  We continue the study of two recently introduced bin packing type problems,
called bin packing with clustering, and online bin packing with delays. A bin
packing input consists of items of sizes not larger than 1, and the goal is to
partition or pack them into bins, where the total size of items of every valid
bin cannot exceed 1.
  In bin packing with clustering, items also have colors associated with them.
A globally optimal solution can combine items of different colors in bins,
while a clustered solution can only pack monochromatic bins. The goal is to
compare a globally optimal solution to an optimal clustered solution, under
certain constraints on the coloring provided with the input. We show close
bounds on the worst-case ratio between these two costs, called "the price of
clustering", improving and simplifying previous results. Specifically, we show
that the price of clustering does not exceed 1.93667, improving over the
previous upper bound of 1.951, and that it is at least 1.93558, improving over
the previous lower bound of 1.93344.
  In online bin packing with delays, items are presented over time. Items may
wait to be packed, and an algorithm can create a new bin at any time, packing a
subset of already existing unpacked items into it, under the condition that the
bin is valid. A created bin cannot be used again in the future, and all items
have to be packed into bins eventually. The objective is to minimize the number
of used bins plus the sum of waiting costs of all items, called delays. We
build on previous work and modify a simple phase-based algorithm. We combine
the modification with a careful analysis to improve the previously known
competitive ratio from 3.951 to below 3.1551.
