INVENTORY CONTROLInventory refers to goods or items which an org. holds in its warehouses waiting to be sold or used. Or they are the usable resources currently kept idle. Broadly speaking inventory management is one way of maintaining for a given financial investment, an adequate supply of something in order to meet an unexpected demand To the manufacture management the word inventory connotesFinished goods available for distribution or salePartly finished goods moving through production stages Raw materials & inventory parts to be in computed in the end productOther inventory includeLibraries inventory is booksBanks inventory is moneyConsulting organization inventory is specialist skillsIn the broader sense inventories include machines, tools, personnel, cash auxiliary equipment of all kinds required in BusinessAll types of inventories have something in common when formulated mathematically Cost of maintaining inventoryCost of Replenishing inventory in order to serve particular policy or objectives. Hence there are costs of:i. Acquiring inventory ii. Holding inventory or carrying cost

INVENTORY DECISIONSA) What is the optimal quantity to order each time in order to minimize total inventory cost? OptionsLarge quantitiesImplicationsNumber of orders will go down; hence, the ordering cost will also go down.Holding/carrying costs go up2. Order small quantitiesImplicationNumber of orders goes up. Therefore the ordering cost go upHolding/carrying cost go downB When should each order be made?C How much safety stock should be kept in anticipation of the variations in demand or time involved in acquiring the item.VARIATIONSDemand/useSupply/Lead timeINVENTORY COSTSThere are four important types of costs associated with inventoryPurchase / production costs. Purchase cost are the costs to be incurred if the items are to be bought from outside the organization while production costs are to be incurred if the items are to be constant per unit or may vary as the quantity produced or purchased increases or decreases.Ordering/set-up costs. Ordering cost these are at times referred to procurement costs (ordering) and are incurred when goods are procured from outside the firm. This include the cost of processing requisition notes or purchases order, cost of following up the order, inspection costs, and quality control costs.

1 | P a g e

Set up cost is incurred when the goods are produced from within. It is associated with developing production schedules, setting up machines for production and acquiring raw materials for use.Holding or carrying costs. Sometimes referred to as the storage costs. They are incurred when our inventory is put in storage. Generally it is proportional to the amount of items stored and the period of storage. They include store man’s salary. Insurance, obsolescence costs, deterioration in value, scrapping and possible rework on our items.These costs are generally expressed as a rate/unit or a percentage of the inventory value SHORTAGE COSTS: Sometimes referred as the stock out cost or unsatisfied demand cost incurred when the amount of the commodity demanded is more than the amount available. If it is associated with the goods being bought from outside the firm, the storage costs can be interpreted asLoss of customers good will due to delayCustomers subsequent reluctant to do business with the firmCost of delayed revenue.If it is however associated with the temporary shortage of the materials required is produce items from within, then it can be interpreted asDelay in the completion of production. Process which might require and invite a penaltyLost production resulting into idle time for the many involving production and machines

TOTAL COST AS A FUNCTION OF QUANTITY ORDERED

2 | P a g e

Carrying/holding costTotal cost

Ordering cost

Cost

ECONOMIC ORDER QUANTITY (EOQ) MODELThis is a classical model, the oldest and simplest to use. To use this we make the following assumptions:The demand for the item is known continuous and constant over timethe lead time i.e. the time between the placement of an order and the receipt of an order is known and constantThe receipt of the inventory is instantaneous i.e. the inventory from an order arrives immediately the stock level reaches zero hence there are no stock shortages or excesses.Within the range of quantities to be ordered the per unit holding cost and the ordering cost for order are fixed and independent of the quantity ordered.The purchase price of the item is fixed and quantity discounts not allowedThe cost of managing inventory is made up solely of two costs i.e. the ordering and the carrying costs

COMPUTATION OF E.O.QALGEBRAIC METHOD

3 | P a g e

Re-order Level

Inventory Level

Q Maximum Stock level

Average Inventory

Q/2

LTLead time

VariablesQ=The E.O.Q or Optimal number of units to order each time in order to minimize the total inventory costC=Cost per unitI= Inventory carrying cost expressed as a percentage of the value of the average inventoryR=Total number of units required annuallyS=Ordering costs per order or set up costa) TOTAL ANNUAL ORDERING COSTSThis is given by ordering cost per orderNumber of orders x ordering cost=Per year per order

Total ordering costR/Q x S =RS/QB) TOTAL INVENTORY CARRYING COSTSThis is obtained by multiplying the unit holding cost by the average No. of unit held in the inventory i.e (Q/2)IC EOQEQUATE THE TWO AND SOLVE FOR QRS/Q=QIC/22RS=Q2CIQ2=2RS/CIQ=√2RS/CIAssumeR=2000 unitsC=Sh10.00 per unitI=10%S=Shs40.00 per uniti) Determine QQ=√2*2000*40/10*10% =√160000 =400unitsThe carrying cost=Q/2 CI=(400*10*0.1)/2=Sh200The ordering cost=RS/Q=2000*40/400=Sh200Minimum cost =Sh200+Sh200=Sh400

4 | P a g e

If you are providing inventory we will have economic batch quantity (EBS)=√2RS/CI(1-d/p)

Where:d- Quantity demandedp- Quantity producedS- Set up costQUANTITY DISCOUNT MODELThe classical E.O.Q model assumes that the unit cost of the item remains uniform and constant throughout the period. Hence no account is taken of Quantity discount this however is unrealistic because structure price discounts are given and obtained when quantities ordered increase. Quantity discount is realized when a firm buys in larger quantities than E.O.Q. The advantages of buying in large quantities includeLower price per unitFewer orders to be placed hence lower ordering costFewer stock outBetter service to customersThe disadvantages areHigher inventory carrying costsMore capital required to be invested in the inventoryGreater chance of deteriorations in valuePilferage of goodsCOST COMPARISON APPROACHIn this method the cost associated with a computed E.O.Q are compared with the cost associated with the Quantities proposed if the buyer was to qualify for the quantify discount.The costs include:The inventory purchase costTotal ordering costsTotal inventory carrying costTC=RC+ QCI/2 + RS/QE.O.Q SITUATION

Compute1 Purchase cost= RC2 Ordering cost = RS/Q3 Carrying cost= QCI / 2QUANTITY DISCOUNT SITUATIONPurchase cost=RCOrdering cost =RS/QCarrying cost Q/2 CI ExampleA printing press uses 1000 packet of paper each year. Ordering cost is shs12 per order. Carrying cost 50cts per packet p.a based on average annual stock. The price per packet is shs.7.50. The supplier has offered a 2 % quantity discount if the printing press purchases 450 or more packets at any one time, should the offer be taken?SolutionR=1000 C=7.50 S=Sh12 I=50cts

5 | P a g e

MULTIPLE PRICE BREAKS MODELThis is used where there are more than one price discount offer hence more than one price break may be available. In this case at any level of quantity purchased, quantity discount is given. A company may therefore end up having several successful quantity discount offers at respective successful purchase quantity levels. The purchase Q. level where Q. Discount is offered is called price breaking hence a company may have several successive price breaks. At each price break E.O.Q is computed, after that Total inventory cost at each of the successive quantity levels at which the price break occurs is determined.At whatever level it is the least we will call that as the optimum E.O.Q. the various E.O.QS are tested to determine if the savings in the purchase cost of the item and the reduced order cost will offset the increases in the holding cost.

ORDER SIZE PRICE1-99 10.00100-199 9.50200-299 9.00300-399 8.70400& over 8.50

We determine E.O.Q at each price break start with the lowest price.E.O.Q=√2RS/CI

Then you start computing the TC=RC+QCI/2+RS/QThe mode of determining optimal order quantity is as followsDetermine E.O.Q of the lowest cost price available if this quantity is feasible i.e. if the E.O.Q falls within the range of the lot size of which the price is used then it represents the optimal solution. If however it is infeasible take the next lowest price in order to determine E.O.Q. If it is also infeasible, try the next lowest price; proceed until you get the feasible.After obtaining feasible E.O.Q determine the total inventory cost corresponding to itDetermine the total inventory cost of the order quantity values corresponding to the cut of points of subsequent order size categoriesAmong these total cost values select the minimum. The quantity on which the least total cost is based is the optimal order quantity.ExampleA furniture house makes and sells chairs, Then information is as follows.Expected annual sales 8000 chairsOrdering cost Shs180 per orderHolding cost 10% of Av. Inventory valueA chair can be purchased according to the following scheduleORDER SIZE UNIT PRICE (SHS)1-999 22.001000-1499 20.001500-1999 19.002000 and above 18.50Determine the E.O.Q for this firm.

6 | P a g e