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**3/7: Inventory Planning & Control**

Roll call / collect homework / hand back hmwk Go over homework (?) Understanding inventory issues The basic numbers involved Holding cost, ordering cost, demand Basic EOQ model EOQ model with allowed shortages Assign homework Have a good Spring Break

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**Holding Cost Made of many things:**

Cost of capital (money tied up in inventory) Expressed as a % of amount invested (% of purch. price) Insurance Breakage Pilferage (Theft) Overhead, etc. Also expressed as a % of amount invested

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**Holding Cost Made of many things:**

Cost of capital (money tied up in inventory) Expressed as a % of amount invested (% of purch. price) Other holding costs Also expressed as a % of amount invested EX: I have $10,000 worth of 100 comic books. I estimate my cost of capital to be 11% and other holding costs to be 4%. What is my total holding cost in dollars? What is my holding cost per unit?

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**Ordering Cost A fixed cost Made of many things:**

Doesn’t change with quantity ordered Is charged each time a order is placed Made of many things: Salaries of purchasing department Cost of preparation of the order documents Cost of processing the order, etc.

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**Demand How much is required of the product**

In the Economic Order Quantity (EOQ) model, we assume that demand is CONSTANT. EX: Each month, I sell 200 comic books.

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**EOQ: The Dilemma We seek a balance while satisfying demand:**

Ordering costs must be kept as low as possible (over time), and Holding costs must be kept as low as possible. So how much do we order each time to minimize overall inventory costs?

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EOQ: The Dilemma So how much do we order each time to minimize overall inventory costs? Daily demand (slope) (d) Inventory ( Q ) Reorder Point (r) time Lead time ( L, l ) Cycle time (T)

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**The Basic EOQ Model EOQ: Economic Order Quantity**

Assumptions of EOQ models: Demand is constant (unvarying ), expressed as annual demand (units per year (or other time unit) ). 2 variable costs: setup cost and holding cost. Lead time is constant & known. Models use continuous review, not periodic review. Quantity discounts are not possible.

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**EOQ: Symbols & Assumptions**

Q: Maximum in inventory, as well as order quantity. What is the average inventory? Daily demand (slope) (d) Inventory ( Q ) Reorder Point (r) time Lead time ( L, l ) Cycle time (T)

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**EOQ: Symbols & Assumptions**

Lead time (L or l ) is constant & known, so we can order replenishment to be received when inventory hits zero. Measured in time units. Daily demand (slope) (d) Inventory ( Q ) Reorder Point (r) time Lead time ( L, l ) Cycle time (T)

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**EOQ: Symbols & Assumptions**

Reorder point (r) is the level of inventory at which a replenishment order will be triggered. Measured in units of inventory (portion of Q). Daily demand (slope) (d) Inventory ( Q ) Reorder Point (r) time Lead time ( L, l ) Cycle time (T)

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**EOQ: Symbols & Assumptions**

Cycle time (T) is the length of time it takes to use up the inventory (Q). Daily demand (slope) (d) Inventory ( Q ) Reorder Point (r) time Lead time ( L, l ) Cycle time (T)

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EOQ: Calculating it EOQ = Annual holding cost of average inventory Annual ordering cost EOQ = AHC + AOC

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**EOQ: Annual Holding Cost**

I = annual holding cost rate (note: RATE, %) C = unit cost of the inventory item Ch = annual cost of holding one unit in inventory Ch = I * C Annual holding cost of the average inventory is: avg. inventory level * ann. holding cost per unit

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**EOQ: Annual Ordering Cost**

D = annual demand for item (measured in units of item) D / Q = number of orders per year Co = Cost per order

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EOQ: Total Annual Cost

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**Example: Magazine Distributor**

Annual demand: 150,000 copies of Vogue Cost of ordering (Co) is $10 Cost per magazine is $1.50 Annual holding cost rate is 10%

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**Ex: Magazine Distributor**

Annual demand: 150,000 copies of Vogue Cost of ordering (Co) is $10 Cost per magazine is $1.50 Annual holding cost rate is 10% We still need to know what the order quantity is.

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**Total Cost vs. Order Quantity**

Combined curve: holding & setup. Annual Cost Minimum annual cost Holding cost curve We’ll find an equation for this amount Setup cost curve Optimal order quantity Order Quantity

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**So How Much Should We Order?**

The best order quantity will be found where AOC = AHC. Annual Cost Combined curve: holding + setup. Minimum annual cost Holding cost curve Setup cost curve Optimal order quantity Order Quantity

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Where AOC = AHC We replace AOC & AHC with their respective equations and then solve for Q. This value of Q is the Economic Order Quantity. We use Q* as its symbol.

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**Back to EX: Magazine Distributor**

Annual demand: 150,000 copies of Vogue Co is $10, cost per magazine is $1.50 Annual holding cost rate is 10% EOQ = 4472 magazines per order

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**But When Should We Order It?**

The reorder point (r) is expressed in units of inventory. Related to the lead time (m) (time it takes for an order to be fulfilled) by looking at the demand per day (d). Days per year is not necessarily 365 – it’s working days per year.

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**And How Long Will the Order Last?**

Since we know how many orders will be placed per year ( D / Q* ), we can calculate the cycle time in days. Go to Excel setup

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**New Situation: Planned Shortages**

Allows for backordering Q: amount of order, S: greatest shortage Therefore Q – S is amount of greatest inventory Q - S Daily demand (slope) (d) Inventory r S time Lead time ( L, l ) Cycle time (T)

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**Shortages: Cycle Time Sections**

T is divided into two distinct phases: t1 & t2 t1 is time with positive inventory. t2 is time with a shortage. Q - S Daily demand (slope) (d) Inventory t1 t2 r S time Lead time ( L, l ) Cycle time (T)

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**Shortages: Average Inventory Cost**

Calculating the average inventory: Q – S is greatest inventory, and S is greatest shortage, but you can’t go lower than zero. We need a weighted average of: The average inventory in t1 and 0 in t2.

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**Shortages: Average Inventory Cost**

Calculating the average inventory: Since we know that t1 = (Q–S) / d , & T = Q/d,

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**Shortages: Average Backorder Level**

And since and

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**Shortages: Average Backorder Level**

We can calculate the average backorder level as:

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**Total Inventory Cost for Shortages**

The total cost of the inventory system that allows for backorders is = AHC + AOC + annual cost of backordering Where Ch = cost to inventory 1 unit for 1 year Cb = cost to backorder 1 unit for 1 year Co = cost per order

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**So the EOQ for Shortages is…**

(Trust me…)

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Homework due 3/21 Ch. 11 #1 a-d (note: “Total Annual Cost” of the Inventory System) (do by hand) Ch. 11 #4 a-d (do with Excel) Ch. 11 #6 a-d (do with Excel) Ch. 11 #15 a-e (do by hand) Ch. 11 #17 (do with Excel)

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