Assignment

Submit 1) a document of your solutions, and 2) your Excel file used for calculations.

There is no “Shell” Excel file for this assignment.

Questions 1-3 refer to this scenario at AKM:

The AKM convenience store buys frozen burritos for $0.90 and sells them for $1.65.  It costs $0.25 to store one frozen burrito from one week to the next. The table above describes weekly demand for burritos at the AKM store.

Suppose lead time is instantaneous.  That is, AKM orders at the end of the week and the burritos are delivered before the beginning of the next week. 

1. If AKM stocks 5 burritos, what is the probability of not stocking out?

1. If AKM stocks 4 burritos, what are expected missed sales in units each week?

1. Suppose now that AKM pays $1.50 per burrito, which it can sell for $2.00, with a $0.50 holding cost from one week to the next. What is the ideal stock level?

Questions 4-7 refer to this scenario at Kate’s Mini-Mart. Any changes in the parameters for one problem carry over to the next problem (unless they are changed again):

Kate's Mini-Mart uses a periodic review, order-up-to inventory model to manage inventory. For one of their more popular products, Tofu Jerky, Kate (the owner) insists on maintaining an 80% cycle service level. Kate buys Tofu Jerky for $1.00 per pack and it sells for $1.40. It costs Kate $0.10 per pack per week to hold inventory. The supplier has a 4 week lead time (with no randomness). Average demand is expected to be 105 per week. Standard deviation of forecast errors is expected to be 55. (Please use the Gamma distribution to model demand during the exposure period.) Kate orders every week (and uses the 80% CSL mentioned above).

1. What is the fill rate?

1. Suppose now that Kate changes the CSL to 90% and that she has only been ordering every two weeks. Also, average demand is now only expected to be 60 per week with a standard deviation of 25.
   In order to have more free time for her many hobbies, Kate would like to reduce her administrative effort by ordering less frequently.
   By how much would safety stock increase if she were to switch from ordering every 2 weeks to ordering every 4 weeks? (Round your answer to the nearest percent.)

1. (More changes at the mini-mart!) Switch back to an 80% CSL and change the selling price for Tofu jerky to $3.50 per pack. The supplier now has only a 2 week lead time (still no randomness) and Kate is back to ordering every week.
   Suppose a slick consultant convinces Kate that she should use a fill rate service level target rather than cycle service level to set inventory control parameters.
   Which statement best describes the change in inventory levels that would happen if Kate decides to stop using the 80% CSL target and instead use a 98% fill rate target?

1. One more time but now Kate uses a 99% fill rate target for setting inventory levels. Supplier lead time is now 3 weeks. Average demand is 90 per week with a standard deviation of 20. Kate is still ordering every week.
   Which statement best describes what will happen to inventory levels if Kate switches from ordering every week to ordering every three weeks?

Questions 8-11 are all True/false. Explain why you chose your answer.

1. True or False? For a firm using a periodic review, order-up-to inventory system, doubling the average lead time doubles the amount of safety stock required to achieve the same level of service. (Assume for this problem that all problem parameters other than the exposure period remain the same.)

1. True or False? Switching to a supply source that has the same average lead time but lower standard deviation of lead time will cause both safety stock and in-transit stock to decrease. (Assume all other problem parameters remain the same.)

1. True or False? A periodic review system places a fixed replenishment quantity (Q) after each review period (i.e. we place an order for the same quantity each review period).

1. True or False? The periodic review system must carry more safety stock than the continuous review system to achieve the same cycle service level, because the exposure period for the periodic review system includes the review period in addition to the lead time.