Operations Research Lecture 12.

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Presentation transcript:

Operations Research Lecture 12

Operations Research Inventory Control

Inventory Physical stock of items held in any business for the production or sales

Type of Inventory Finished Goods ! Finished Product Raw Material In-Process Finished Goods !

Inventory Costs Shortage Cost Rs C1 /item/unit time Item Cost, Rs C1/item Ordering Cost, Rs C2 /order Holding Cost Rs C1 /item/unit time Shortage Cost Rs C1 /item/unit time

Inventory Models (EOQ Models) The inventory control model can be broadly classified into two categories: Deterministic inventory problems Probabilistic inventory problems

Model 1: Purchasing Model with no Shortages The following assumptions are made in deriving the formula for economic order quantity. Demand (D) is at a constant rate. Replacement of items is instantaneous (lead time is zero).

Cont ! The cost coefficients C1, C2, and C3 are constant. There is no shortage cost or C4 = 0.

Cont ! Quantity Time

Model The total cost for this model for one cycle is made up of three cost components. Total cost / period = (Item cost + set up cost + holding cost / period)

Cont ! Item cost per period = (Cost of item) x (number of items ordered / period) Purchase or set up cost per period = C2 (only one set up per period)

Cont ! Item holding cost per period = (Holding cost)x(average inventory per period)x(time per period) Therefore the total cost per period

Cont ! But the time for one period Therefore the total cost per unit time,

Purchase cost = Item holding cost. Cont ! Purchase cost = Item holding cost.

Cont ! This Gives

Alternate Method This minimum inventory cost per unit time can also be found by differentiating C with respect to Q and equating it to zero. That is

Cont !

Further more ! D is the demand per year

Example The demand rate for a particular item is 12000 units/year. The ordering cost is Rs 100 per order and the holding cost is Rs 0.80 per item per month. If no shortages are allowed and the replacement is instantaneous, determine: (a) The economic order quantity (b) The time between orders (c) The number of orders per year (d) The optimum annual cost, if the cost of item is Rs 2 per item.

Solution C1 = Rs. 2.0 / item C2 = Rs. 100 / order C3 = Rs. 0.80/item/month = Rs. 9.6/item/year D = 12000 items/year

Cont ! (a)The economic order quantity

Cont ! (b)The time between orders

Cont ! (c)The number of orders / yr

Cont ! (c) The optimum annual cost

Model 2 Purchasing Model with Shortages

Operations Research Lecture 12