Operations Research Lecture 13.

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Presentation transcript:

Operations Research Lecture 13

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

D is the demand per year

Model 2 Purchasing Model with Shortages

In this model, shortages are allowed and consequently a shortage cost is incurred. Let the shortages be denoted by ‘S’ for every cycle and shortage cost by C4 per item per unit time. This model is illustrated in Figure

Q T Q Im s t t2 t1 t = t1 + t2

Figure shows that the back ordering is possible (i. e Figure shows that the back ordering is possible (i.e.) once an order is received, any shortages can be made up as the items are received. Consequently shortage costs are due to being short of stock for a period of time. The cost per period includes four cost components. Total cost per period = Item cost + Order cost + Holding cost + Shortage cost

Item cost per period = (item cost) x (number of items/period) = C1xQ Order cost per period = C2 Holding Cost per period = Average stock / period x t1 x holding cost / unit / unit time Shortage Cost per period = Average shortages / period x t2 x shortage cost

Example

The demand for an item is 18000 units/year The demand for an item is 18000 units/year. The cost of one purchase is Rs 400. The holding cost is Rs 1.2 per unit per year. The item cost is Rs 1 per item. The shortage cost is Rs 5 per unit per year. Determine: (a) The optimum order quantity. (b) The time between orders. (c) The number of orders per year. (d) The optimum shortages. (e) The maximum inventory. (f) The time of items being held. (g) The optimum annual cost.

= 1500 units / month C1 = Rs 1.0 / item C3 = Rs 1.2 / year/ item Data D = 18000 units / year = 1500 units / month C1 = Rs 1.0 / item C3 = Rs 1.2 / year/ item C2 = Rs 400 /order C4 = Rs 5.0 / year / item

Optimum Order Quantity

Time Between Orders

Number of Orders per year Number of orders per year = 12 / 2.57 = 4.66

Optimum Shortages

Maximum Inventory

The Time when Items being held

Order cost = Rs 400 per order Optimum Annual Cost Annual cost = Item cost + Ordering cost + Holding cost + Shortage cost Item cost = Rs 3857 per order Order cost = Rs 400 per order

Holding Cost

Shortage Cost

Total Cost per order

= (Number of orders / year) x Cost = Rs 4.66 x 4656.89 = Rs 21701 Annual Cost Annual Cost = (Number of orders / year) x Cost = Rs 4.66 x 4656.89 = Rs 21701

Operations Research Lecture 13