IEOR 3402: Assignment 5
IEOR 3402代写 1.*Nahmias, 5.12.You may assume fractional number of handbags.Assume that the holding cost (the amount tied up in inventory) is
1.
*Nahmias, 5.12. You may assume fractional number of handbags.
- Assume that the holding cost (the amount tied up in inventory) is incurred only by those units not sold at the store.
- For part (a), also compute the expected purchase cost, expected revenue from the store, expected revenue from the discount fifirm, and expected holding cost.
- For part (b), fifirst express your answer in terms of the standard normal CDF function. Then, use the standard normal CDF table to look up the value, and simplify your answer.
2. IEOR 3402代写
*Page 287 8th edition (262 7th edition) of Nahmias suggests that when units are ordered in discrete quantities and demand is continuous, then Q is rounded to the closest integer. Is it correct? If so, provide a convincing argument. Otherwise, give a counter example.
3.
*Page 287 8th edition (262 7th edition) of Nahmias claims that when the demand is assumed to be discrete, the “optimal solution procedure is to locate the critical ratio between two values of F(Q) and choose the Q corresponding to the higher value.”
Suppose, in the newsvendor model, that demand D is discrete in the sense that there exists a sequence of real numbers, {x1 , x2 , …}, representing all potential demand quantities, and 0 ≤ x1 ≤ x2 ≤ … Let pi be the probability of [D = xi ]. Furthermore, suppose that all of these quantities are admissible order-up-to stocking levels. Prove the smallest y such that
is an optimal stock level.
4. IEOR 3402代写
*Aegon and Daenerys are planning for a wedding reception at Valyria Ridge, an upscale winery overlooking King’s Landing. Since the invited guests have not replied on time, they are uncertain about the actual number of guests that will be attending the reception. To the best of the couple’s knowledge, the number of guests will be normally distributed with the mean 170 and the standard deviation 20.
A manager at Valyria Ridge requests the couple for an estimate for the number of guests in order to prepare wild game and mead. He guarantees that he will prepare food for 10 servings more than the estimate, and will charge based on the higher of the estimate and the actual number of guests. In an unfortunate case that a guest cannot be served, the goodwill cost will be 10 times the per-person charge. Aegon and Daenerys need to provide an estimate for the manager at Valyria Ridge.
(a) Write down an appropriate objective function for the decision that Christine and Tim need to make.
(b) What is the optimal solution? Use Excel if necessary.
5. IEOR 3402代写
*Consider the lot size reorder point (Q,R) system discussed in class.
(a) For computing the holding cost, the average inventory level is approximated by R−λτ+ Q/2. Why is it an approximation, not an exact value?
(b) For computing the penalty cost, we used the expected number n(R) of shortages that occur in one cycle, and multiplied this quantity by a per-unit penalty cost p. How is it difffferent from computing the penalty cost for the ”EOQ Model with Planned Backo-rders”?
6.
*Let φ(.) be the standard normal probability density function. Show.
7.
Nahmias, 5.13. You may assume demand is normally distributed. If necessary, use the standard normal CDF table.
8.*Nahmias, 5.39.
9.Nahmias, 5.40.
10. IEOR 3402代写
Dragonstone Warehouse Limited (DWL) acts as a distributor for a product manufactured by Drogon Company. DWL uses an (R, Q) type of control system. Drogon has a particular way of delivering the quantity Q: They deliver Q/2 at the end of the lead time of one month, and the other Q/2 at the end of two months. Assume that this business has the following characteristics:
K = 100
R = 40
λ = 360units/year
c = $1.00
I = 25%per year.
Furthermore, the standard deviation of forecast errors over one month is 10 units.
(a) What is the numerical value of the safety stock? Explain your answer.
(b) Suppose that a replenishment is triggered at t = 0, and no order is outstanding at this time. Describe in words what conditions must hold in order for there to be no stockout up to time t = 2 months.
(c) Suppose that Drogon offffered DWL the option to receive the whole quantity Q after a lead time of one month, but at a higher unit price. Outline the steps of an analysis to decide whether or not the option should be accepted.
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