Question 12.15: Finding the Optimal Stocking Level When Demand Has a Poisson...

Operations Management

Finding the Optimal Stocking Level When Demand Has a Poisson Distribution
Demand for long-stemmed red roses at a small flower shop can be approximated using a Poisson distribution that has a mean of four dozen per day. Profit on the roses is $3 per dozen. Leftover flowers are marked down and sold the next day at a loss of $2 per dozen. Assume that all marked-down flowers are sold. What is the optimal stocking level?

The "Step-by-Step Explanation" refers to a detailed and sequential breakdown of the solution or reasoning behind the answer. This comprehensive explanation walks through each step of the answer, offering you clarity and understanding.
Our explanations are based on the best information we have, but they may not always be right or fit every situation.

The blue check mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.

This Question has been Answered.

Already have an account?

Related Answered Questions

Question: 12.11

Computing Stockout Risk for the Fixed-Interval Model Given the following information: LT = 4 days OI = 12 days d = 10 units/day σ d = 2 units/day A = 43 units Q = 171 units Determine the risk of a stockout at a. The end of the initial lead time. b. The end of the second lead time. ...

Verified Answer:

a. For the risk of stockout for the first lead tim...

Question: 12.13

Finding the Optimal Stocking Level When Demand Is Normally Distributed Cindy’s Cider Bar also sells a blend of cherry juice and apple cider. Demand for the blend is approximately normal, with a mean of 200 liters per week and a standard deviation of 10 liters per week. Cs = $2.40 per liter, and Ce = ...

Verified Answer:

SL =

SL = \frac{C_s}{C_s + C_e}=\frac{\$2.4...

Question: 12.p.4

Reorder point. This type of problem can be recognized when the demand rate (d ), lead time (LT), and desired service level or stockout risk are given. Use these steps to solve this type of problem: 1. Match the choice of formula to the standard deviation(s) that are given in the problem (e.g., if ...

Verified Answer:

\overline{d}

  = 400 bars of soap pe...

Question: 12.p.6

ROP for variable demand rate and variable lead time. The motel replaces broken glasses at a rate of 25 per day. In the past, this quantity has tended to vary normally and have a standard deviation of three glasses per day. Glasses are ordered from a Cleveland supplier. Lead time is normally ...

Verified Answer:

\overline{d}

= 25 glasses per day ...

Question: 12.p.8

Single-period. This type of problem can be recognized when a probability distribution or empirical distribution for demand of a “perishable” item is given along with unit shortage and excess costs, or information that can be used to calculate them. Use the following steps to solve the problem. 1. ...

Verified Answer:

C_s

is unknown

C_e

=...

Question: 12.8

Computing the ROP and Safety Stock When the Mean and Standard Deviation of Lead Time Demand Are Given Suppose that the manager of a construction supply house determined from historical records that demand for sand during lead time averages 50 tons. In addition, suppose the manager determined that ...

Verified Answer:

Expected lead time demand = 50 tons

σ_{dLT}...

Question: 12.9

Computing the ROP When Demand Is Variable A restaurant uses an average of 50 jars of a special sauce each week. Weekly usage of sauce has a standard deviation of 3 jars. The manager is willing to accept no more than a 10 percent risk of stockout during lead time, which is two weeks. Assume the ...

Verified Answer:

\overline{d}

= 50 jars per week ...

Question: 12.p.5

ROP for constant demand and variable lead time. The motel in the preceding example uses approximately 600 bottles of water each day, and this tends to be fairly constant. Lead time for water delivery is normally distributed with a mean of six days and a standard deviation of two days. A service ...

Verified Answer:

d = 600 bottles per day SL = 90 percent, so z = +1...

Question: 12.p.7

Fixed-order-interval. This type of problem can be recognized when an order interval is given (e.g., inventory is ordered every 10 days) along with the demand rate, lead time, and quantity on hand at order time. Use Formula 12–16 to find the optimal order size. A lab orders a number of chemicals ...

Verified Answer:

\overline{d}

= 15.2 ml per day ...

Question: 12.p.3

Quantity discounts. This type of problem can be recognized when a list showing prices for each quantity range is given along with the basic EOQ information. a. If unit holding cost is constant, use these steps to solve the problem: 1. Use Formula 12–2 to find Q. 2. Locate Q in the price schedule. ...

Verified Answer:

a. Compute the EOQ for $2 per pound. The quantity ...