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**Logistics Systems Engineering**

SMU SYS 7340 NTU SY-521-N Logistics Systems Engineering Inventory - Requirements, Planning and Management Dr. Jerrell T. Stracener, SAE Fellow

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**Inventory Requirements1**

Why hold inventory? Enables firm to achieve economics of scale Balances supply and demand Enable specialization in manufacturing Provides uncertainty in demand and order cycle Acts as a buffer between critical interfaces within the channel of distribution

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**Inventory Requirements**

Economics of scale Price per unit LTL movements Long production runs with few line changes Cost of lost sales Balancing supply and demand Holidays Raw material availability Specialization Manufacturing process Longer production runs

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**Inventory Requirements**

Protection from Uncertainties Future prices Shortages World conflicts Plant catastrophe Labor disputes Improve customer service Buffering See following graph

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**Inventory Requirements**

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**Inventory Planning2 Cycle Stock In transit Safety Stock**

Speculative Stock Seasonal Stock Dead Stock

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Inventory Planning2

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Inventory Planning2

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**Inventory Mangement3 Economic Order Quantity (EOQ)**

Minimizes the inventory carrying cost Minimizes the ordering cost Total Cost Annual Cost EOQ Inventory Carrying Cost Ordering Cost Size of Order

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**Inventory Management EOQ formula: where**

P = the ordering cost (dollars/order) D = Annual demand (number of units) C = Annual inventory carrying cost (percent of product cost or value) V = Average cost per unit inventory

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Inventory Management Note, if the number is 124 units and there are 20 units per order, then the order quantity becomes 120 units Adjustments to the EOQ Includes volume transportation discounts Considers quantity discounts

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**Inventory Management Adjustments to the EOQ (continue) where**

Q1 = the maximum quantity that can be economically ordered r = the percentage of price reduction if a larger quantity is ordered D = the annual demand in units C = the inventory carrying cost percentage Q0 = the EOQ based on current price

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**Safety Stock Requirements4**

Formula for calculating the safety stock requirements: where sc = units of safety stock needed to satisfy 68% of all probabilities R = average replenishment cycle sR = STD of replenishment cycle S = average daily sales sS = STD of daily sales

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**Calculating Fill Rate Formula for calculating the fill rate: where**

FR = Fill rate sc = combined safety stock required to consider both variability in lead time and demand EOQ = order quantity I(K) = service function magnitude factor based on desired number of STD

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Calculating Fill Rate I(K) Table

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References Douglas M. Lambert and James R. Stock, “Strategic Logistics Management”, third edition, (Boston, MA: Irwin, 1993), pp 2 Ibid, pp 3 Ibid, pp 4 Ibid, pp. 415 5 Ibid, pp. 420

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**Logistics Systems Engineering**

SMU SYS 7340 NTU SY-521-N Logistics Systems Engineering Mathematical Computations of Inventory Dr. Jerrell T. Stracener, SAE Fellow

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**Mathematical Computations**

Problems with ordering too much Items affecting ordering cost Cost Trade-Offs Chart Economic Order Quantity (EOQ) EOQ considering discounts Uncertainties Basic Statistics Safety Stock Requirements Calculating Fill Rate

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**Problems with ordering too much**

Financial Statements Quick Ratio Inventory Turnover Debt Ratio Basic Earning Power (BEP) Return on Total Assets (ROA) Inventorying Warehousing

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**Problems with ordering too much**

Obsolescence Pricing Obligation to Shareholders Demotion Market Share

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**Items affecting ordering cost**

Transmitting the order Receiving the order Placing in storage Processing invoice Restocking Cost Transmitting & processing inventory transfers Handling the product Receiving at field location Cost associated with documentation

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**Cost Trade-Offs: Most Economical OQ**

Total Cost Lowest Total Cost (EOQ) Inventory Carry Cost Ordering Cost

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**Inventory Management EOQ formula: where**

P = the ordering cost (dollars/order) D = Annual demand (number of units) C = Annual inventory carrying cost (percent of product cost or value) V = Average cost per unit inventory

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**Inventory Management Example**

A company purchased a line of relay for use in its air conditioners from a manufacturer in the Midwest. It ordered approximately 300 cases of 24 units each 54 times per year. The annual volume was about 16,000 cases. The purchase price was $8.00 per case, the ordering cost were $10.00 per order, and the inventory carrying cost was 25 percent. The delivered cost of a case of product would be $9.00 ($8.00 plus $1.00 transportation). What is the EOQ?

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**Inventory Management At what rate should the company order skates?**

Solution: P = $10 per shipment D = 16,000 units per year C = 0.25 V = $9.00, and

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**Inventory Management Solution:**

Note, if the number is 377 units and there are 20 units per order, then the order quantity becomes 380 units

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**Inventory Management Assumptions:**

A continuous, constant and known rate of demand A constant and known replenishment or lead time A constant purchase price that is independent of the order quantity or time A constant transportation cost that is independent of the order quantity or time The satisfaction of all demand (no stock-outs are permitted)

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**Inventory Management Assumptions: No inventory in transit**

Only one item in inventory, or at least no interaction An infinite planning horizon No limit on capital availability

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Inventory Management Adjustments to the EOQ formula must be made to address Volume transportation discounts Quantity discounts Thus, the formula becomes:

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**Inventory Management where,**

Q1 = the maximum quantity that can be economically ordered r = the percentage of price reduction if a larger quantity is ordered D = the annual demand in units C = the inventory carrying cost percentage Q0 = the EOQ based on current price

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**Inventory Management Example**

Using the same example as previous, assume that the relays weighed 25 pounds per case. The freight rate was $4.00 per 100 lbs. on shipments of less than 15,000 lbs., and $3.90 per 100 lbs on shipments of 15,000 to 39,000 lbs. Lastly, on shipments of more than 39,000 lbs, the cost is $3.64 per 100 lbs. The relays were shipped on pallets of 20 cases. What is the cost if the company shipped in quantities of 40,000 pounds or more?

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**Inventory Management Solution:**

Cost per case: $3.64/100 lbs x25 lbs= $0.91. r = [($ $8.91) / $9.00] x 100 = 1.0% And Q1 is:

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Uncertainties What drives managers to consider safety stocks of the product? Economic conditions Competitive actions Change in government regulation Market shifts Consumer buying patterns Transit times Supplier lead times

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Uncertainties What drives managers to consider safety stocks of the product? Raw material Suppliers not responding Work stoppage

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**Basic Statistics Properties of a Normal Distribution**

Resembles a bell shape curve Measures central tendency Probabilities are determined by its mean, u and standard deviation, s, where and the theoretically infinite range is

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Basic Statistics Normal Curve

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**Safety Stock Requirements**

Example: Given

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**Safety Stock Requirements**

Formula for calculating the safety stock requirements: where sc = units of safety stock needed to satisfy 68% of all probabilities R = average replenishment cycle sR = STD of replenishment cycle S = average daily sales sS = STD of daily sales

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**Safety Stock Requirements**

And where: Example Calculate the Safety Stock Requirements based on the two following tables:

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**Safety Stock Requirements**

Given: Sales History for Market Area

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**Safety Stock Requirements**

Solution: Calculation of STD of Sales Where S= 100, and n= 25, and Sfd2 = 10,000

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**Safety Stock Requirements**

Solution: Given - Replenishment Cycle Where R = 10, and n = 16, and Sfd2 = 40

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**Safety Stock Requirements**

Solution:

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**Safety Stock Requirements**

Solution(continue): Finally, we have

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**Calculating Fill Rate Formula for calculating the fill rate: where**

FR = Fill rate sc = combined safety stock required to consider both variability in lead time and demand EOQ = order quantity I(K) = service function magnitude factor based on desired number of STD

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**Calculating Fill Rate Example**

Using the data from the previous example, what will the fill rate be if a manager wants to hold 280 units as safety stock? Assume EOQ = 1,000.

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**Calculating Fill Rate Solution:**

The safety stock determined by the manager is 280 units. Thus, K is equal to 280 / 175 = From the table in the end, we see that I(K) = Hence,

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Calculating Fill Rate Insert table 10-8, p 422

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**Calculating Fill Rate Differences**

Safety Stock: policy of customer service and inventory availability Fill Rate: represents the percent of units demanded that are on hand to fill customer orders. The magnitude of stock-out.

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**Calculating Fill Rate Conclusion**

K (the safety factor) is the safety stock the manager decides to hold divided by EOQ Therefore: The average fill rate is 99.59%. That is, of every 1,000 units of product XYZ demanded, will be on hand to be sold if the manager uses 280 units of safety stock and orders 1,000 units each time.

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