Stir together the cabbage, carrot, sauerkraut, cider, sugar, caraway seeds and allspice in a slow-cooker. Bury the pork chops in the cabbage mixture, pressing down to compact. Top with the kielbasa and the potatoes.
Cover and cook on low heat for 7 hours, or on high for 3-1/2 hours, or until potatoes are tender.
Heat 1 tablespoon oil in ovenproof Dutch oven. Add pork chops; cook until browned, about 6 minutes, turning over halfway through cooking. Stir in cabbage, carrot, sauerkraut, cider, sugar, caraway and allspice. Top with kielbasa and potatoes. Cover and cook in preheated 325°F oven for 2 hours or until potatoes are tender.