Question

Managers at a consumer product company, ABC General, are currently debating how to Set the most cost effective competitive customer service levels for a new brand EL SKIMOS. The Accounting manager has suggested 5 days of sales as safety stock. The Marketing manager has argued for 15 days, while the operations/manufacturing manager Seeks a compromise level of 10 days. The General Manager wants your specific Recommendation with justification and supporting quantitative analysis.

Here are some relevant information about EL-SKIMOS to help you in your analysis:

Average daily demand during lead time =15 units /day

Standard deviation of daily demand = 2 units

Average replenishment time =7 days

Standard deviation of replenishment time = 3 days

Typical order quantity = 100 units

What is your analysis of the inventory system at ABC. Include your estimates for average inventory, safety stock and reorder point)?

What are your specific recommendations regarding the inventory systems at ABC?

Answer 1

Average Replenishment Lead Time, LT-bar = 7 days.

Average daily demand during Lead Time, d-bar = 15 units per day.

Standard deviation of daily demand, _d = 2 units.

Standard deviation of Replenishment Lead Time, _LT = 3 days.

Here both demand and lead time are varying.

Case 1 – Suggestion of Accounting Manager:

Safety Stock = 5 days of sales = 5 x 15 = 75 units.  

Safety Stock, SS = z . [LT-bar.(_d)² + (d-bar)². (_LT)²]

          75             = z x [7 x (2)² + (15)² x (3)²]

          75              = z x 45.31

z = 75 / 45.31 = 1.655 ≈ 1.66

Service Level from Standardized Normal Curve for a z value of 1.66 = 0.9515 = 95.15%

Stockout Risk = 100 – 95.15 = 4.85%

Case 2 – Suggestion of Marketing Manager:  

Safety Stock = 15 days of sales = 15 x 15 = 225 units.  

Safety Stock, SS = z . [LT-bar.(_d)² + (d-bar)². (_LT)²]

          225           = z x [7 x (2)² + (15)² x (3)²]

          225            = z x 45.31

z = 225 / 45.31 = 4.97

Service Level for a z value of 4.97 = 100% (approximately).

Stockout Risk = 0% (approximately).

Case 3 – Suggestion of Operations/Manufacturing Manager:

Safety Stock = 10 days of sales = 10 x 15 = 150 units.  

Safety Stock, SS = z . [LT-bar.(_d)² + (d-bar)². (_LT)²]

          150           = z x [7 x (2)² + (15)² x (3)²]

          150            = z x 45.31

z = 150 / 45.31 = 3.31

Service Level from Standardized Normal Curve for a z value of 3.31 = 0.9995 = 99.95%

Stockout Risk = 100 – 99.95 = 0.05%

The safety stock is minimum in Case 1 and the stockout risk is within 5%. Since the company wants the most cost effective competitive service level, it should go for the suggestion of the Accounting Manager.

Average inventory = Order quantity / 2 = 100 / 2 = 50 units.

Safety Stock = 75 units.

Reorder Point = Expected Demand during Replenishment Lead Time + Safety Stock = (d-bar x LT-bar) + Safety Stock = (15 x 7) + 75 = 105 + 75 = 180 units.

Therefore, the company ABC General should go for fixed order quantity inventory system with Safety Stock of 75 units, Reorder Point of 180 units and a Service Level of 95.15%