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[post][Stock control
by Tony Mock21 May 2007         
Stock control features in the syllabuses of several ACCA examination papers. The areas usually tested in these papers are:
determiningan economic order quantity (EOQ) – calculations to assess how manyunits of a particular stock item to order at a time
finding anoptimal re-order level (optimal ROL) – providing some idea of the levelto which stocks can be allowed to fall before placing an order for more
discussionsof various practical aspects of stock management – often referred to bystudents with no practical experience as ‘theory’.
Advantages and disadvantages of holding stock
Thebasis of the theoretical calculations of an EOQ and an optimal ROL isthat there are advantages and disadvantages of holding stock (of buyingstock in large or small quantities). The advantages include:
the need to meet customer demand
taking advantage of bulk discounts
reducing total annual re-ordering cost.
The disadvantages include:
storage costs
cost of capital tied up in stock
deterioration, obsolescence, and theft.
Theaim behind the calculations of EOQ and ROL is to weigh up these, andother advantages and disadvantages and to find a suitable compromiselevel.
EOQ
When determining how much to order at a time, an organisation will recognise that:
as order quantity rises, average stock rises and the total annual cost of holding stock rises
as order quantity rises, the number of orders decreases and the total annual re-order costs decrease.
Thetotal of annual holding and re-order costs first decreases, thenincreases. The point at which cost is minimised is the EOQ. This costbehaviour is illustrated by the graph in Figure 1.
Figure 1
The way in which this EOQ is calculated is based on certain assumptions, including:
constant purchase price
constant demand and constant lead-time
holding-cost dependent on average stock
order costs independent of order quantity.
The assumptions result in a pattern of stock that can be illustrated graphically as shown in Figure 2.
Figure 2
The Formula
Usingthe standard ACCA notation in which:CH = cost of holding a unit ofstock for a yearCO = cost of placing an orderD = annual demand
also:TOC = total annual re-ordering costTHC = total annual holding costx = order quantity
then:average stock = x/2
THC = x/2 × CH
and:number of orders in a year = D/x
TOC = D/x × CO
The total annual cost (affected by order quantity) is:C = THC + TOC = x/2 × CH + D/x × CO
Thisformula is not supplied in exams – it needs to be understood (andremembered).The value of x, order quantity, that minimises this totalcost is the EOQ, given by an easily remembered formula:

Use of EOQ Formula
Youneed to take care over which figures you put into the formula,particularly in multiple-choice questions. The areas to beware of fallinto two categories:
Relevant costs – only include those costsaffected by order quantity. Only include those holding costs which (intotal in a year) will double if you order twice as much at a time. Onlyinclude those order costs which (in total in a year) will double if youorder twice as often. (Thus, fixed salaries to storekeepers or buyingdepartment staff will be excluded.)
Consistent units – ensure thatfigures inserted have consistent units. Annual demand and cost ofholding a unit for a year. Both holding costs and re-ordering costsshould be in £, or both in pence.
Bulk Discounts
A common twistto exam questions is to ask students to evaluate whether bulk discountsare worth taking. While prices reduce, total annual holding costs willincrease if more stock is ordered at a time, so the matter needs alittle thought. The common approach is one of trial and error. Thisinvolves finding the total annual cost (holding cost, re-ordering costand purchasing cost) at the level indicated by the EOQ and at thelevel(s) where discount first becomes available.Figure 3 shows totalcosts (now including cost of purchasing the stock) plotted againstorder quantity with discount incorporated.
Figure 3
Point Arepresents the cost at the order quantity indicated by the EOQ. Ifstock is ordered in larger quantities, total costs will increase topoint B1, at which stage bulk discounts are available, bringing thecosts down to point B. Any calculations will involve finding which costout of A, B or C is the lowest, as Example 1 will show.
Example1Moore Limited uses 5,000 units of its main raw material per month. Thematerial costs £4 per unit to buy, supplier’s delivery costs are £25per order and internal ordering costs are £2 per order. Total annualholding costs are £1 per unit. The supplier has offered a discount of1% if 4,000 units of the material are bought at a time.
Required:
Establish the economic order quantity (EOQ) ignoring the discount opportunities.
Determine if the discount offer should be accepted.
Example 1 solutions
Re-order levels
Asimportant as how much to order at a time is the question of when toorder more stock. If an order is placed too late, when stocks have beenallowed to run too low, a ‘stock-out’ will occur, resulting in either aloss of production or loss of sales, or possibly both.
If orders areplaced too soon, when there are still substantial supplies in stock,then stock levels and holding costs will be unnecessarily high. There-order level as explained below should not be confused with the stockcontrol levels referred to in textbooks – this article ignores these.When it comes to calculating re-order levels, three sets ofcircumstances can be envisaged.
Lead-time is zero‘Lead-time’ is theinterval between placing an order with a supplier and that orderarriving. It is unlikely that this could be reduced to zero – it wouldrequire astonishingly co-operative and efficient suppliers. If it werepossible, a re-order level of zero could be adopted. An organisationcould simply wait until it ran out of stock, click its corporatefingers, and stock would arrive instantaneously.
Constant demand, fixed finite lead-time
Theassumption of constant demand is consistent with the assumptionsunderlying the EOQ formula. If suppliers take some time to providegoods, orders need to be placed in advance of running out. Figure 4illustrates the problem and its solution.
Figure 4
If thelead-time is, say, 5 days, an order has to be placed before stocks havebeen exhausted. Specifically, the order should be placed when there isstill sufficient stock to last 5 days, i.e:
Re-order level (ROL) = Demand in lead-time
So,if lead-time for a particular stock item is 5 days and daily demand is30 units, the re-order level would be 5 days at 30 units per day, 150units.
Variable demand in the lead-time
If demand in lead-timevaried, it could be described by means of some form of probabilitydistribution. Taking the previous example of the demand in lead-timebeing 150 units, we’re considering the possibility of demand being morethan 150 or less than that. See Figure 5.
Note: This aspect of stockcontrol produces a few problems. The EOQ formula requires that demand(and lead-time) for a stock item be constant. Here the possibility ofdemand varying or lead-time varying or both varying is introduced.Setting that problem aside, most ACCA syllabuses at the lower levelsavoid any discussion of uncertainty or probability distributions.However, uncertainty in lead-time demand in stock control has featuredin exams.In these circumstances, a firm could place an order with asupplier when the stock fell to 150 units (the average demand in thelead-time). However, there’s a 33% chance (0.23 + 0.08 + 0.02 = 0.33)that demand would exceed this re-order level, and the organisationwould be left with a problem. It is therefore advisable to increase there-order level by an amount of ‘buffer stock’ (safety stock).
Buffer stock
Bufferstock is simply the amount by which ROL exceeds average demand inlead-time. It is needed when there is uncertainty in lead-time demandto reduce the chance of running out of stock and reduce the cost ofsuch shortages.
If a ROL of 160 units was adopted, this wouldcorrespond to a buffer stock of 10 units (and reduce the chance ofrunning out of stock to 0.08 + 0.02 = 0.1, or 10%). A ROL of 170 isequivalent to a buffer stock of 20 and reduces the chance of runningout to 2%, and a ROL of 180 implies 30 units of buffer stock (and nochance of running short).
Optimal Re-order Levels
This leaves theproblem of how to calculate the optimal ROL. There are two common waysin which one could determine a suitable re-order level (if theinformation was available):
A tabular approach – Calculate, for eachpossible ROL (each level of buffer stock) the cost of holding differentlevels of buffer stock and the cost incurred if the buffer isinadequate (‘stock-out’ costs). The optimal re-order level is thatlevel at which the total of holding and stock-out costs are a minimum.
A‘service level’ approach – An organisation has to determine a suitablelevel of service (an acceptably small probability that it would run outof stock), and would need to know the nature of the probabilitydistribution for lead-time demand. These two would be used to find asuitable ROL.
Tony Mock is a freelance lecturer and writer and an ACCA subject coordinator
   
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