Learn Hardcore Russian: Директор пообещал новое расписание на следующую неделю. - The director promised a new schedule for next week.

Russian distinguishes aspect. Обещать (imperfective) describes an ongoing, repeated, or unbounded action; пообещать (perfective) presents a single, completed act. Пообещал tells us he made the promise (viewed as a complete event). You could say обещал, but it can sound like “was promising/used to promise” or “had promised” without the same completed-event feel. The neutral, one-time report is usually perfective: пообещал.

Why is it новое расписание and not новый расписание?

Because расписание is a neuter noun. Adjectives must agree with the noun’s gender, number, and case. Neuter nominative/accusative singular of “new” is новое (not masculine новый, not feminine новая).

What case is на следующую неделю, and why?

It’s accusative. With time expressions, на + accusative often means “for (the period of)” or “intended for.” Hence:

следующую = feminine accusative singular (agreeing with неделю)
неделю = feminine accusative singular of неделя

Contrast: на следующей неделе (prepositional) means “next week” in the sense of “during next week.” “В следующую неделю” is not idiomatic for this meaning; Russian uses на with “week.”

What’s the difference between на следующую неделю and на следующей неделе here?

…новое расписание на следующую неделю = a schedule for the next week (the schedule applies to that week).
…новое расписание на следующей неделе = a new schedule next week (it will appear/be issued next week).

So the first targets what the schedule is for; the second targets when it will be available. Keeping на следующую неделю adjacent to расписание helps show it modifies the noun, not the verb.

Can I change the word order?

Yes; Russian word order is flexible. Acceptable variants include:

Директор пообещал новое расписание на следующую неделю. (neutral)
Директор пообещал на следующую неделю новое расписание. (slight emphasis on the time frame)
На следующую неделю директор пообещал новое расписание. (fronted time frame)

Just keep the time phrase near расписание if you want the “for next week” reading. If you say …на следующей неделе, it will usually read as “next week (when)” rather than “for next week.”

If the director is a woman, does the verb change?

Yes, past-tense verbs agree with the person’s sex:

Male: Директор пообещал…
Female: Директор пообещала…

The noun директор is grammatically masculine, but agreement in the past is with the actual speaker’s sex. The feminine noun директриса exists but is stylistically marked/dated and much less common.

How do I pronounce it? Where is the stress?

Stresses:

дире́ктор
пообеща́л (note the long “щ” sound [shch]; the two unstressed “о” reduce)
но́вое
расписа́ние
на
сле́дующую
неде́лю

Is расписание the best word here? What about график?

Both can mean “schedule,” but:

расписа́ние: timetables, class schedules, transport schedules (расписание уроков, расписание поездов).
гра́фик: work shifts/hours, production plans, personal schedules (график работы).

Depending on context, you might hear новый график на следующую неделю for shift plans, but for classes or transport, расписание is standard.

Is расписание countable? How do I say “schedules”?

Yes. Singular: расписа́ние. Plural: расписа́ния.

новое расписание = a new schedule
новые расписания = new schedules
несколько расписаний = several schedules

Is it natural in Russian to “promise a schedule” directly?

Yes. Пообещать can take a direct object: пообещал премию/отчёт/новое расписание. It’s understood as “promised that there will be / to provide / to publish.” If you want to be explicit, use an infinitive:

пообещал опубликовать/дать/составить новое расписание

Can I say к следующей неделе or со следующей недели instead?

Different meanings:

к следующей неделе = by next week (deadline). Example: Директор пообещал новое расписание к следующей неделе.
со следующей недели = starting from next week (effective date). Example: Директор пообещал новое расписание со следующей недели.
на следующую неделю = for next week (the schedule applies to that week).

How would this change with different tenses or number?

Present (imperfective): Директор обещает… (is promising / promises)
Future (perfective): Директор пообещает… (will promise, one-time act)
Past feminine: Директор пообещала…
Past plural: Директора/директоры пообещали… (both plurals exist; директора is very common for job titles)