Backorder Inventory Model
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Backorder Inventory Model In this model, we assume that stock outs (and backordering) are allowed. In addition to previous assumptions, we assume that sales will not be lost due to a stock out. Because, we will back order any demand that can not be fulfilled B: Backordering cost per unit per year b: The amount backordered at the time the next order arrives Q – b: Remaining units after the backorder is satisfied
Total Annual Cost = Annual Setup Cost + Annual Holding Cost + Annual Backordering Cost
Annual Setup (Ordering) Cost = (D/Q) . S
Annual Holding Cost = (Average Inventory Level) . H By using the graphical ratios, we know that:
T1 / T = (Q – b) / Q Therefore, if we replace T1/T in the above equation we get
Average Inventory Level = (Q – b)2 / 2Q
By using the graphical ratios, we know that: T2 / T = b / Q Therefore, if we replace T2/T in the above equation we get Average Backordering = b2 / 2Q and
We find optimum order quantity (Q*) and optimum backordering quantity (b*) by taking the derivatives of dTC/dQ = 0 and dTC / db = 0 and then putting the values in their places.
Quantity Discount Model
A quantity discount is simply a reduced price (P) for an item when it is purchased in LARGER quantities. A typical quantity discount schedule is as follows: Since the unit cost for the Third discount is the lowest, We might be tempted to order 2000 or more units. However, this quantity might not be the one that minimizes the Total Cost. Remember that, As the quantity goes up, the holding cost increasesHere, there is a trade off between reduced product price (P) and increased holding cost (H). Total Cost = Setup Cost + Holding Cost + Product Price (Cost) Total Cost = DS / Q + QH / 2 + PD where P is the price per unit To determine the minimum Total Cost, we perform the following process which includes 4 steps: Step 1: Assume that I: is a percentage value, and I . P represents the holding cost as a percentage of price per unit (P). For each discount alternative, calculate a value of Q* = [2DS / IP]1/2 Here, instead of using a value of H, the holding cost is equal to I . P
That is, If the item is expensive (such as a Class A Item), Its holding cost will be higher. Since the price of item (P) is a factor in Annual Holding Cost, we can no longer assume that the holding cost is constant (such as H) when price changes. Step 2: For any discount alternative, If the calculated optimum order quantity (Q*) is too low to qualify for the discount range, Then, Adjust the order quantity upward to the lowest quantity that will qualify for the particular discount alternative. Step 3: Using the total cost (TC) equation above, compute a total cost for every order quantity (Q). Use the adjusted Q values. Step 4: Select the discount alternative which has the minimum Total Cost (TC).
Total Annual Cost = Annual Setup Cost + Annual Holding Cost + Annual Backordering Cost
Annual Setup (Ordering) Cost = (D/Q) . S
Annual Holding Cost = (Average Inventory Level) . H By using the graphical ratios, we know that:
T1 / T = (Q – b) / Q Therefore, if we replace T1/T in the above equation we get
Average Inventory Level = (Q – b)2 / 2Q
By using the graphical ratios, we know that: T2 / T = b / Q Therefore, if we replace T2/T in the above equation we get Average Backordering = b2 / 2Q and
We find optimum order quantity (Q*) and optimum backordering quantity (b*) by taking the derivatives of dTC/dQ = 0 and dTC / db = 0 and then putting the values in their places.
Quantity Discount Model
A quantity discount is simply a reduced price (P) for an item when it is purchased in LARGER quantities. A typical quantity discount schedule is as follows: Since the unit cost for the Third discount is the lowest, We might be tempted to order 2000 or more units. However, this quantity might not be the one that minimizes the Total Cost. Remember that, As the quantity goes up, the holding cost increasesHere, there is a trade off between reduced product price (P) and increased holding cost (H). Total Cost = Setup Cost + Holding Cost + Product Price (Cost) Total Cost = DS / Q + QH / 2 + PD where P is the price per unit To determine the minimum Total Cost, we perform the following process which includes 4 steps: Step 1: Assume that I: is a percentage value, and I . P represents the holding cost as a percentage of price per unit (P). For each discount alternative, calculate a value of Q* = [2DS / IP]1/2 Here, instead of using a value of H, the holding cost is equal to I . P
That is, If the item is expensive (such as a Class A Item), Its holding cost will be higher. Since the price of item (P) is a factor in Annual Holding Cost, we can no longer assume that the holding cost is constant (such as H) when price changes. Step 2: For any discount alternative, If the calculated optimum order quantity (Q*) is too low to qualify for the discount range, Then, Adjust the order quantity upward to the lowest quantity that will qualify for the particular discount alternative. Step 3: Using the total cost (TC) equation above, compute a total cost for every order quantity (Q). Use the adjusted Q values. Step 4: Select the discount alternative which has the minimum Total Cost (TC).
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