# Integration of Mathematical and Simulation Models for Operational Planning of FMS

By Maheshwari, Sharad K. | Academy of Information and Management Sciences Journal, July 1999 | Go to article overview

# Integration of Mathematical and Simulation Models for Operational Planning of FMS

Maheshwari, Sharad K., Academy of Information and Management Sciences Journal

INTRODUCTION

Flexible Manufacturing Systems (FMSs) are automated small-batch manufacturing systems consisting of a number of numerical and computerized numerical controlled metal cutting machinetools linked together via an automated material handling system (MHS), Real-time control of machines and MHS is accomplished by computers and data transmitting links. The main objective of these integrated systems is to achieve the efficiency of automated high-volume mass production while retaining the flexibility of low-volume job-shop production. The flexibility in FMS is introduced via several factors which may include versatile machine tools, small set-up and tool changing time, relatively large tool carrying capacity and the ability to automatically transfer tools between the machines. These factors allow a part to take alternate route while under process in the system. The possibility of the alternate routings adds an important element to the overall flexibility of these manufacturing systems.

An FMS possesses enormous potential for increasing overall productivity of manufacturing systems due to its flexibility. However, the task of operational level planning of FMS is more complex compared to traditional systems. During the operational planning of an FMS, small batches of parts are selected for simultaneous production in a manufacturing cycle. Several planning decisions such as, part production ratio, tool loading, machine grouping, and resource allocation (Stecke, 1983) are considered at the operational stage.

Numerous research studies are available in literature related to these operational planning problems (for review see: Buzacott & Yao, 1986; O'Grady & Menon, 1986). In general, the research studies in FMS production planning utilize the mathematical modeling approach to solve the problem. However, these mathematical models do not capture dynamic aspects (scheduling and other time-based factors) of the system. To address the dynamic aspects, discrete event simulation is widely employed (for review see: Gupta, Gupta & Bector, 1989). In typical FMS environment, the operational plamiing and scheduling problems are addressed at two different levels.

Since at the operational planning level, scheduling aspects are not considered, the results from the mathematical planning models are generally not realistic for FMS (Leung, Maheshwari & Miller, 1993). For example, the machine workload at the planning model results may be highly balanced, but due to scheduling constraints it may not be achievable during the actual operation of the FMS. This variance in the outcome of two models may result in the poor utilization of resources, longer makespan, etc.

In this paper, the part assignment and tool allocation problem in FMS is considered. The solution procedure utilized to solve the problems combines mathematical model with a discrete event si-tnulafion model. This procedure provides both optimal and realistic solution to mathematical model by integrating it with a simulation model. The remainder of the paper is organized as follows. The next section, briefly, reviews the literature on operational planning in FMS. Section 3 provides an overview of the problem and solution procedure. Section 4 provides proof of convergence of the procedure. This is followed by presentation of the example problems and the results obtained from these problems. Section 7 provides guidelines for parameter modificafion based on the example problems.

LITERATURE REVIEW

The operational planning problem in FMS has been extensively examined in the research literature. Mostly, operational planning problem is formulated as a mathematical model. The scheduling and control issues are not considered at this stage. Stecke (1983) formulated the machine loading problem as a non-linear programming model. Several different loading objectives were considered. These objectives included balancing the assigned machine processing times, maximizing the number of consecutive operations of a part on each machine, maximizing the sum of operation priorities, and maximizing the tool density of each magazine. …

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