运筹学练习题代写 IEOR 3402代写 时间序列代写 预测分析代写

IEOR 3402: More Practice Questions

运筹学练习题代写 1.We consider the forecasting of stationary time series, where each observation is represented by a constant plus a random fluctuation, i.e.,

1.

We consider the forecasting of stationary time series, where each observation is represented by a constant plus a random fluctuation, i.e.,

(a) What is the expected age of the data used in the forecast?

(b) What are the expected value of the error and the variance of the error?

(c) Compare your answers in (a) and (b) to the corresponding quantities associated with the regular unweighted moving average of order 3.

2. 运筹学练习题代写

Angel Cookie Company makes a variety of sugar-free chocolate chip cookies in a plant in New Jersey. Based on orders received and forecasts of buying habits, it is estimated that the demand requirement for the next four months is 400, 600, 300 and 700, expressed in thousands of cookies. All demands must be satisfied. Assume that each worker can produce 5 thousand cookies per worker per month. Currently there are 70 workers employed, and there is no starting inventory of cookies. Assume that the costs of hiring and Hiring are $1000 and $5000, respectively. Each cookie sells for $1.00, and incurs holding cost of $0.05.

(a) What is the minimum constant workforce required to meet demand over the next four months?

(b) Write down the linear programming formulation for minimizing costs for this problem. You may allow fractional hires/fires.

(c) Now suppose that the cost of hiring workers in each period is $1000 for each worker until 100 workers are hired, and $3000 for each additional worker beyond 100. No more than 150 workers can be hired in a month. Repeat the previous section under this assumption.

3. 运筹学练习题代写

A manufacturing firm located in Long Island, NY currently produces an item in a threemonth time supply at a time. The production of the product is instantaneous. An analyst, attempting to introduce a more logical approach to selecting run quantities, has obtained the following estimates of characteristics for the item:

Delivery Lead-time = 3 months

Demand Rate = 4000 units/year

Fixed Ordering Cost = $5

Production Cost = $4 per 100 units

Holding Cost Rate = 0.25 $/unit/year

(Above, the holding cost rate represents the “interest rate”, which is 25 percent per annum.)

(a) What is the economic order quantity of the item?

(b) What is the time between consecutive replenishments of the item when the EOQ is used?

(c) The production manager insists that the fixed ordering cost figure of ✩5 is only a guess.

Therefore, he insists on using his simple three-month supply rule. Indicate how you would find the range of the fixed ordering cost values for which the EOQ solution in (a) would be preferable (in terms of a lower total replenishment and carrying costs) to the three-month supply.

(d) Suppose now that the production rate is finite, and is given by ρ units/year, where λ < ρ < ∞. Then, as the production rate ρ increases, does the optimal cost increase or decrease? Provide an intuitive explanation in English.

4.

In a basic EOQ setting, the objective is to minimize the time-average cost per year (or some other time period). If the objective is instead to minimize the total cost of a cycle (time between order placements), find the optimal order quantity. Is this quantity greater or smaller than the economic order quantity (EOQ)? Give the intuition for why the solution differs from the EOQ the way that it does in this problem?

5. 运筹学练习题代写

In the real world, it is often difficult to estimate the model parameters accurately. In this situation, the cost and demand parameters are at best an approximation of the actual parameters. Suppose that we compute the EOQ solution based on the approximate fixed cost and interest cost parameters K and I, but the actual fixed cost and interest cost rate are K_a and I_a. We assume that the purchasing cost c and the demand rate λ is estimated accurately. Let Q denote the estimated order quantity. Let Q_a be the optimal order quantity had the actual parameters Ka and Ia been known.

(a) Compute Q/Q_a.

(b) What is the ratio between the cost (sum of holding and fixed order costs) corresponding to the estimated order quantity and the optimal cost?

(c) Suppose the retailer is confident that his actual fixed cost is at most 120% but no less than 80% of the estimated fixed cost. We assume that she has estimated the interest cost rate accurately. Determine the maximum deviation of the realized cost obtained by using estimated parameters from the optimal cost. (you do not need to simplify the final answer if you do not have a calculator)

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