Pivot String column on Pyspark Dataframe

Assuming that (id |type | date) combinations are unique and your only goal is pivoting and not aggregation you can use first (or any other function not restricted to numeric values):

from pyspark.sql.functions import first

(df_data
    .groupby(df_data.id, df_data.type)
    .pivot("date")
    .agg(first("ship"))
    .show())

## +---+----+------+------+------+
## | id|type|201601|201602|201603|
## +---+----+------+------+------+
## |  2|   C|  DOCK|  null|  null|
## |  0|   A|  DOCK|  PORT|  PORT|
## |  1|   B|  PORT|  DOCK|  null|
## +---+----+------+------+------+

If these assumptions is not correct you'll have to pre-aggregate your data. For example for the most common ship value:

from pyspark.sql.functions import max, struct

(df_data
    .groupby("id", "type", "date", "ship")
    .count()
    .groupby("id", "type")
    .pivot("date")
    .agg(max(struct("count", "ship")))
    .show())

## +---+----+--------+--------+--------+
## | id|type|  201601|  201602|  201603|
## +---+----+--------+--------+--------+
## |  2|   C|[1,DOCK]|    null|    null|
## |  0|   A|[1,DOCK]|[1,PORT]|[1,PORT]|
## |  1|   B|[1,PORT]|[1,DOCK]|    null|
## +---+----+--------+--------+--------+

In case, if someone is looking for SQL style approach.

rdd = spark.sparkContext.parallelize(
    [
        (0, "A", 223,"201603", "PORT"), 
        (0, "A", 22,"201602", "PORT"), 
        (0, "A", 422,"201601", "DOCK"), 
        (1,"B", 3213,"201602", "DOCK"), 
        (1,"B", 3213,"201601", "PORT"), 
        (2,"C", 2321,"201601", "DOCK")
    ]
)
df_data = spark.createDataFrame(rdd, ["id","type", "cost", "date", "ship"])
df_data.createOrReplaceTempView("df")
df_data.show()

dt_vals=spark.sql("select collect_set(date) from df").collect()[0][0]
['201601', '201602', '201603']

dt_vals_colstr=",".join(["'" + c + "'" for c in sorted(dt_vals)])
"'201601','201602','201603'"

Part-1 (Note the f format specifier)

spark.sql(f"""
select * from 
(select id , type, date, ship from df)
pivot (
first(ship) for date in ({dt_vals_colstr})
)
""").show(100,truncate=False)

+---+----+------+------+------+
|id |type|201601|201602|201603|
+---+----+------+------+------+
|1  |B   |PORT  |DOCK  |null  |
|2  |C   |DOCK  |null  |null  |
|0  |A   |DOCK  |PORT  |PORT  |
+---+----+------+------+------+

Part-2

spark.sql(f"""
select * from 
(select id , type, date, ship from df)
pivot (
case when count(*)=0 then null 
else struct(count(*),first(ship)) end for date in ({dt_vals_colstr})
)
""").show(100,truncate=False)

+---+----+---------+---------+---------+
|id |type|201601   |201602   |201603   |
+---+----+---------+---------+---------+
|1  |B   |[1, PORT]|[1, DOCK]|null     |
|2  |C   |[1, DOCK]|null     |null     |
|0  |A   |[1, DOCK]|[1, PORT]|[1, PORT]|
+---+----+---------+---------+---------+