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Operations Research Inventory Management

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Definition The word inventory means a physical stock of material or goods or commodities or other economic resources that are stored or reserved or kept in stock or in hand for smooth and efficient running of future affairs of an organization at the minimum cost of funds or capital blocked in the form of materials or goods (Inventories). The function of directing the movement of goods through the entire manufacturing cycle from the requisitioning of raw materials to the inventory of finished goods in an orderly manner to meet the objectives of maximum customer service with minimum investment and efficient (low cost) plant operation is termed as inventory control

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**Classification Direct inventories (i) Raw material inventories:**

(ii) Work-in -process inventories or in process inventories (iii) Finished goods inventories: (iv) Spare parts inventories:

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**Classification (B) Indirect Inventories (i) Fluctuation Inventories:**

(ii) Anticipation inventory: (iii) Lot size inventory or Cycle inventories : (iv) Transportation Inventories:

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**Inventory Models: Deterministic Demand**

Economic Order Quantity (EOQ) Model Economic Production Lot Size Model Inventory Model with Planned Shortages Quantity Discounts for the EOQ Model

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**Economic Order Quantity**

Assumptions Demand is constant throughout the year at D items per year. Ordering cost is $Co per order. Holding cost is $Ch per item in inventory per year. Purchase cost per unit is constant (no quantity discount). Delivery time (lead time) is constant. Planned shortages are not permitted.

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**Economic Production Lot Size**

The economic production lot size model is a variation of the basic EOQ model. A replenishment order is not received in one lump sum as it is in the basic EOQ model. Inventory is replenished gradually as the order is produced (which requires the production rate to be greater than the demand rate). This model's variable costs are annual holding cost and annual set-up cost (equivalent to ordering cost). For the optimal lot size, annual holding and set-up costs are equal.

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**Economic Production Lot Size**

Assumptions Demand occurs at a constant rate of D items per year. Production rate is P items per year (and P > D ). Set-up cost: $Co per run. Holding cost: $Ch per item in inventory per year. Purchase cost per unit is constant (no quantity discount). Set-up time (lead time) is constant. Planned shortages are not permitted.

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**EOQ with Planned Shortages**

With the EOQ with planned shortages model, a replenishment order does not arrive at or before the inventory position drops to zero. Shortages occur until a predetermined backorder quantity is reached, at which time the replenishment order arrives. The variable costs in this model are annual holding, backorder, and ordering. For the optimal order and backorder quantity combination, the sum of the annual holding and backordering costs equals the annual ordering cost.

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**EOQ with Planned Shortages**

Assumptions Demand occurs at a constant rate of D items/year. Ordering cost: $Co per order. Holding cost: $Ch per item in inventory per year. Backorder cost: $Cb per item backordered per year. Purchase cost per unit is constant (no qnty. discount). Set-up time (lead time) is constant. Planned shortages are permitted (backordered demand units are withdrawn from a replenishment order when it is delivered).

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**EOQ with Quantity Discounts**

The EOQ with quantity discounts model is applicable where a supplier offers a lower purchase cost when an item is ordered in larger quantities. This model's variable costs are annual holding, ordering and purchase costs. For the optimal order quantity, the annual holding and ordering costs are not necessarily equal.

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**EOQ with Quantity Discounts**

Assumptions Demand occurs at a constant rate of D items/year. Ordering Cost is $Co per order. Holding Cost is $Ch = $CiI per item in inventory per year (note holding cost is based on the cost of the item, Ci). Purchase Cost is $C1 per item if the quantity ordered is between 0 and x1, $C2 if the order quantity is between x1 and x2 , etc. Delivery time (lead time) is constant. Planned shortages are not permitted.

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**EOQ with Quantity Discounts**

Assumptions Demand occurs at a constant rate of D items/year. Ordering Cost is $Co per order. Holding Cost is $Ch = $CiI per item in inventory per year (note holding cost is based on the cost of the item, Ci). Purchase Cost is $C1 per item if the quantity ordered is between 0 and x1, $C2 if the order quantity is between x1 and x2 , etc. Delivery time (lead time) is constant. Planned shortages are not permitted.

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