A formal set of algorithms for project scheduling with critical path scheduling/material requirements planning

Abstract

A hybrid model combining the critical path method (CPM) with material requirements planning (MRP) has been suggested (Aquilano) as a more robust method for scheduling projects and resources. The primary advantage of this technique is that resource acquisition lead times as well as inventory records are integrated into the process of computing the project schedule. This paper presents a set of formal CPM/MRP algorithms that may be used to compute the early and late start schedules as well as the critical sequence. A number of modifications have been incorporated into the CPM/MRP technique to improve the viability of CPM/MRP as a tool for application to actual project scheduling problems. A simple example project is used to demonstrate the CPM/MRP model. The CPM/MRP technique is designed to overcome a basic shortcoming of previously suggested project scheduling methodologies. CPM was initially designed to schedule projects subject to technological constraints only. Later, additional techniques were introduced to consider constraints upon various aspects of resource availability (Davis). None of the suggested techniques attempted to integrate resource acquisition lead time with the generation of requirements for resources. Obviously such a technique would require the integration of inventory records into the scheduling technique. The combination of CPM and MRP provides a possible vehicle for overcoming this drawback in CPM. Both CPM and MRP are linear models that generate schedules based upon precedence relationships. An integrated approach is useful since activities could be scheduled subject to information about the inventory position. An activity may be scheduled as soon as all resources are on hand. It is only delayed by those resources which must be acquired and activities which proceed it in the project network. CPM/MRP also shows promise as an aid to constrained resource scheduling since computations regarding resource availability are an integrated part of the technique. The effect of resource allocation decisions is immediately evident in the MRP‐type time phased records. Results of the tests run on short projects of up to 300 activities and resources have shown that the program does work satisfactorily. Execution time for a 300 item network tested was approximately ten seconds on a CYBER 175.

Project-driven supply chains: integrating safety-stock and crashing decisions for recurrent projects

“…Clearly, the project scheduling and material ordering decisions are coupled, and the question is how to jointly optimize both sets of decisions for a project. Aquilano and Smith (1980 There is a lack of rigorous mathematical modeling that integrates the issues of projects and material supply chains, and resolves them jointly. We refer to O'Brien, et al …”

Scheduling recurrent construction

“…However, only one link from 5 to 1 and one from 5 to 2 are necessary. Others have explained how to construct pegging relationships that include batching [1,6,10,38].…”

“…The late start complete graph (LSC) method applies late start critical path logic to the complete graph, one that includes pegging and resource precedence arcs [1,38,41]. Our version of LSC ensures a feasible schedule by scheduling backwards from product delivery dates, rather than due dates, using B i , the pegging and resource relationships for each task i.…”

The integration of CPM and material management in project management

“…This means that each activity should be classified by the cost of resources and material required for its execution. Aquilano and Smith-Daniels (1980) and Smith-Daniels and Aquilano (1984) developed a system which provides a complete integrated project scheduling device. The system is based on treating activities, resources and material as entities in a Material Requirement Planning (MRP) type logic and exploding the 'project Bill Of Material' (BOM).…”