D = 60 units per week, or 3120 units per year S = $30 per order H = 25% of selling price, or $20 per unit per year

Ex: Determine ROP Constant demand, constant lead time, LT>0. Q=300 units, LT=8 days, TBO=30 days.

Fixed Quantity Model Variable demand~N, constant lead time, LT>0. Probability ofstockout (1.0–0.85 = 0.15) Cycle-service level = 85% Average demand during lead time R Probability ofstockout (1.0–0.85 = 0.15) Cycle-service level = 85% Average demand during lead time R

Ex: Determine EOQ, ROP Variable demand~N, constant lead time, LT>0. The Discount Appliance Store uses a fixed order quantity model. One of the company’s items has the following characteristics: Demand = 10 units/wk (assume 52 weeks per year, normally distributed) Ordering and setup cost (S) = $45/order Holding cost (H) = $12/unit/year Lead time (L) = 3 weeks Standard deviation of demand rate = 8 units per week Service level = 70%

Fixed Interval Model Variable demand~N, constant lead time, LT>0. OI=Time between orders A=Amount on hand at order time

Fixed Interval Model Time On-hand inventory IP 1 IP 3 IP 2 Order received Order received OH Order placed Order placed LT OI

Ex: Fixed Interval Model, page 572 d=30 units per day  d =3 units per day LT=2 days Service level 99% OI=7 days A=71 units

Fixed Quantity Model vs. Fixed Interval Model