2 Problems to Solve:

Please show all answers using the 2 decimal places convention (do NOT round an intermediate or final answer to a whole number).

Please Show All Work Leading To the Final Answers, Including All Steps and Equations Used to Solve Each Step.

Problem 1

Supreme Cola is a supplier of fountain equipment to restaurants, bars and cafeterias. The fountain equipment is manufactured at their York PA plant site. A national distribution center (DC) for the fountain equipment is also maintained adjacent to the plant. Supreme has one common platform design to which they add various features and accessories to create 10 different product options.

The company is interested in using the Order-up-to approach at their DC. Depending upon the length of the review interval, the company is considering three alternatives:

1. Alternative 1: L=8; demand is normally distributed with mean = 100 units and std.

dev. = 40 units.

2. Alternative 2: L=4; demand is normally distributed with mean = 200 units, and std

dev. = 56 units.

3. Alternative 3: L=2; demand is normally distributed with mean = 400 units, and std.

dev. = 75 units.

Answer the following questions.

i. For each alternative, determine the optimal order-up-to level (S*) as to achieve:

• an In-stock probability of 98%.
• a Fill rate of 96%.

ii. For an in-stock probability target of 97%, determine the alternative which will

minimize on-hand inventory.

iii. For a fill rate target of 98%, determine the alternative which will minimize the

expected on-hand inventory.

Present your results in summary format in the following table making sure to show all calculations leading to the final answer.

Alternative. S* for In-stock S* for Fill Rate. Exp on-hand Inventory for Exp. On-hand

Prob = 98% = 96% In-stock Probability =97% inventory for FR=98%

1 _________________ ________________ ____________________________ _______________________

2 _________________ ________________ ____________________________ _______________________

3 _________________ ________________ ____________________________ _______________________

Problem 2

A large toy company Mttel currently allows toy retailers to place orders with a delivery lead time of 3 weeks. The Gigantic Pocket Monster (Gipokmon) is a new toy that Mttel has introduced. TOYS-are-MINE plans to uses the order-up-to model (with a fill-rate target of 98%) to plan orders and deliveries to their retailers.

Given that this is a new toy, sales estimates are somewhat uncertain. The market research team is fairly confident that weekly demand would be normally distributed with a mean of 90 units. However, since this is a new product, demand uncertainty, as characterized by the standard deviation, is harder to estimate and could be either:

• standard deviation of 45; or
• standard deviation of 40 units; or
• standard deviation of 35 units.

Please Show All Work Leading To the Final Answers, Including All Steps and Equations Used to Solve Each Step.

In order to budget working capital investment in inventories, you are required to provide an estimate of expected on-hand inventories for each level of uncertainty by completing the following table.

Uncertainty Level. z S* Exp. On-hand

inventory

=45 _____________________ ____________________ _________________________

=40 _____________________ ____________________ _________________________

=35 _____________________ ____________________ _________________________