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1. ABC analysis divides on-hand inventory into three classes, generally based uponQuestion 3 options:

annual dollar volume.

unit price.

item quality.

annual demand.

the number of units on hand.

2. Average daily demand for a product is normally distributed with a mean of 5 units and a standard deviation of 2 unit. Lead time is fixed at 3 days. What is the reorder point if the service level is 80% (round your number)?

3. Insurance and taxes on inventory are part of the costs known as setup or ordering costs.

4. A certain type of computer costs $1,000, and the annual holding cost is 25% of the product cost. Annual demand is 10,000 units, and the order cost is $140 per order. What is the approximate economic order quantity (round your number)?

5. Units of safety stock are additions to the reorder point that allow for variability in the rate of demand, the length of lead time, or both.

ture or false

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MGSC 3317 Week 10 Handout – Inventory Management 1- Annual demand of a retailer is 8,000 units. The ordering cost is $200 per order. The retailer approximated that the annual holding cost per unit is $4. a) Calculate the optimum order quantity and find the total ordering and holding costs. b) After reviewing the past data, the company realized that the actual holding cost is $8 per unit per year. Calculate the optimal ordering quantity and determine how much the company was losing annually according to wrong approximation of holding cost. c) Find the number of orders per year and the time between orders. a. 2𝐷𝑆 2(8,000)(200) 𝑄 ∗ = 𝐸𝑂𝑄 = √ =√ = 894.42 𝐻 4 Total Inventory cost = 𝑄 𝐷 894.42 8,000 (4) + (200) = $3,577.7 𝐻+ 𝑆= 2 𝑄 2 894.42 b. 2𝐷𝑆 2(8,000)(200) 𝑄 ∗ = 𝐸𝑂𝑄 = √ =√ = 632.45 𝐻 8 𝑄 𝐷 632.45 8,000 (8) + (200) = $5,059.6 𝐻+ 𝑆= 2 𝑄 2 632.45 894.42 8,000 (8) + (200) = $5,366.5 Total cost when we mistakenly calculated 894.42 as EOQ = 2 894.42 5,366.5 − 5,059.6 Cost Difference = × 100 = 6.06% 5,059.6 This indicates the robustness of EOQ Model. Total Inventory cost = c. Number of orders = T𝐵𝑂 = Instructor: Majid Taghavi 𝐷 8,000 = = 12.64 𝐸𝑂𝑄 632.45 𝐸𝑂𝑄 632.45 = = 0.079 years = 28.85 Days 𝐷 8,000 Page 1 of 3 MGSC 3317 Week 10 Handout – Inventory Management 2- Finding Safety Stock by Balancing Holding and Stockout Costs A product has a reorder point of 260 units and is ordered 10 times a year on average. The following table shows the historical Demand Probability distribution of demand values observed during lead time. Currently, stockouts are 240 0.18 valued at $1.5 per unit per occurrence, while inventory holding costs are $2 per unit 250 0.12 per year. Should the firm add safety stock? If so, how much safety stock should be 260 0.4 added? 270 0.2 280 0.1 With no safety stock, ROP=260 Possible values for 𝑠𝑠 = 0, 10, and 20 ss Additional Holding Cost Stockout Cost Total Cost 0 $0 0.2(270 − 260)($1.5)(10) + 0.1(280 − 260)( $1.5)(10) = $60 $60 10 10($2) = 20 0.1(280 − 270)( $1.5)(10) = $15 $35 20 20($2) = 40 $0 $40 The minimum total cost happens when 𝑠𝑠 = 10 ROP = 260 + ss = 270 Instructor: Majid Taghavi Page 2 of 3 MGSC 3317 Week 10 Handout – Inventory Management 3- The daily demand for the soap in a hotel is 275 bars, with a standard deviation of 30 bars. Ordering cost is $10 and the inventory holding cost is $0.30/bar/year. The average lead time from the supplier is 5 days, with a standard deviation of 1 day. The lodge is open 365 days a year. a) What is the economic order quantity for the bar of soap? b) What should be the safety stock for the bar of soap if management wants to have a 99 percent cycle-service level? What is the reorder point? c) What is the total annual inventory cost for the bar of soap? a. 2𝐷𝑆 2(275 × 365)(10) 𝑄 ∗ = 𝐸𝑂𝑄 = √ =√ = 2,587 𝐻 0.3 b. 𝛼 = 99% ⇒ 𝑍 = 2.33 2 ̅ 2 𝜎𝐿𝑇 𝜎𝑑𝐿𝑇 = √𝐿̅𝜎𝑑2 + 𝐷 = √5(30)2 + 2752 (1)2 = 283.06 𝑠𝑠 = 𝑍𝜎𝑑𝐿𝑇 = 2.33(283.06) = 660 𝑅𝑂𝑃 = 275(5) + 𝑠𝑠 = 1,375 + 660 = 2,035 c. 𝑇𝐶 = 𝑄 𝐷 2,587 275(365) 𝐻 + 𝑆 + 𝑆𝑆. 𝐻 = (0.3) + (10) + 660(0.3) = $974 2 𝑄 2 2,587 4- Cynthia Knott’s seafood restaurant buys fresh Nova Scotia lobsters for $6 per pound and sells them for $10 per pound. Any lobster did not sell that day are sold to her cousins nearby grocery stores for $5 per pound. Cynthia believes that demand follows the normal distribution, with a mean of 25 pounds and a standard deviation of 4 pounds. How many pounds should she order each day? 𝑐𝑈 = 𝑝 − 𝑐 = 10 − 6 = $4 𝑐𝑂 = 𝑐 − 𝑠 = 6 − 5 = $1 𝑆𝑒𝑟𝑣𝑖𝑐𝑒 𝐿𝑒𝑣𝑒𝑙 = 𝐹(𝑆) = 𝑐𝑈 4 = = 0.8 𝑐𝑂 + 𝑐𝑈 1 + 4 𝛼 = 80% ⇒ 𝑍 = 0.84 Optimal Stocking level: 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑑𝑒𝑚𝑎𝑛𝑑 + 𝑍𝜎 = 25 + 0.84(4) = 28.36 Instructor: Majid Taghavi Page 3 of 3

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