OPERATIONS AND LOGISTICS MANGEMENT

WHAT IS INVENTORY

• Refers to goods or materials that are held by an organization for future usage.It includes

(i) raw materials, (ii) purchased parts, (iii) components, (iv)sub assemblies, (v) work-in-process, (vi) finished goods and (vii) supplies

• One main reason that organisations maintain inventory is that it is rarely possible to forecast / predict sale levels, production times, demand and usage needs exactly

• An inventory system is the set of policies and controls that monitors levels of inventory, in order to minimise the inventory cost and to guarantee a smooth operation of the organisation

PURPOSES

• To maintain independence of operations• To meet variation in product demand• To allow flexibility in production scheduling• To provide a safeguard for variation in raw

material delivery time• To take advantage of economic purchase

order size

Inventory costs• Holding (or carrying) costs: storage facilities, handling,

insurance, pilferage, breakage,obsolescence, depreciation, taxes, and the opportunity cost of capital.

• Ordering costs: typing, calling, transportation, receiving, etc. This cost does not dependon quantity ordered.

• Shortage costs (stockout costs): the loss due to losing a specific sale, customers goodwill,or future business.

• Setup (or production change) costs: line conversion, equipment change-over, reportpreparation, etc.

• Cost of the item.

Inventory models

Inventory models

• modelled quantitatively based on demand patterns

• Deterministic inventory models- demand rate of an item is assumed to be constant.

• Probabilistic inventory models- demand for an item fluctuates and is specified in probabilistic terms.

• Based on the frequency at which orders are placed for procuring inventory

• Single Period models- Typically orders are made only once. used for one time ordering for seasonal products or spare parts purchases.

• Multi Period models- Orders are placed multiple times over the entire production cycle.

• Continuous Review (also called Fixed Quantity or Q system):

Inventory is reviewed continuously and when inventory drops to a certain (prefixed) reorder level, a fixed quantity is ordered. This model is generally used for high volume, valuable, or important items.

• Periodic Review (also called as P system): Inventory is reviewed at (prefixed)

periodic intervals irrespective of the levels to which inventory drops; an order is placed to bring up the inventory to the maximum level. This is used for moderate volume items

Other inventory systems

• Optional replenishment system: Inventory is reviewed on a fixed frequency and a specific quantity is ordered, if inventory is below a certain level. This is a mix of the P and Q systems.

• Two-bin system: An inventory amount equal to R is kept in reserve in a second bin. When the first bin is emptied, the second bin is emptied into the first and an order of size Q is placed.

• One-bin system: This is the P-system where one bin is reviewed at a fixed interval and inventory is brought up to a certain level.

• ABC Inventory planning: Inventory items are classified into

three groups on the basis of annual dollar volume. Inventory items with a high dollar volume are more frequently reviewed compared to a low dollar volume.

• A: high dollar volume items, say 15% of the total number of items

• B: moderate dollar volume items, say the next 35%

• C: low dollar volume items, the last 50%

Probabilistic Models

• In probabilistic models, demands are described by probability distributions based on which inventory is decided.

Single-period inventory model with probabilistic demand

• inventory is perishable and demand for that particular inventory exists only for the period at which it is ordered (or) procured.

• Example : Newspaper selling, Fashion sellingThe newspaper ordered for today will

not be sold at the same price tomorrowSpring-summer designs will not sell

during the autumn-winter season

• Increment analysis is used to determine the optimal order quantity for a single-period inventory model with probabilistic demand

• How much to order question by comparing the cost or loss of ordering one additional unit with the cost or loss of not ordering one additional unit.

Notation used• Co : Cost per unit of overestimating demand; represents

the loss of ordering one additional unit that may not sell.• Cu : Cost per unit of underestimating demand; represents

the loss of not ordering one additional unit for which demand existed otherwise.

• Let the probability of the demand of inventory being more than a certain level y is P(D >y), and the probability of the demand of inventory being less than or equal to this level y is P(D <= y).

• Then, the expected loss (EL) is given by either of the two conditions below.– Overestimation: EL(y + 1) = Co P(D <= y)– Underestimation: EL(y) = Cu P(D > y)

• P(D <= y) =Cu/(Cu + Co)• The above expression provides the general

condition for the optimal order quantity y in the single-period inventory model. The determination of y depends on the probability distribution

Deterministic Models

• The order quantity (how much) and reorder point (when) are determined deterministically by minimising the total inventory cost that can be expressed as a function of these two variables.

• The total inventory cost (TC) is generally composed of the following components:

• TC = Tc + To + Ts + D*C;

Single-item static (EOQ) model with no shortages

• applicable when the demand for an item has constant, or nearly constant, rate and when the entire quantity ordered arrives in inventory at on point in time

• zero lead time=it is the time difference between arrival of orders and instant at which order is placed

Single-item static (EOQ) model with shortages

• A shortage is a demand that cannot be supplied immediately.

• The impact of shortage is either a lost business or back-ordering.

• A back-ordering is a condition where in orders are continued to be accepted, even when the inventory is zero, so as to supply as and when orders are replenished.

• Automobile dealers are good examples for this model.• This model mainly applies to industries, where holding

costs are much higher than shortage costs and lead time is either less or can be reduced easily

assumptions

• Shortage cost is small• No demand is lost because of shortage as the

customers will back order• Delayed delivery is accepted• Replenishment is instantaneous