John Player store replenishmentBibekananda Patel

Inventory

An inventory system is the set of policies and controls that monitor levels of inventory and determine

– what level should be maintained, – when stock should be replenished and – how large order should be.

Effective Inventory ManagementA system to keep track of inventoryA reliable forecast of demandKnowledge of lead timesReasonable estimates of

Holding costs Ordering costs Shortage costs

Key Inventory Terms Lead time: time interval between ordering and receiving the

order

Holding (carrying) costs: cost to carry an item in inventory for a length of time

Ordering costs: costs of ordering and receiving inventory

Shortage costs: costs when demand exceeds supply

Product

• Formal Shirts

Boundary Conditions

• As the storage capacity of this item is 750 units we can’t have a EOQ > 750 units.

• And, as the lead time is 10 days we should have a stock of 10 days while ordering.

Month-wise sales Estimates for 2008Yr 2008 DemandJanuary 238

February 242

March 227

April 230

May 162

June 156

July 137

August 172

September 319

October 388

November 286

December 300

Total Demand 2857

Average Demand per month 239

Standard Deviation 72.16

SD/Mean = 0.301

i.e. we can’t apply EOQ model (SD/mean > 0.01)

Formula for EOQ

EOQ 595.04

EOQ ApproachOC 200

HC 0.27Yr 2008 Demand Order Number Quantity Holding CostJanuary 238 1 707 February 242 - 65.34March 227 - 122.58April 230 2 685 May 162 - 43.74June 156 - 84.24July 137 - 110.97August 172 3 879 September 319 - 86.13October 388 - 209.52November 286 4 586 December 300 - 81Total Demand 2857 2857 803.52

Total Order Cost (4x200) = 800.00Total of

Cost 1603.52

EOQ ApproachOC 200

HC 0.27Yr 2008 Demand Order Number Quantity Holding CostJanuary 238 1 707 February 242 - 65.34March 227 - 122.58April 230 2 685 May 162 - 43.74June 156 - 84.24July 137 - 110.97August 172 3 491 September 319 - 86.13October 388 4 674  November 286 - 77.22December 300 5 300  Total Demand 2857 2857 590.22

Total Order Cost (4x200) = 1000.00 Total 1590.22

Factors Affecting Replenishment

Replenishment of merchandise is dependent on:

1. Storage capacity of the store - 750 units2. Lead times for supply of goods – 10 Days3. Rate of sales – 10% growth4. Relative stock positions across the chain – Assumed as Zero5. Ensuing events like seasonality – Sale pattern shows 3

clusters for this product.6. Holding cost – Rs. 0.27

Depending upon the sales pattern there are three seasons;

• Jan-Apr• May-Aug• Sept-Deci.e. we have three EOQ model

Table showing calculated total cost (according to days of stock)

120 days demand = 937

per day demand = 937/120 = 7.8

Total OC = OC * No of Orders

Total Cost = Total OC + Total HC

Days of Stock Order Quantity in units

Demand in units HC in Rs. OC in Rs. No of

ordersTotal OC

in Rs.Total HC

in Rs.Total Cost

in Rs.

120 937 937 0.27 200 1 200.00 379.485 579.49

105 820 937 0.27 200 2 400.00 284.6138 684.61

90 703 937 0.27 200 2 400.00 189.7425 589.74

75 586 937 0.27 200 2 400.00 126.495 526.50

60 469 937 0.27 200 2 400.00 63.2475 463.25

45 351 937 0.27 200 3 600.00 31.62375 631.62

40 312 937 0.27 200 3 600.00 21.0825 621.08

35 273 937 0.27 200 4 800.00 10.54125 810.54

30 234 937 0.27 200 4 800.00 0 800.00

25 195 937 0.27 200 5 1000.00 0 1000.00

15 117 937 0.27 200 8 1600.00 0 1600.00

10 78 937 0.27 200 12 2400.00 0 2400.00

Table showing calculated total cost (according to days of stock)

120 days demand = 627

per day demand = 627/120 = 5.05

Total OC = OC * No of Orders

Total Cost = Total OC + Total HC

Days of Stock Order Quantity in units

Demand in units HC in Rs. OC in Rs. No of

ordersTotal OC

in Rs.Total HC

in Rs.Total Cost

in Rs.

120 627 627 0.27 200 1 200.00 253.8675 453.87105 549 627 0.27 200 2 400.00 190.3838 590.3890 470 627 0.27 200 2 400.00 126.9 526.9075 392 627 0.27 200 2 400.00 84.5775 484.5860 314 627 0.27 200 2 400.00 42.3225 442.3245 235 627 0.27 200 3 600.00 21.16125 621.1640 209 627 0.27 200 3 600.00 14.1075 614.1135 183 627 0.27 200 4 800.00 7.05375 807.0530 157 627 0.27 200 4 800.00 0 800.0025 131 627 0.27 200 5 1000.00 0 1000.0015 78 627 0.27 200 8 1600.00 0 1600.0010 52 627 0.27 200 12 2400.00 0 2400.00

Table showing calculated total cost (according to days of stock)

120 days demand = 1293

per day demand = 1293/120 = 10.78

Total OC = OC * No of Orders

Total HC = HC * Order quantity

Total Cost = Total OC + Total HC

Days of Stock Order Quantity in units

Demand in units HC in Rs. OC in Rs. No of

ordersTotal OC

in Rs.Total HC

in Rs.Total Cost

in Rs.

120 1,293 1293 0.27 200 1 200.00 523.46 723.46105 1,131 1293 0.27 200 2 400.00 392.55 792.5590 970 1293 0.27 200 2 400.00 261.77 661.7775 808 1293 0.27 200 2 400.00 174.49 574.4960 647 1293 0.27 200 2 400.00 87.28 487.2845 485 1293 0.27 200 3 600.00 43.64 643.6440 431 1293 0.27 200 3 600.00 29.09 629.0935 377 1293 0.27 200 4 800.00 14.55 814.5530 323 1293 0.27 200 4 800.00 0 800.0025 269 1293 0.27 200 5 1000.00 0 1000.0015 162 1293 0.27 200 8 1600.00 0 1600.0010 108 1293 0.27 200 12 2400.00 0 2400.00

Graph of Stock Replenishment for a single season

Total cost incurred in the year 2008

• Total Cost;= 463.25 + 442.32 + 487.28= 1392.85

Conclusion

• From the EOQ model approach the total cost is found to be Rs.1590.22

• And the from the model John Player follows is found to be Rs. 1392.85

• So comparing both the model the letter one is cost effective.