Operations Research Lecture 11

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 Planning Determination of the type and the quantity of inventory items that would be required at future points for maintaining schedules

Inventory Control Primarily concerned with the inventory cost control

Two Important Questions How much to stock or how much to buy? How often to buy or when to buy?

Answer Economic Order Quantity Model Economic Batch/ Lot Size Mode

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

Item Cost C1 This is the cost of the item whether it is manufactured or purchased. If it is manufactured, it includes such items as direct material and labor, indirect materials and labor and overhead expenses. When the item is purchased, the item cost is the purchase price of 1 unit. Let it be denoted by Rs. C1 per item.

Purchasing or Setup or acquisition or Ordering Cost C2 Administrative and clerical costs are involved in processing a purchase order, expediting, follow up etc., It includes transportation costs also. When a unit is manufactured, the unit set up cost includes the cost of labor and materials used in the set up and set up testing and training costs. This is denoted by Rs. C2 per set up or per order.

Inventory Holding Cost C3 If the item is held in stock, the cost involved is the item carrying or holding cost. Some of the costs included in the unit holding cost are   Locked up capital in inventory (Interest), Storage-space costs, Items handling costs, Taxes on inventories,

Cont ! Insurance costs for inflammable and explosive items, Obsolescence, Deterioration of quality, theft, spillage and damage to times, Cost of maintaining inventory records.   This cost is denoted by Rs. C3 item/unit time. The unit of time may be days, months, weeks or years.

Shortage Cost C4 The shortage cost is due to the delay in satisfying demand (due to wrong planning); but the demand is eventually satisfied after a period of time. Shortage cost is not considered as the opportunity cost or cost of lost sales. The unit shortage cost includes such items as

Shortage Cost C4 Overtime requirements due to shortage, Clerical and administrative expenses. Cost of expediting. Loss of goodwill of customers due to delay. Special handling or packaging costs. Lost production time.   This cost is denoted by Rs. C4 per item per unit time of shortage.

Inventory Models (EOQ Models) The inventory control model can be broadly classified into two categories: (1) Deterministic inventory problems. (2) Probabilistic or stochastic inventory problems.

In the deterministic type of inventory control, the parameters like demand, ordering quantity cost, etc are already known or have been ascertained and there is no uncertainty. In the stochastic inventory control, the uncertain aspects are taken into account.

First let us consider the inventory control of the deterministic type. We will discuss four EOQ models, the first one is the well known Wilson’s inventory model.

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

Operations Research Lecture 11