# Resource Optimization of Product Development Projects with Time-Varying Dependency Structure

## TL;DR

This paper introduces an analytical framework for optimizing resource allocation in product development projects with dependencies that change over time, using convex optimization and system modeling to reduce project durations.

## Contribution

It develops a novel convex optimization-based approach for resource allocation in dynamic dependency structures, extending beyond static assumptions in prior work.

## Key findings

- Optimal resource allocation can be efficiently computed via convex optimization.
- The framework applies to asynchronous and aperiodic information exchange.
- Boundary analyses offer managerial insights for empirical project processes.

## Abstract

Project managers are continuously under pressure to shorten product development durations. One practical approach for reducing the project duration is lessening dependencies between different development components and teams. However, most of the resource allocation strategies for lessening dependencies place the implicit and simplistic assumption that the dependency structure between components is static (i.e., does not change over time). This assumption, however, does not necessarily hold true in all product development projects. In this paper, we present an analytical framework for optimally allocating resources to shorten the lead-time of product development projects having a time-varying dependency structure. We build our theoretical framework on a linear system model of product development processes, in which system integration and local development teams exchange information asynchronously and aperiodically. By utilizing a convexity result from the matrix theory, we show that the optimal resource allocation can be efficiently found by solving a convex optimization problem. We provide illustrative examples to demonstrate the proposed framework. We also present boundary analyses based on major graph models to provide managerial guidelines for improving empirical PD processes.