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200 units demanded daily

200 * 5 =1000 units supplied per week… This is the base stock level demand. In a week 1000 units ought to be available in stock in readiness to the week’s orders.

Assumptions made

Beginning Inventory =0 units

Week ends on Friday (5 days)

Fill factor rate is 100 % – no shortage nor surplus

Shortage of the units on demand is not acceptable at the end of every week.

NB; to better understand this, consideration is first made to the initial week. Suppose for that week, the planned supply would be 1000 units, and the weekly demand is 1000 units, and the starting inventory is 0 units, the end inventory for that week would thus be 0+1000-1000 = units. The units delivered within the week have ready demand.



For a 100% fill rate, the received units must be equal to the number of units demanded. This means that there will be no surplus or shortage.


Demand is across the 7 days in a week; a total of 7 * 200 units will be the weekly demand. This is equal to 1400 units. As for the entire period, 1400 * 8 would be the overall demand. This is equal to 11200.

For week one, considering that there would be supply on Friday, there must be in stock enough supply to service orders through Thursday; the first batch of supply must be enough to service 200 *4 = 800 units.

Assuming 0 initial inventories with the first delivery on a Monday morning; 800 units delivery would be enough to service week’s orders through Thursday. As there is anticipated to be another supply on Friday of 800 units for use on Friday, Saturday and Sunday, this will leave a surplus of 200 units to add on the Monday’s supply. This is well illustrated in Excel sheet two. With this plan, the 7 week equal supply of 800 units (on Mondays and Fridays), will be enough to service the 8 weeks demand of 200 units per day assuming a form factor of 100 per cent.


As illustrated in the excel sheet, there would be no difference in cost if either of the delivery        means were used. This is because the units demanded are the same for the entire 8 weeks period.


The Excel sheet 4 illustrates the two models. On occasions with backlogs as evidenced, the company had loss of revenue resulting from penalties amounting to $1500 dollars respectively per week. This has implications on the profits/expected revenue. The loss in profits amounts to $1500*8=$12000 over the entire period. On the other hand, the case with stock-outs would also impact on the profit expectations of the company. This however would be dependent on the expected profit margin per unit. For instance, for a 10% profit margin, the lost profit would be $500 for week one and $1000 for the succeeding weeks. Anyhow, both the stock outs and backlogs have profit implications with the backlogs having the severest of the impacts (going by the above illustration and an assumption of 10% profit margin)


From the excel sheet 5 calculations of fill rate and cycle service level, the inventory’s ability to service a customer’s order during the cycle of replenishment is so low. In contrast, there is a high likelihood of the customers’ orders being served on time. The fill rate is relatively higher and on most instances 100%. On the backlog instances, the fill rate was 100 per cent and so was there an increase in the service level (highest). For a fill rate of below 100 %, the service level was way too low (-ve) and this was during the stock outs.)

The proposed variable quantity ordering policy/model

Considering the penalties on backlogs and the loss of sales from stock outs, a policy for stock replenishment would be helpful to improve profits, cycle service level and the fill rate. For instance, whenever the level (R) of inventory of the product gets to less than 1600 units, then make order equivalent to (1600- R) units as the inventory replenishment. This way, the profit, fill rate and the cycle service levels would be greatly boosted.


When the standard deviation was 25, the average fill factor according to the calculations in excel sheet number 6 was 0.99076. To begin with. Applying the formula;

Fill Rate = 1 – (Backorder Expected)/ Demand Expected in a given period) = 99.076%

99.076 = 1 – (X)/2629

The Expected Backorder would be 2629 units in a week.

This is the expected value of initial inventory to warrant 99.076 Fill rate for the first week.



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