Dynamic control of a closed two-stage queueing network for outfitting process in shipbuilding

Highlights

• An innovative model for outfitting processes in shipbuilding.

• Queueing networks models capture the variation of the process.

• System control is based on an analytical congestion model.

• A new MDP model captures the essential features of the problem.

• A regression-based heuristic benefits from an exact MDP and a simpler MVA model.

• A pre-processing stage yields a fast real time heuristic that performs very well.

Abstract

The U.S. Naval shipbuilding industry faces significant challenges to build ships on-time and within budgeted cost. To achieve greater efficiency and timeliness in shipbuilding, we developed a flexible two-stage queueing model under a CONWIP job release policy to enhance the planning and control of the outfitting process, one of the key processes in shipbuilding. The model is formulated using Markov Decision Processes which can provide (1) the optimal dynamic control policy and (2) the optimal cost. The numerical results showed that the optimal control policy is a state dependent threshold type policy and very complex to analyze. Therefore, we developed a static model to simplify the dynamic model and used Mean Value Analysis to gain insights. Using both data from the dynamic model and the static model, we developed a regression model to calculate a threshold policy heuristic. Testing reveals that the performance of this heuristic is very close to the optimal.

Introduction

“U.S. shipbuilders produce the finest warships in the world, but cost growth is eroding the purchasing power of the Navy”, which is warned in [1] by the Office of the Deputy Under Secretary of Defense. Over the last decade, the U.S. shipbuilding industry has improved significantly on productivity as a result of Navy and industry initiatives and investment. However, there are still large technology gaps in some U.S. shipyards that present opportunities to make further substantial improvements, particularly in the preproduction functions which include design, production engineering, and planning according to [1]. Research presented in this paper focuses on developing a flexible queueing model of ship outfitting processes and using Markov Decision Processes to develop a more efficient dynamic control in order to reduce the ship construction time and cost. At the same time, shipbuilding also motivates us to identify, design, and solve new problems in the control of flexible queueing networks.

Shipbuilding is a unique industry that uses a wide variety of manufactured components and requires a large number of workers possessing various skills as well as specialized facilities. There are two major processes in shipbuilding: hull construction and outfitting. Hull construction includes all the activities associated with fabricating and assembling the hull, while outfitting refers to the process of fabrication and installation of nonstructural components. Hull construction normally uses the block construction method, which is also called Modularization. This construction method has been used in ship production since World War II. The ship is divided geometrically into blocks. Depending on the ship size and type, a typical ship may consist of hundreds of blocks. The main hull construction work flow contains the processes of part assembly, block assembly, grand block assembly, and final hull construction, as pictured below in Fig. 1. Typically, ship blocks are assembled in a block assembly area and then joined together to form grand blocks in a nearby area, these grand blocks are lifted by large cranes to the drydock for the final erection.

Outfitting in shipbuilding includes painting, pumps, piping systems, main propulsion system, electrical system, air conditioning (HVAC), etc. It represents as much as 50% of the cost of the ship and up to 50% of ship construction time in many instances (see [2]). The scheduling of outfitting greatly depends on the schedule of the hull construction and therefore it is a highly integrated assembly process. Outfitting activities can almost always be performed during or after any stages of the hull construction. It is nearly always more efficient to process the outfitting at an early stage due to better ergonomics with easier access and greater feasibility to employ large machinery.

Research presented in this paper focused on the ship outfitting process. Taking the sequence in which blocks are assembled as an input, our model and methodology contribute toward an effective dynamic control policy for the best stage at which to perform block׳s outfitting: block assembly or grand block assembly.

The challenges of controlling the best stage at which to perform outfitting arises in part from the time and cost differences of processing the same outfitting work at different stages. The outfitting process can delay the entire ship production system due to unexpected delays, system variations, capacity limitations, and technological constraints. Contemporary outfitting planning relies heavily on the experience and judgment of key personnel. The combinatorial and stochastic nature of outfitting planning and the lack of prior efforts to incorporate control methodologies suggests that there is an opportunity to create new models for ship outfitting processes to enhance overall shipbuilding performance. Although our model makes simplifying assumptions, our goal is to contribute a stochastic model which can capture the variability of ship outfitting in order to provide a more effective and accurate outfitting planning decision and control approach.

In the past, there has been little operations research literature in the area of ship outfitting. Some early production research on ship outfitting includes [2], [3], [4]. Storch et al. [3] introduce the basic outfitting processes and the Zone Outfitting Method. Goldbach [4] describes the planning and execution of pre-outfitting in structural assemblies. Graves and McGinnis [2] clearly discuss and analyze current outfitting problems, and use a deterministic activity network model to formulate the outfitting planning problem. A mixed integer programming model of outfitting with sequence constraints was developed to address this outfitting planning problem. More recent research on the scheduling of the outfitting process has been conducted in [5], which provides a methodology that can automatically generate an outfitting sequence and planning.

All these studies only consider the deterministic processing time of the outfitting process and provide static outfitting planning. Approaches such as these will fail when dealing with common problems in shipbuilding, such as demand change during production and high variability in processing times. Therefore, we must investigate the outfitting problem with variability and develop a control policy that can change dynamically according to the stage of the shipbuilding system. Our previous research in ship outfitting in paper [6] presented a static two-stage $G/G/1$ queueing model using Kingman׳s approximation to provide the outfitting work distribution policy at a strategic level. The model presented in this paper is a dynamic queueing model using Markov Decision Processes to analyze the optimal control of the outfitting activities based system dynamics. To our knowledge, this is a rare model for which Mean Value Analysis (MVA), a static model, is a fairly effective approximation for the dynamic control problem. This MVA approximation is then used to provide an improved heuristic by incorporating the MDP results over a training test suite to yield an effective regression-based heuristic (which is another approach that has not received much attention).

The remainder of this paper is organized as follows. In Section 2, we develop a two-stage closed queueing network for the outfitting process and formulate the problem using Markov Decision Processes (MDP). The numerical examples from the MDP illustrate the structure of the optimal control policy, in which extensive numerical analysis suggests to be of threshold type. The optimal control policy is difficult to strongly characterize by a theoretical analysis of the MDP model, as structural properties for this problem are not very effective in defining a heuristic. Therefore, we develop a static queueing model in Section 3 and use MVA to gain more insight into this model. In Section 4, a heuristic is developed using a regression model and information from both the dynamic and static models, which is more effective in controlling the outfitting activities and also simpler to implement. Finally, we discuss conclusions and directions for future research in Section 5.