ENM5303 Operations Management

• A firm forecasts demand for an item using exponential smoothing with α = 3. The following table is a history of forecast versus actual demand for the past year.

Month              Actual Demand (units)             Forecast of Demand (Units)

 Jan 75 70 Feb 60 72 March 72 68 Apr. 63 69 May 75 67 June 69 69 July 80 69 Aug. 60 72 Sep. 66 68 Oct. 68 67 Nov. 71 67 Dec. 72 68

The company reviews the inventory status of this item every 6 months. It is now reviewing the item to make a reorder decision for the period January to June. The current inventory level is 60 units. When an order is placed, delivery of the order is instantaneous. If the company wishes to provide a 95% service level over the next six months, what is the size of the order that should be placed?

Note: Service level is defined as the probability of not stocking out over a cycle.

• What is the optimal production plan for the following problem?

 Cost Per Unit Period Range 1 2 3 4 0 < X ≤ 10 7 5 8 8 10 < X ≤ 20 8 7 7 9 20 < X ≤ 30 9 9 8 10 30 < X ≤ 40 10 10 12 12

Demand and inventory holding costs are as follows:

 Period Demand Inventory Holding Cost 1 26 1 2 32 2 3 40 2 4 32 3

• Water-jet machining department has six machines that perform cutting operations. Water-jet cutting utilizes a high-velocity stream of water as the cutting The jets are approximately 0.01 inch in diameter and operate at velocities of 2000 to 3000 fps. At such velocities, the jets can cut through wood, plastics, and some ceramics. Twenty pieces of plastics need to cut and their expected cutting times are given below.

 Workpiece Cutting Time A 12 B 14 C 3 D 10 E 16 F 22 G 25 H 21 I 16 J 10 K 3 L 4 M 17 N 32 O 41 P 21 Q 19 R 50 S 40 T 6

Assume that not all the water-jet machines are ready at time t= 0 and their available times are

 Machine M1 M2 M3 M4 M5 M6 Available time 10 3 0 15 2 16

Determine an optimal schedule that minimizes the mean flow time of the work pieces.

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