A construction company orders cement every week. The lead time for receiving the

Question

A construction company orders cement every week. The lead time for receiving the cement is five weeks. The following table includes the demand forecast (in tons) for the following weeks. The forecast CV is 30% and demand is normally distributed. The target cycle service level is 98%. Current inventory is 758 tons, and there are 3742 tons expected to arrive from prior orders.

Week 11

a. Calculate the order up to level (OUL) for the Week 6 order. Show all work.

b. Calculate the order quantity for the Week 6 order. Show all work

Week 6 200 tons

Week 11

500 tons Week 7 300 tons Week 12 400 tons Week 8 400 tons Week 13 300 tons Week 9 500 tons Week 14 200 tons Week 10 600 tons Week 15 100 tons

Explanation / Answer

Average demand per week, d = (200+300+400+500+600+500+400+300+200+100)/10 = 350 tons

Standard deviation of weekly demand, s = CV*Average demand = 0.30*350 = 105 tons

Lead time (L) = 5 weeks

z value for 98 % CSL = 2.054

a) Order upto level (OUL) for week 6 order = d*(L+1) + z*s*(L+1)

= 350*(5+1) + 2.054*105*(5+1)

= 2628 tons

b) Inventory Position (IP) = Current inventory + Open orders - Backorders = 758 + 3742 - 0 = 4500 tons

Order quantity = MAX{0, (OUL - IP)}

= MAX{0, (2628 - 4500)}

= MAX{0, -1872}

= 0 tons

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