# PRODUCT-MIX ANALYSIS WITH DISCRETE EVENT SIMULATION. Raid Al-Aomar. Classic Advanced Development Systems, Inc. Troy, MI 48083, U.S.A.

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3 following features characterize a product-mix determination problem: 1. Maximization of contribution to profit and overhead. 2. Constraints resulting from resource limitations. 3. Bound constraints on planned production. Product-mix determination under such characteristics is usually approached using a traditional Linear Programming (LP) model. The LP model is formulated so that the solution eventually leads to the amount that should be produced from each product type in a production batch so that the overall profit is maximized. Product-mix decisions can be then validated using a DES model of the underlying system. Using DES, the product-mix can be analyzed and the system design can be adapted to different changes in product-mix. 3.1 Product-Mix Decisions via LP LP is a quantitative method of product-mix analysis with extensive applications in the production and business arenas. Many firms have found that Linear Programming (LP) methods are useful techniques for assisting in the product-mix decisions. LP is an analytical approach that is utilized to determine the optimum product-mix so that a certain criterion is met. Using LP an objective function is maximized or minimized subject to a certain set of constraints. In most cases, the least costly mix of products is obtained from the solution of the LP problem. Other LP applications beside product-mix determination include capital budgeting, financial planning, work scheduling, and line balancing (Winston (1994)). Therefore, product-mix determination can be considered as one application of LP for short-term scheduling. LP problems can be solved using graphical method or using simplex method (see Winston (1994)). Most large-scale problems nowadays are solved using software tools by the computer. However, it is always essential to gain at least a basic understanding of the solution methodology along with the knowledge of how to formulate and set up the problem, interpret the results, and draw the right inferences. Johnson and Montgomery (1974) presented a mathematical formulation for the product-mix problem as a constrained LP model. They also illustrated two approaches for dealing with uncertainty in demand. Applying the LP model requires the following information: 1. Revenue obtained from selling one unit of each product type. 2. Unit variable cost of producing a unit of each product type. 3. Required minimum production level of each product type in the planning period. 4. Maximum potential sales of each product type in the planning period. 5. Number of units of each resource that are required to produce one unit of each product type. 6. Amount of each resource available during the planning period. 3.2 Product-Mix Analysis via DES The LP as an analytical approach assumes that production and business processes involved in the production plan are capable of meeting the production requirements within the planning period. However, because of the stochastic variability in real-world processes, the limitations caused by control logic on the floor, along with the dynamic nature of demand and sales, a LP model may result in a product-mix that cannot be actually obtained from the current design of production and business processes. Variability impacts the availability of production resources, control logic may result in process lock-ups and delays, and dynamic demand and sales may lead to frequent changes in the production plan. Therefore, in. DES model can be involved in the product-mix analysis in two ways, as a part of the system design stage to build flexibility in the system design that accounts for projected product-mixes, and as a part of the production implementation stage in order to adapt the production system to dynamic changes in the product-mix. An illustration of involving DES in the system design stage is shown in Figure 2. PROCESS DESIGN PROCESS DES MODEL ACTUAL PROCESS Figure 2: Utilizing DES in the System Design Stage In this approach, the process design is enhanced before implementing the actual process in order to establish the flexibility required for handling different product mixes. This may include designing flexibility in buffer capacities, resource rates and availability, and logical design. Further, designing the system includes designing the supply chain that provides the necessary parts for assembly operations. An illustration of involving DES in the system implementation stage is shown in Figure 3. In this approach, the actual process design is enhanced based on the actual dynamic changes in product mixes as decided by market demand and products sales. This may include 1387

5 INPUT OUTPUT P1 P10 SUBS BUFFERS A1 B P2 PRODUCTION PROCESS FLOW P9 A2 P5a P6a SUBS BUFFERS A1 P3 PRODUCT TYPE A P8 A1 B B P4 A2 A2 PRODUCT TYPE B P7 P5b P6b Figure 6: Process Flow of Car Toy Production Line Table 1: Description of Production Processes in the Toy Production Line Production Process Description Dedication P1 Checking input body of car toy All product types P2 Inserting the car interior All product types P3 Fixing the car interior into the car body All product types P4 Loading body closures All product types P5a Adhering Hood & Deck-lid closures Product type A P5b Adhering Hood & Deck-id closures Product type B P6a Adhering doors-closures Product type A P6b Adhering doors-closures Product type B P7 Overall quality check All product types P8 Installing car wheels All product types P9 Packaging the car toy All product types P10 Labeling output packages All product types two types of car toys (A 1 and A 2 ). However, based on a recommendation of a recent market research, the company decided to introduce a new product type (B) of the car toy to the market. The structure of the production process remains the same. However, new sub-assemblies are added to feed the line with the parts dedicated to the new product and duplication of stations 5 and 6 was found necessary to keep up with the required production rates. 5.1 Product-Mix Decisions via LP To determine the product-mix for the three products in the production plan, a Linear Programming (LP) model was developed based on the projected demand of the market research, the costs and unit prices recommended by the marketing, and the availability of sub-assemblies feeding subs and in-system production processes. The objective of the LP model is to determine the number of units produced per hour from each production type within the existing constraints so that profit is maximized. Throughput of each product type is measured in terms of net Job Per Hour (JPH). Table 2 presents the results of solving the LP model. To meet these production requirements of the LP model, the product-mix that should be implemented in the production plan is shown in Table Product-Mix Analysis via DES A DES simulation model is built and validated to represent the production line of car toys. The model considers production rates, buffering, tool failures, and the availability of sub-assemblies operations. The simulation model is built in order to meet the following goals: 1. Determine the system net throughput capability using the product-mix requirement determined by the LP model. 1389

6 2. Utilize the DES model to adapt the production line to the required product-mix. 3. Provide a full-blown product mix analysis that represents system capability at a sweep of product mixes. In the DES model, the rates shown in Table 4 were used at the feeding subs for each product type and the buffer size and availability of each feeding sub are shown in Table 5. The simulation results based on run controls of 24 hours warm-up period and a run-time of a month of 3-shift production schedule lead to the net throughput capability values shown in Table 6. Comparing the system net throughput capability obtained from the DES model to that obtained from the LP model leads to the conclusion that the system (in its actual performance) cannot meet net throughput requirement for the proposed product-mix. This is because the system DES model considers the dynamic and stochastic variability of real-world processes in its estimation for net throughput capability. Since mainline operations were proven to meet requirements, three parameters are altered using the DES model in order to adapt the system to the required Productmix: 1. The rates of the sub-assemblies feeding subs. 2. The Stand Alone Availability (SAA) of the feeding subs. 3. The buffer sizes between the feeding subs and the mainline operations. Using the DES model, the new rates of the feeding subs are adjusted as shown in Table 7. Also, using the DES model, the new SAA and buffer sizes of the feeding subs are adjusted as shown in Table 8. After adapting the system to the proposed product-mix requirements, the new net throughput capability obtained from the DES model is shown in Table 9. The results of the DES model imply that the system net throughput capability (70.4 JPH) is met for the proposed product-mix (75% of type B, 12.5% of type A 1, and 12.5% of type A 2 ). Further the DES model is utilized to provide a full-blown product-mix analysis to determine system net throughput capability at a sweep of product-mixes. The results of product-mix analysis with DES are summarized in Table 10. Table 2: System Net Throughput Requirements Product Type Product B Product A1 Product A2 Total JPH Net Throughput 52.8 JPH 8.8 JPH 8.8 JPH 70.4 JPH Table 3: System Product-Mix Requirements Product Type Product B Product A1 Product A2 Total Percentage 75.0% 12.5% 12.5% 100.0% Table 4: Rates of Production Line Feeding Subs Sub-Assembly Product B Product A1 Product A2 Interior 63.5 JPH 75.0 JPH 75.0 JPH Closures 60.0 JPH 88.0 JPH 88.0 JPH Wheels 60.0 JPH 58.0 JPH 50.0 JPH Table 5: SAA and Buffer Sizes for System Feeding Subs Sub-Assembly Buffer Size Sub Stand Alone Availability Interior 7 85% Closures 6 85% Wheels 7 85% Table 6: Simulation Results of System Capability Product Type Product B Product A1 Product A2 Total JPH Net Throughput 50.8 JPH 8.4 JPH 8.6 JPH 67.8 JPH Table 7: Adjusted Rates of the Feeding Subs Sub-Assembly Product B Product A1 Product A2 Interior 60.9 JPH 75.0 JPH 75.0 JPH Closures 60.1 JPH 88.0 JPH 88.0 JPH Wheels 65.0 JPH 58.0 JPH 50.0 JPH 1390

7 Table 8: Adjusted SAA and Buffer Sizes of the Feeding Subs Sub-Assembly Buffer Size Stand Alone Availability Interior 15 90% Closures 14 90% Wheels 7 90% Table 9: System Capability after Adaptation Product Type Product B Product A1 Product A2 Total JPH Net Throughput 53.2 JPH 8.7 JPH 8.9 JPH 70.8 JPH Table 10: Full-blown Product-Mix Analysis with DES Product-Mix Product Net Throughput (JPH) System Net B A1 A2 B A A2 JPH 100.0% 0.0% 0.0% % 5.0% 5.0% % 10.0% 10.0% % 12.5% 12.5% % 15.0% 15.0% % 20.0% 20.0% % 25.0% 25.0% % 30.0% 30.0% % 35.0% 35.0% % 40.0% 40.0% % 45.0% 45.0% % 50.0% 50.0% % 100.0% 00.0% % 0.0% 100.0% CONCLUSION The paper presented a practical approach for conducting product-mix analysis with Discrete Event Simulation (DES). The approach suggests starting the analysis with a traditional Linear Programming (LP) model to determine the optimum product-mix that meets the business targets. A DES model is then utilized to check the actual system performance at the optimum product-mix. If the simulation results match the results of the LP model, the decision-maker s confidence increases and the DES model is used to validate the system design. Otherwise, the DES model is utilized to enhance system parameter settings and process configuration so that the optimum product-mix is reached. Finally, the DES model is used to adapt the system design to most possible combinations of the product-mix. This approach can be implemented at the production system micro-level as well as the enterprise macro-level. REFERENCES Al-Aomar, Raid Utilizing Discrete Event Simulation as a Design Tool: Procedure and Case Study. In Proceedings of the 1997 Simulation for Manufacturing Improvement Conference, Detroit, MI. Al-Aomar, Raid and Dan Cook Modeling at the Machine-control Level with DES. In Proceedings of the 1998 Winter Simulation Conference, ed. D. J. Mederios, Edward F. Watson, John S. arson, and Mani S. Manivannan, AutoMod 1999, AutoMod User s Manual for Version 9.0. AutoSimulations, Inc., Bountiful, Utah. Johnson, Lynwood A. and Douglas C. Montgomery Operations Research in Production Planning, Scheduling, and Inventory Control. John Wiley & Sons, Inc. Law, M. Averill and W. David Kelton Simulation Modeling and Analysis. McGraw-Hill, Inc. Pegden, C., R. Shannon and R. Sadowski Introduction to Simulation Using SIMAN, 2 nd Edition. McGraw Hill Book Co. Vonderembse, Mark A. and Gregory P. White Operations Management Concepts, Methods, and Strategies. West Publishing Company. Winston Wayne Operations Research Applications and Algorithms. 3 rd Edition, Duxbury Press. 1391

8 AUTHOR BIOGRAPHY RAID AL-AOMAR is a senior Project Engineer at Classic Advanced Development Systems, Inc. in Troy, Michigan. He is responsible for applying state-of-the-art DES simulation tools in designing manufacturing processes for the Auto industry. He received a B.S. in Industrial Engineering from the University of Jordan in Amman- Jordan and a M.S. in Manufacturing Engineering and a Ph.D. in Industrial Engineering from Wayne State University in Detroit-Michigan. His interests include workcell and material handling systems design and analysis with DES, simulation-optimization methods, and artificial intelligence. His address is Classic-co.com>. 1392

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