Multiple project portfolio scheduling subject to mass customized service Bzdyra K.*, Banaszak Z.**, Bocewicz G.* * Dept. of Computer Science and Management, Koszalin University of Technology, Śniadeckich 2, 75-453 Koszalin, Poland, (
[email protected]). ** Dept. of Business Informatics, Warsaw University of Technology, Narbutta 85, 02-524 Warsaw, Poland, (
[email protected]) Abstract. Declarative framework enabling to determine conditions as well as to develop a decision making software supporting small and medium size enterprises aimed at unique, multi project-like and mass customized oriented production is discussed. The set of unique production orders grouped into portfolio orders is considered. To each production order treated as an activity network common shared resources operation times of which are known in advance are allotted. The problem concerns of scheduling of a newly inserted projects portfolio subject to constraints imposed by a multi–project environment The answer sought is: Whether a given portfolio can be completed within assumed time period in a manufacturing system in hand? The goal is to provide a declarative model enabling to state a constraint satisfaction problem aimed at multi projectlike and mass customized oriented production scheduling. The attached calculation example illustrates the computational efficiency of the proposed solution. Keywords: project portfolio, scheduling, declarative modeling,
1
Introduction
Current manufacturing environment can be characterized in terms of many factors but the key one for companies confronting the challenge of remaining competitive in an era of globalization is undoubtedly the capability of fast and accurate decision making, especially so in the mass customized production/services domain. An optimal assignment of available resources to production steps in a multi-product job shop (MPJS) is often economically indispensable. The goal is to generate a plan/schedule of production orders for a given period of time while minimize the cost that is equivalent to maximization of MPJS’s profit. In that context executives want to know how much a particular production order will cost, what resources are needed, what resources allocation can guarantee due time production order completion, and so on. So, a manager needs might be formulated in a form of standard, routine questions, such as: Does the production order can be completed before an arbitrary given deadline? Is it possible to undertake a new production order under given (constrained in time) resources availability while guaranteeing disturbance-free execution of the already executed orders? What values and of what variables guarantee the production order will completed following assumed set of performance indexes?
adfa, p. 1, 2011. © Springer-Verlag Berlin Heidelberg 2011
In recent years, focus has come to be on the Resource-Constrained Project Scheduling Problem (RCPSP) which involves scheduling project activities subjected to temporal and resource constraints, while minimizing the total project duration. Two different approaches have been taken in solving the RCPSP. The first approach includes exact algorithms, which produce optimum solutions [6, 7]. The second approach is comprised of algorithms that provide admissible solutions refer to [3, 4, 8, 9]. These all demonstrate good results for the limited objective of resource allocation, but fail to truly support decision makers on all stages of project execution. Very limited work focuses on the joint technological processes, transportation routing and financial [2]. Furthermore, there is another aspect of the addressed problem, namely multi-criteria decision making under uncertain conditions. Fuzzy multicriteria decision making is primarily adopted for selecting, evaluating and ranking of alternative solutions to problems [3]. Studies conducted so far on declarative models implemented in fuzzy sets framework [1, 11], show that the proposed concept of reverse projects portfolio planning provides a promising alternative to commercially available ones. Therefore the new methods and techniques addressing the impact of real-life constraints on online decision making are of great importance [4]. To do this in a way compatible with real life settings necessitate the use of stochastic and fuzzy logic frameworks [6]. The fuzzy model of project portfolio online control can be specified as a declarative one and then implemented using constraint programming techniques and finally implemented as a decision support system [3]. Regardless of its character and scope of business activities a modern enterprise, has to build a project-driven development strategy in order to respond to challenges imposed by growing complexity and globalization. In that context this contribution can be seen as continuation of our former work aimed at multi-product production flow planning focused on coordination of processes and activities related to work order processing [1, 3, 4, 10]. Our main goal is to propose a new modeling framework enabling to evaluate and prototype alternative flows of production orders portfolio (POP) in the manufacturing systems disposing untapped potential in production capacity. The following questions are of main interest [5]: Can the assumed MPJS processing simultaneously set of production orders meet the deadlines imposed by a given, newly introduced POP? Does there exist MPJS enabling to perform assumed variety of POPs? The rest of the paper is organized as follows: Section 2 introduces to a concept of POP through an illustrative example. Section 3 provides the declarative problem formulation focused at POPs prototyping. Computational experiments and conclusions are presented in Sections 4 and 5, respectively.
2
Illustrative example
Considered MPJS consists of the set of machines ॸ ൌ ሼ݉ଵ ǡ ǥ ǡ ݉ ǡ ǥ ǡ ݉ெ ሽ (where ݉ means the ݅-th machine and ܯܮa number of machines in the system) required for execution of operations belonging to different Project Portfolios. In the system, the family of project portfolios ܼ כൌ ሼܼଵ ǡ ǥ ǡ ܼ ǡ ǥ ǡ ܼ ௩ ሽ, composed of production orders
