1 Exercises Solution

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Politecnico di Milano MANUFACTURING SYSTEMS ENGINEERING EXERCISE a) In the problem there are 2 stochastic parameters: the demand of part type D and the availability of the machine type2. Each parameter has two possible outcomes. It must be noticed that the machine type2 can be purchased even if the part type D will not be produced. Since the two parameters are independent, there are 4 possible scenarios, resulting by the combinations as reported in the following table: yes no high (0.95) low (0.92) scenario prob=0.6 prob=0.4 prob=0.6 prob=0.4 1 x x 0.6 * 0.6 = 0.36 2 x x 0.6 * 0.4 = 0.24 3 x x 0.4 * 0.6 = 0.24 4 x x 0.4 * 0.4 = 0.16 demand part type D availability machine Type2 probability b) Notation and Data s = scenario (s=1,2,3,4) i = machine type (i=1,2,3,4) prob (s) = scenario s probability dem (j,s) = demand of product j in scenario s [part/year] T (i,j) = machine capacity needed to process one unit of product j on the machine type i [hour/part] c (i) = cost of machine type i [cost unit/machine] h (i,s) = capacity of machine type i in scenario s [hour/year] actual (i) = number of machine type i in the system [machine] budget = budget to purchase new machines [cost unit]           1, 230 21 / 0.93 4491.9 2,1 2,3 230 21 / 0.95 4588.5 2,2 2,4 230 21 / 0.92 4443.6 h s day hours day s h h day hours day h h day hours day                                    0.36 0.24 0.24 0.16 prob       6000 6000 6000 6000 8000 8000 8000 8000 10000 10000 10000 10000 12000 12000 0 0 dem       0.6 0.8 0.7 0.9 0.51 0.68 0.595 0.72 T    40000 48000 c    4491.9 4491.9 4491.9 4491.9 4588.5 4443.6 4588.5 4443.6 h    3 0 actual     200000budget  The decision variables are the number of…