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Production Planning & Control Q.1 From the data below, develop an Exponential Smoothing with trend and seasonal correction for 2012 from the data 2010 and 2011. Assume α= 0.1, β= 0.1, γ=0.3, �^# = 220, �^ # = 220 and T1=0. What is the forecast for March 2013? Demand Seasonal Month 2010 2011 Average Index, It January 90 110 100 0.962 February 85 95 90 0.865 March 90 100 95 0.913 April 100 120 110 1.058 May 125 141 133 1.279 June 120 130 125 1.202 July 110 120 115 1.106 August 100 120 110 1.058 September 95 105 100 0.962 October 85 95 90 0.865 November 85 95 90 0.865 December 90 90 90 0.865 1248 12.00 Q.2 Consider the demand schedule given in the following table. Suppose that there is no initial inventory and that the sources of production in each period are regular time at a cost of $100 per unit, overtime at a cost of $107 per unit, and subcontracting at a cost of $113 per unit. The inventory holding costs are $2 per unit per period. No shortages are to be planned. Regular time capacity is 180 units in each period and overtime capacity is 36 units. Subcontracting up to 50 units is available in each period. a) Solve aggregate plan using transportation method. b) Suppose that the capacity in a period is a function of the work force level during the period and that there is a cost of changing the work force level from period to period. There is no cost to change the production rate, however, overtime is required when scheduled production is an excess of the regular time capacity of the work force. Production costs are higher on overtime than on regular time. Assume backorders are allowed. Formulate the problem with LP. Q.3. The demand for an item in each of two periods is uniformly distributed from 0- 10; i.e., f(D) = 0.10, 0 £ D £ 10. The cost of purchasing is $2 per item. If excess inventory remains at the end of a period, it is changed at $6 per item. The shortage cost is $10 per item. Find the optimum two-period policy for α =1. Q.4. An end item is fabricated from a single component supplied by a local distributor. The end item is produced on a cycle every four weeks, or 13 times in a year, during weeks 3,7,11,15,19,23,27,31,35,39,43,47, and 51. Annual demand for the end item is 52.000 units. Each component cost $3.50, and the order cost is $125 per lot. The annual inventory holding cost is 20% of the unit cost, and the lead time is a constant one week. a) What is the total annual cost with EOQ? b) What is the total annual cost with MRP with lot for lot ordering? c) Compare the EOQ and MRP costs.

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