Solving the Single Machine Problem with Quadratic Earliness and Tardiness Penalties

ŶǀƬĩ šŚưƬĩ ƽ ƵŶǀĪģ ƱŚƯŻ ƪŗŚƀƯ ƵŻƹźƯř ƮŤƀǀs Żř ƽŹŚǀƀŝ Źŵ ƽŶƴŝ Ŷų ƹ ƽŶǀƫƺţ ƽŚƷ ƾƘǀsƹ ŵźŝŹŚĩ ƾţŚƯ ƶŤƟŚƿ ŶƳř ƶƫŚƀƯ ƶƫŚƤƯ Ʋƿř Źŵ ƱŚƯŻ ƽ ƽŶƴŝ n Ĩţ ƽƹŹ źŝ ŹŚĩ ƉźƟ ƲŤƟźĭ źƔƳŹŵ Śŝ ƹ ƲǀƃŚƯ ƲǀƃŚƯ ƽŹŚĪǀŝ ƭŶƗ ƱŚƯŻ ƽƹŚƀţ ƹ ŚƷŹŚĩ ƕŚƐƤƳř ƱŵƺŞƳ ŻŚŬƯ ƲǀƴĤưƷ ƹ ƁŻřŵźě ƽŚƷ ŵŹƺƯ źŝ Ź ƾƯ Źřźƣ ƾs ŵźǀĭ ƿżƷ ŵƺūƹ ƪǀƫŵ ƶŝ ƱƺƴĩŚţ ƵŶƃ ƭŚŬƳř šŚƘƫŚƐƯ Żř ƽŹŚǀƀŝ Źŵ ƶƴ ƽŚƷ ƶƴƿżƷ Śƿ ƹ Ʊŵřŵ ƪƿƺŰţ źƿŵ Żř ƾƃŚƳ ƶưƿźū ƽŹřŶƸĮƳ ƽŚƷ ŚƷŹŚĩ ŵźĩźƿŵ ƹ ŵźĩŵƹŻ ƽŚƷ ƶŝ ƾƯ źƷŚƓ ƝŶƷ ƖŝŚţ Źŵ ƾƐų šŚŞǀĩźţ šŹƺƇ ƾţŹƺƇŹŵ ŵƺƃ ƶƫŚƤƯ Ʋƿř ƝŶƷ ƖŝŚţ ƶĩ ƱŻƹ ƕƺưŬƯ Ʊŵźĩ ƶƴǀưĩ ƶưƿźū Źřŵ ƾƯ ƭƹŵ ƶūŹŵ ŵźĩŵƹŻ ƹ ŵźĩźƿŵ ƽŚƷ ŶƃŚŝ Ʋƿř Źŵ ƶƫŚƀƯ ƪů ƽřźŝ ƂƷƹĦě ƽřźŝ ƹ Ţsř ƵŶƃ ƵŵŚƠŤsř Ʊřźĩ ƹ ƶųŚƃ ƁƹŹ Żř ơƺƟ ƽ ƵŵŚǀě ƶųŚƃ ƮŤƿŹƺĮƫř ƽŻŚs ƹ ŵŚƸƴƄǀě LJŚŝ ŵƹŶů ƹ ƲǀƿŚě ŵƹŶů ƶŞƬƛ ƪƇř ƽŵřŶƘţ Ʊřźĩ Ţsř ƵŶƃ ƵŵŚǀě ƹ ƶƳƺưƳ ƪŗŚƀƯ Ŷǀƫƺţ Żř ƵŵŚƠŤsř Śŝ ƽŵŚƸƴƄǀě ƁƹŹ ŢƿŚƸƳ Źŵ ƁƹŹ ƽŻŚs ŵ Ʊō ƾƿřŹŚĩ ƹ ƶŤƟźĭ Źřźƣ ƾsŹźŝ ŵŹƺƯ ŚƸƳō ƽƹŹ źŝ ƶŝ ƪŗŚƀƯ ƪů Ź Ţsř ƵŶǀsŹ šŚŞŧř

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