hw2solutions - Solutions to HW 2 IEOR 130 Prof Leachman 1...

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Solutions to HW 2 IEOR 130 Prof. Leachman 1. First, consider the case of on-time delivery in a single time period. Let D(i) denote the scheduled output quantity of product i. Let P(i) denote the actual output quantity of product i. The fraction of product i delivered on time is F(i) = Min { D(i), P(i) } / D(i) . We could do a weighted average of the on time delivery scores for all products to arrive at an on-time delivery score for the factory. That is, OTD = Sum { [D(i)][F(i)] } / Sum (D(i)), or, equivalently, OTD = Sum Min { D(i), P(i) } / Sum D(i) Note the numerator sums over all production that is demanded, and the denominator sums over all demand. Next, we consider the case of a stream of time periods in which surplus in period t-1 can be used to make up for shortfall in period t. Let DD(i,t) denote the cumulative scheduled output quantity of product i by the end of period t, and let PP(i,t) denote the cumulative actual output quantity by the end of period t. The fraction of product i delivered on time in period t is F(i,t) = Min { D(i,t), P(i,t) + Max { 0, PP(i,t-1) - DD(i,t-1) } } / D(i,t) .
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