Question

Two products are considered for evaluation, the data of which is as given per week.

Historical Data for Product A

Week	1	2	3	4	5	6	7	8
Massachusetts	33	45	37	38	55	30	18	58
New Jersey	46	35	41	40	26	48	18	55
Total	79	80	78	78	81	78	36	113

Historical Data for Product B

Week	1	2	3	4	5	6	7	8
Massachusetts	0	3	3	0	0	1	3	0
New Jersey	2	4	0	0	3	1	0	0
Total	2	7	3	0	3	2	3	0

The lead time is 1.5 weeks and the standard deviation of lead time is 1.25 weeks. Refer the attached King Safety Stock analysis for conceptual clarity and answer the following questions,

i) If the lead time is considered to be constant, what would be the safety stock for product A & B?

ii) If the lead time is not constant and is as given in the data above but independent of the demand, what would be the safety stock for product A & B?

iii) If the lead time is not constant and is as given in the data above but dependent on the demand fluctuations, what would be the safety stock for Product A & B?

Answer 1

Available Data:

Historical Demand data for Product A (Pa) and Product B (Pb)

Lead Time (L) for Pa and Pb = 1.5 weeks

Standard Deviation of Lead time (SDL) = 1.25 weeks

Assumption: Cycle Service Level (CSL) of Product A and B is 95%

i) Case 1: Lead time is considered to be constant. This means SDL = 0

Safety Stock of Product A = NORMSINV (CSL) * (Lead Time)^0.5*Standard Deviation of Product A (SDa)

  = NORMSINV (0.95) * (1.5)^0.5*19.4

= 1.645*1.225*19.4

Safety Stock of Product A = 39.02 units ~ 39 units

Safety Stock of Product B = NORMSINV (CSL) * (Lead Time)^0.5*Standard Deviation of Product B (SDb)

  = NORMSINV (0.95) * (1.5)^0.5*2.1

= 1.645*1.225*2.1

Safety Stock of Product A = 4.15 units ~ 4 units

ii) Lead time is not constant and is as given in the data above but independent of the demand, This means SDL = 1.25 weeks

Safety Stock of Product A = NORMSINV (CSL) * (L*SDa² + SDL²D_avg²)^0.5

  = NORMSINV (0.95) * (1.5*19.4² + 1.25²*77.9²)^0.5

= 1.645 * 100.224

Safety Stock of Product A = 164.85 units ~ 165 units

Safety Stock of Product B = NORMSINV (CSL) * (L*SDb² + SDL²D_avg²)^0.5

  = NORMSINV (0.95) * (1.5*2.1² + 1.25²*2.5²)^0.5

= 1.645 * 4.017

Safety Stock of Product A = 6.6 units ~ 7 units

iii) Lead time is not constant and is as given in the data above but dependent of the demand, This means SDL = 1.25 weeks

Safety Stock of Product A = NORMSINV (CSL) * (L)^0.5*SDa² + NORMSINV (CSL) *SDL*D_avg

  = NORMSINV (0.95) * (1.5)^0.5*19.4 + NORMSINV (0.95) *1.25*77.9

= 1.645*1.225*19.4 + 1.645*1.25*77.9

= 39.02 + 160.11

Safety Stock of Product A = 199.14 units ~ 199 units

Safety Stock of Product A = NORMSINV (CSL) * (L)^0.5*SDb² + NORMSINV (CSL) *SDL*D_avg

  = NORMSINV (0.95) * (1.5)^0.5*2.1 + NORMSINV (0.95) *1.25*2.5

= 1.645*1.225*2.1 + 1.645*1.25*2.5

= 4.15 + 5.14

Safety Stock of Product A = 9.29 units ~ 9 units