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Planning tools for managing the supply chain
Computers & Industrial Engineering 46 (2004) 763–779 www.elsevier.com/locate/dsw
Planning tools for managing the supply chain Ste´phanie Hurtubise*, Claude Olivier, Ali Gharbi Design and Control of Production System Laboratory, Automated Production Engineering Department, E´cole de technologie supe´rieure, Universite´ du Que´bec, Montre´al, Que., Canada H3C 1K3 Available online 26 June 2004
Abstract In this paper, we introduce a new way to manage the supply chain. The proposed solution reduces the problem’s complexity using a two-stage hierarchical production planning method and is applicable to realistic transportation optimization problems. The approach is based on planning and operations scheduling models, and is designed to minimize travel and production costs within a flexible organizational network. In the aggregate planning phase, a mathematical model involving an aggregation of products, demand and time periods is solved. It is at this initial stage that the size of the problem is reduced and its output is used as input to the detailed phase in order to improve resolution time. The second stage produces a detailed schedule. It is shown that the proposed approach generates good and feasible solutions to practical problems within a reasonable computational time. q 2004 Elsevier Ltd. All rights reserved. Keywords: Flexible manufacturing networks; Networked manufacturing; Supply chain management; Hierarchical production planning; Scheduling of manufacturing systems
1. Introduction Today’s manufacturing enterprises face enormous competitive pressures stemming from the current dynamic and open business contexts. Global competition and market demand for customized products, delivered ‘just in time’, exert real stress on manufacturers. Recently, new production paradigms, such as the extended enterprise, as well as agile, virtual and networked manufacturing, have appeared in response to the increasingly dynamic conditions of the marketplace (Goldman, Nagel, & Preiss, 1995; Jagdev & Browne, 1998). These new concepts prompt geographically dispersed manufacturers to build alliances with their suppliers and customers in order to work more closely with them. They need to work to build manufacturing networks which bridge large sections of the supply chain. * Corresponding author. Tel.: þ1-514-396-8806; fax: þ1-514-396-8595. E-mail addresses: [email protected] (S. Hurtubise), [email protected] (C. Olivier), [email protected] (A. Gharbi). 0360-8352/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.cie.2004.05.018
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Planning the supply chain is a very complex task. Supply chain managers are responsible for, among other things, the planning activities relevant to products, manufacturing processes, technology selection, material flows and control systems. They have to enter into agreements with many players and they orchestrate their operations through exploitation of the capabilities offered by other manufacturers and by their suppliers. Their services and logistics departments are responsible for coordination of production, transportation and storage activities (D’Amours, Montreuil, Lefranc¸ois, & Soumis, 1999). Managers initially have to choose suppliers from among a large number of intervening parties—or processors—and these are flexible, which is what makes the decision complex. Managers have to schedule jobs on these processors in order to make the network operational and to minimize operating costs, while dealing with a multi-enterprise, multi-product and multi-machine environment, as well as demands which fluctuate over time. This gives rise to a large-scale scheduling problem of the job shop type which is really difficult to solve. Efficient supply chain management requires solution of complex and difficult planning problems. Because of their combinational nature, these large-scale system planning problems are usually too large to solve using standard mathematical programming approaches, but can be handled using hierarchical production planning (HPP) (Hax & Meal, 1975), where the production planning problem is organized into a hierarchy of subproblems. HPP is widely used in the production planning literature (Miltenburg, 2001). Subproblems are solved sequentially starting at the top of the hierarchy with the solution of one subproblem imposing constraints on the following one. The aim of this paper is to introduce a new way to manage flexible manufacturing networks in a supply chain. Because this large-scale scheduling problem is too difficult to solve using standard approaches, our first task is to reduce the problem’s complexity. The proposed method for doing so uses a two-stage HPP approach which combines aggregate and detailed mathematical models for planning and scheduling operations, while at the same time minimizing travel and production costs within a flexible network organization. At the end of the 1980s, pioneers like Anderson and Paine (1975), Miles and Snow (1978), Miles, Snow and Charles (1992), Snow, Miles, and Coleman (1992), and many others, started working on the network organization, defining concepts and systemic approaches. More recently, with the arrival of e-commerce, supply chains and manufacturing networks have become a prolific research area. The Network Organization Technology Research Center1 and Production System Design and Control Laboratory2 had developed approaches and tools to address various aspects of this question. Montreuil, Lefranc¸ois, Ramudhin, and D’Amours (1992), for example, introduced the concept of symbiotic manufacturing networks. Then, Ramudhin, Montreuil, and Lefranc¸ois (1994) studied the problem of distributing a set of activities, with precedence constraints in the form of an assembly tree, among a set of competing firms with the objective of minimizing total cost. As well, Olivier (1998), and Olivier, Montreuil, Lefranc¸ois, and Maley (1996, 1994) proposed an approach for evaluating, from cost and flow perspectives, alternative layouts for manufacturing systems organized within an agile network. They also introduced concepts for planning and control of virtual manufacturing networks (VMNs). Hurtubise (2001) contributed to the development of production planning tools for supply chain planning in the context of an agile manufacturing system. D’Amours, Montreuil, Soumis, and Moke (1999, 1996) presented a network model to optimize design and operation decisions for the make-to-order case, 1 2
Affiliated with Universite´ Laval, Que´bec (Que´bec), Canada. Affiliated with E´cole de technologie supe´rieure, Universite´ du Que´bec, Montre´al (Que´bec), Canada.
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minimizing a cost-time trade-off under standard manufacturing constraints. Optimization models have also been developed to address the planning process of the supply chain. An efficient way to manage the planning of a supply chain is through a network approach. Because they are part of the extensive process of supply chain design and management, aggregate planning at the bidding level and then detailed planning for actual production can be efficiently modeled with networks. We have already introduced a conceptual framework for the management of manufacturing networks (Hurtubise, Olivier, & Gharbi, 2000), which integrates various tools in order to quantitatively evaluate networked manufacturing and to efficiently manage it. The framework is used to determine which firms will make up a particular manufacturing network, as well as to control their activities. In order to reduce the complexity of the supply chain planning problem, this paper proposes a solution which uses a two-stage HPP method. The approach combines the aggregate and detailed planning models introduced in our conceptual framework. In the aggregate planning phase, a mathematical model involving an aggregation of products, demand and time periods are solved. In the detailed planning phase, the output of the first-level model imposes constraints on a second model which produces a detailed schedule. Linear programming models are used by suppliers of a supply chain for evaluating their production capacity and for assigning a precise time-phase workload to shop-floor machines. The conceptual framework is summarized in Section 2. Next, the aggregate and detailed models are explained in Section 3. Then, data flow exchange between models is illustrated in Section 4 using a numerical example. Finally, the resulting production plans are compared and analyzed in Section 5.
2. Framework for the management of manufacturing networks Network design is an iterative process which begins with a networking firm wishing to carry out a production program through the exploitation of a network: its supply chain. The process of the framework for network management requires four steps. The first step is the identification, by the networking firm, of potential suppliers capable of executing different tasks for each program activity. After identifying these potential suppliers, the firm invites them to bid on specific aspects of the chain. In order to respond to the offer, bidding firms must prepare an aggregate production plan to evaluate their production capacity within a given time fence. Different approaches can be used. The model developed by Olivier et al. (1994) is one of several. This approach considers individual pieces of equipment—or processors—as nodes in a network, making it possible to find the appropriate subset of processors from a whole set that will meet the job’s requirements. If the bidding firm has enough capacity, the model will yield the production delay required and identify which processor nodes should be utilized. The model for the generation of an aggregate production plan is presented in Section 5. Once the bids have been collected, the networking firm plans its supply chain and manages it dynamically according to demand variation over time. This second step can be achieved with the D’Amours et al. (1996) approach, by which the network suppliers, subcontractors, business units and transporters are identified who should be chosen in order to make the network operational and to minimize operating costs. The bidding firms are then informed as to whether or not their tender has been successful. The third step is the generation of a detailed production plan by all firms whose offers have been accepted. This can be done based on the best potential equipment identified during the aggregate production planning phase. A precise time-phase workload is then assigned only to processor nodes
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identified in the aggregate plan. The latest model developed by Olivier (1998) is used to generate detailed production plans. The functionality of a model developed for this task and integrated with the model for aggregate production is presented in Section 3. Finally, the fourth and last step is the control loop. The networking firm carries out an operations control task by comparing its production plan with the suppliers’ production reports and making the necessary corrections to ensure on-time delivery of the final product. In such manufacturing networks, the nodes can be internal to a given organization as well as external businesses from around the world (D’Amours et al., 1996). The generic term ‘supplier’ may thus apply to internal work cells, departments, factories and divisions, as well as to external businesses.
3. Methodology The proposed approach is aimed at managing the supply chain. First, the best suppliers, or processors—those that will make the network operational, have to be chosen. Second, jobs have to be scheduled on these processors in such a way that operating costs within a realistic production plan are minimized. This generates a very complex production planning problem which is really very difficult to solve. In order to arrive at a feasible detailed schedule, therefore, the complexity of the problem must first be reduced using aggregate planning. The approach proposed here is presented using the example of a flexible manufacturing system (FMS) associated with one supplier in a supply chain. The difficulty in planning for a large-scale FMS is addressed using the HPP paradigm. The essential philosophy of HPP is to make use of the time line to control the amount of detail and of aggregation with the higher levels of aggregation focusing on the longer time horizon while providing guidance to lower levels which are concerned with shorter time intervals (McKay, Safayeni, & Buzacott, 1995). This approach is based on the aggregate and detailed planning models developed in the conceptual framework. Common mathematical models developed to generate aggregate production plans can handle a large quantity of variables, often more than 20,000, and can be solved very quickly. An aggregate plan is optimal, but, in such a plan, data is usually accumulated in daily periods, i.e. manufacturing systems have daily time ‘buckets’, which is what makes the plan difficult to execute because there is no indication as to how the work will be scheduled. Moreover, the temporal sequence of production tasks is not embedded in aggregate planning models; only daily capacity is supported. Fig. 1a shows a Gantt chart showing an aggregate schedule. In the context of scheduling operations in a network, time buckets should be much shorter so as to result in an accurate plan. Unlike an aggregate plan, a detailed plan incorporates the temporal sequence of production tasks and does give indications about how the work will be scheduled. Fig. 1b shows a Gantt chart showing a detailed schedule. In this paper, a detailed planning model able to schedule production in hourly periods is used, and yields feasible schedules which may be used to simplify execution and control of real operations. But, since a problem’s size rapidly increases when precision level is increased, the problem’s complexity has to be considerably reduced in order to generate a precise plan within a reasonable resolution time. To do so, an approximation is carried out: for each product, the detailed planning model will consider only the variables and constraints that concern work centers identified by the aggregate plan and sections between these work centers. All other nodes will be withdrawn from the initial solution. This approach reduces the number of possibilities to evaluate.
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Fig. 1. Differences between an aggregate and a detailed schedule.
The solution will not be optimal, but the fundamental objective here is not to achieve optimality, but to rapidly identify a good, feasible solution. In this way, the detailed model may resolve problems of realistic size within a reasonable time. At the first hierarchical planning level, therefore, the production model developed by Olivier et al. (1994) is used to generate the aggregate plan for evaluating the supplier’s capacity. The detailed planning model developed by Olivier (1998) is then used at the second hierarchical planning level in order to assign a precise time-phase workload to shop-floor machines, based on the best potential nodes specified at the first level by the aggregate plan. 3.1. Aggregate planning At the first stage of the bidding process, a supplier must prepare an aggregate production plan to evaluate its production capacity. This includes selection of the equipment that will be assigned to that job, routing of parts in the production system, estimation of the capacity and manpower required, and, obviously, estimation of the cost involved in the whole operation. Introduced by Olivier et al. (1994),
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VMNs integrate most of this information. For instance, when individual pieces of equipment, or processors, are considers as nodes in a network, it is possible, using the model, to find the right subset of processors from a whole set that will fulfil the job’s requirements. Hence, a supplier first applies the aggregate planning model (Olivier et al., 1994) to evaluate its capacity to respond to an offer. Then, a general LP model involving an aggregation of products, demand and time periods is solved (see e.g. Nahmias, 2001). The global approach of this process is based on a multi-commodity, multi-flow linear optimization model. The objective is to minimize multi-product manufacturing costs and the total interworkstation handling costs subject to constraints on capacity, while meeting total demand for products. Fig. 2 presents a diagram showing the data flow through the aggregate planning model. The input parameters required are the supplier’s production and capacity parameters and the potential processor nodes. The supplier’s production and capacity parameters contain demand requirements from clients, operating costs, capacity requirements and availability, bills of operations (routings), etc. The information generated by the aggregate model makes up the aggregate production plan, which does not take into account temporal aspect and operations sequencing. The aggregate plan includes workflow patterns, workload distribution among processor nodes and the planned utilization of those nodes. A workload pattern can be defined as the pattern of tasks planned to be accomplished by each processor in a given time slot. In aggregate planning, there is only one time slot—or time bucket. This pattern includes the specific groups of products to be processed on each processor in this time period. The workflow pattern expresses the planned routings of items between processors. If the supplier who wants to bid has enough capacity to respond to one or more offers, the model identifies which processor nodes should be utilized at the time of production plan processing. Based on these initial results, a supplier sends its bids to the networking firm. Bids contain available capacity and quotations for specific time periods.
Fig. 2. Data flow diagram for the aggregate planning process.
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3.2. Detailed planning A supplier uses the detailed planning model (Olivier, 1998) for generating its detailed production plan. Like the aggregate planning process, it is based on a linear optimization model which minimizes production, material handling and storage costs subject to constraints on capacity, while meeting total demand. However, this model takes into account temporal aspects and operations sequencing, and generates detailed production patterns. Time bucket length depends on the desired level of accuracy. Given the considerable number and diversity of potential processors, it would not be easy, or even realistic, to generate a detailed production plan using all the flexibility available in a manufacturing facility. For this reason, the complexity of the problem needs to be reduced. Hence, this approach uses the aggregate production plan as an input to the detailed planning model. In the first step of hierarchical planning, the best potential processors are chosen for each family of products, through the aggregate model. A family includes products with the same routing. The output of the first level, i.e. workload and workflow patterns, are used to determine one VMN for each family of products. For each family, the right subset of processors that will fulfil the job’s requirements while minimizing travel and production costs is identified. At the detailed planning phase, those VMNs impose constraints on the planning model of the second step of hierarchical planning, which will produce a detailed schedule. In this second stage, the detailed model assigns a precise time-phase workload only to processor nodes which were identified at the first stage of the process. Using the aggregate plan as input to the detailed model, only a part of the information is retained, making it possible to take into account the temporal aspects with many fewer constraints, while maintaining a good range of flexibility. Even if this approach does not generate the optimal solution, it will produce a very good, feasible, detailed production plan, and this plan will be generated within a reasonable time. Fig. 3 presents a diagram showing the data flow through the detailed planning model. The data flow is similar to that of the aggregate planning model, the difference mainly being the size of the time buckets, long on aggregate planning but much shorter on detailed planning, and work scheduling specifications which are not available with aggregate scheduling, but specified in a detailed plan. In addition to the supplier’s production and capacity parameters, input parameters now include the potential processor nodes (VMNs) that may process each family of products. Those VMNs were identified at the first stage, as previously mentioned. The detailed planning model is used individually by each supplier to generate its detailed production plan. The information generated by this model makes up the detailed production plan. In addition to workflow and workload patterns, the plan also includes buffer levels. In detailed planning, buffers are currently required to balance flow between processors. Based on these results, suppliers may forward delivery schedules, operations reports and job status to the networking firm. Fig. 4 shows the supply chain management process and highlights the approaches that are used here.
4. Numerical example The use of the aggregate and detailed models, as well as the data flow exchange between them, is demonstrated here. The case used as an example concerns a firm which makes and assembles dashboards
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Fig. 3. Data flow diagram for the detailed planning process.
for the automotive industry. The manufacturing system is composed of agile processors in a flexible network. The product line has been aggregated to six dashboard families. In the same way, routing has been aggregated to four levels. Dashboards are made up of three to four indicators, which are speedometers, revolution counters and general gauges for fuel and temperature level. Some components may come from external suppliers and are then not processed by the current manufacturing system. Fig. 5 shows product routing and network layout, while Table 1 presents the data corresponding to the numerical example, i.e. product composition, processing time, processor capacity and demand. Workstations in the last level of the routing are for final assembly. They are named type [C] processors. The third level is made up of assembly processors for speedometers [S], revolution counters [T] and general gauges [G]. A two-component assembly processor makes speedometers and revolution counters. These components are named [AS] and [BS] for [S] indicators as well as [AT] and [BT] for [T] indicators, and are made at the second level of the routing. The first level is made up of processors for coil fabrication [B] which is required for the assembly of the [BS], [BT] and [G] components. Machines process components one at a time. When a component is processed, it is directly transferred to a buffer next to the machine. There is one buffer for each processor. Components wait in the buffer until they are required at the subsequent processor. Costs represent real traveling expenses and these include labor and equipment expenditures. In order to limit quantity of data, traveling costs are not listed here. However, these costs are proportional to the distance between processors; e.g. it costs 0.025$ to move one component from processor G1’s buffer to processor C2, and it costs 0.2125$ to move one component from processor G1’s buffer to processor C10. Since buffers are just next to their processors, there is no cost associated with moving a component from a processor to its buffer.
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Fig. 4. Supply chain management process.
The aggregate planning model is used first, to identify which processor nodes should be utilized at the time of production plan processing. In aggregate planning, data is usually gathered in daily or weekly periods. As can be seen in the aggregate schedule shown in Fig. 1a, the model identifies how many products are processed by each processor for that one time period. Hence, an aggregate plan does not consider delays produced by transfer of products from one routing level to another. It is thus important to limit work center utilization in the aggregate plan so as to keep a safety margin of time in order to accommodate delays and keep the detailed plan feasible. The detailed planning model is then executed, based on the best potential nodes specified in the aggregate plan. In this example, planning models are used arrive at a daily production plan in which a precise timephase workload to shop-floor machines is assigned, while traveling costs are minimized and total demand for all products, considering the limited capacity of processors, is respected. The aggregate model uses a daily time bucket, and work center utilization is reduced by 15% to keep a safety margin of time, as explained above. The detailed model uses hourly time buckets and then generates the 24 production plans required for an entire production day, i.e. one plan for every hour. The latter model automatically considers delays generated by product transfers due to routing. Actually, products made at the first routing level during the first hour (the first time bucket) may not be in transit
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Fig. 5. Product routing and network layout.
before the second hour and may be assembled at the second level work centers only from the third hour, thereby introducing delays into the schedule. Let us look again at Fig. 1. Knowing that the aggregate model planned for 2290 component Bs from family F to move to processor B6, we can determine that this represents 19.1% of this work center’s capacity, as demonstrated by the second bar in Fig. 1a. As it has been stated before, an aggregate plan does not give any indication about work scheduling because the temporal sequence of production tasks is Table 1 Data for numerical example Component, sub-assembly or product
Composition
Component B Component AS Component AT
– – –
Sub-assembly Sub-assembly Sub-assembly Sub-assembly Sub-assembly
1 1 2 1 1 2 1 2 1 1 2
Product Product Product Product Product Product
BS BT G S T
family family family family family family
A B C D E F
Each processor’s capacity
Demand
7.2 5.6 6.3
24 h ¼ 86,400 s 24 h ¼ 86,400 s 24 h ¼ 86,400 s
– – –
B B B AS; 1 BS AT; 1 BT
2.85 2.14 11.76 23.5 25.2
24 h ¼ 86,400 s 24 h ¼ 86,400 s 24 h ¼ 86,400 s 24 h ¼ 86,400 s 24 h ¼ 86,400 s
– – – – –
G; 1 G; 1 G; 1 G; 0 G; 1 G; 0
26.1 26.1 26.1 26.1 26.1 26.1
16 h ¼ 56,600 s 16 h ¼ 56,600 s 16 h ¼ 56,600 s 16 h ¼ 56,600 s 16 h ¼ 56,600 s 16 h ¼ 56,600 s
1512 3349 5625 713 532 5424
T; 0 S T; 0 S T; 1 S T; 1 S T; 1 S T; 1 S
Processing time (s)
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not embedded in aggregate planning. However, a detailed plan does incorporate the temporal sequence. Fig. 1b gives an example of how work is scheduled on work centers by a detailed plan. All the empty spaces correspond to delays introduced into the schedule by routing and product transfers. Hence, the 15% margin of time kept in the aggregate plan makes it possible to take account these delays in the detailed plan. As a result, work center availability does not have to be reduced in a detailed planning model, and it is set to 100%.
5. Results Traveling costs for both production plans are presented in Table 2. Results show that the cost of the aggregate plan, where work center utilization is reduced to 85% is 11.5% higher than the cost of the optimal aggregate plan. Since work center utilization has been reduced to keep a margin of time, some workload has to be assigned by the aggregate model to processors located on more expensive sections when work centers on the most economic sections are saturated, resulting in a more expensive plan. Table 2 results also show that the cost of the detailed plan is 8.5% higher than that of the optimal aggregate plan. The detailed plan costs less than the aggregate plan with reduced availability because its work center availability is not reduced. In the detailed plan, work centers on the most economic sections may be used up to 100%, while they may only be used up to 85% in the previous aggregate plan. Workflow patterns for whole families of products are summarized in Figs. 6 and 7. Fig. 6 shows a section of flow patterns produced by the aggregate planning model. Each flow includes flows for all six families of products. In order to simplify representation, only flows between workstations of type [B] and [G] and between workstations [G] and [C] are shown, because the complexity of the flows and their spreading patterns are the same for the other levels. Workflow patterns between G1 and C2 for each product processed by these work centers are exploded in the lower right corner of Fig. 6. Fig. 7 shows a section of flow patterns produced by the detailed planning model on nodes identified by the aggregate plan. In Fig. 7, each flow includes the flows for all the 24-hourly production plans. The flow patterns shown in Figs. 6 and 7 demonstrate that the least expensive sections between routing levels are well patronized until work centers on these sections are occupied to full capacity. Flow patterns for the aggregate plan are a little more spread out than for the detailed plan, and the least expensive sections are less occupied. That is because work center utilization has been reduced in aggregate planning to keep a margin of time, as explained above. As desired, workflow patterns for the detailed plan follow those of the aggregate plan. In Fig. 6, no processor is used at more than 85% of its capacity, as was specified for the aggregate model. However, in Fig. 7, many processors of type [C] are now used at 100%, since this is allowed in the detailed plan. Table 2 Traveling costs for detailed and aggregate plans Scenario
Cost
Difference
Aggregate plan with 100% availability of work centers Aggregate plan with reduced availability of work centers Detailed plan on nodes identified by aggregate plan
$5039.04 $5617.05 $5467.28
– 11.5% 8.5%
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Fig. 6. Workflow patterns for the aggregate plan with reduced work center availability.
Patterns for product families A and F are summarized in the following figures. These figures are presented in order to explain the use of VMNs as input to the detailed planning model. Fig. 8 shows sections of flow patterns produced by the aggregate planning model for family A, and Fig. 9 shows sections of flow patterns produced by the detailed planning model on nodes identified by the aggregate
Fig. 7. Workflow patterns for the detailed plan on nodes identified by the aggregate plan.
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Fig. 8. Workflow patterns for aggregate plan for product family A.
plan for product A (family A only contains one product). Demand for product A is [1512]. In the aggregate plan, all final products are assembled at processor C2 and the general gauges required for final assembly are all assembled at processor G1. Coil production is split between two processors of type B, i.e. [644] at B1 and [2380] at B2. Then, the VMN for family A retains only those processors identified in the aggregate plan and discards the others. This VMN is shown in Fig. 8. The detailed planning model may only process product A through processors included in its VMN. Fig. 9 demonstrates that this condition is respected. Moreover, in the detailed plan, coils required for product A are now all made by processor B2 and none are made by B1. As shown in Fig. 6, B2 was used at its maximum allowed capacity of 85% of that in the aggregate plan; the remaining components had to be processed at B1, even though it was more expensive to move the components from B1 to G1 than
Fig. 9. Workflow patterns for detailed plan for product A.
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Fig. 10. Workflow patterns for aggregate plan for product family F.
from B2 to G1. In the detailed plan, B2 may now be used up to 100%, and it has enough capacity to totally hoard B1’s production. Hence, in order to minimize travel costs, all components assigned to B1 in the aggregate plan were assigned to B2 in the detailed plan. In the same way, Fig. 10 shows sections of flow patterns produced by the aggregate planning model for family F. This family includes three products [F1, F2, F3] for which demand is [2712, 904, 1808], respectively. Figs. 11– 13 show sections of flow patterns produced by the detailed planning model on nodes identified by the aggregate plan for disaggregated products F1, F2 and F3. Again, Figs. 10 – 13 demonstrate that workflow patterns for the detailed plan for products F1, F2 and F3 follow those of the aggregate plan for family F and that the least expensive sections between routing levels are well patronized until work centers on these sections are occupied to full capacity. Flow patterns for the detailed plan are still less spread out than for the aggregate plan because processors located on the least expensive sections are more occupied.
Fig. 11. Workflow patterns for detailed plan for product F1.
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Fig. 12. Workflow patterns for detailed plan for product F2.
When solving the aggregate plan, the optimization model has to consider all processor nodes and all sections between processors. For each family, that represents 6 alternatives for type [B] processors, 5 alternatives for type [G] processors, 80 alternatives for type [C] processors, 30 alternatives for workflow between levels [B] and [G] and 50 alternatives for workflow between levels [G] and [C]. After solving the plan, if we consider family A, the aggregate plan uses 2 processors [B], 1 processor [G] and 1 processor [C] from among the sets. In the same way, if we consider family F, which includes three products, the aggregate plan uses 4 processors [B], 4 processors [G] and 5 processors [C] from among the sets. Remember that, in this initial production plan, data is accumulated in daily time buckets. These results are then used as input to the detailed model. Actually, for product A, the detailed model has to consider 2 variables instead of 6 for processors [B], 1 variable instead of 5 for processors [G], 2 variables instead of 10 for processors [C] and 3 variables instead of 80 for sections to use between those levels. Similarly for products F1, F2 and F3, the detailed model has to consider 4 variables instead
Fig. 13. Workflow patterns for detailed plan for product F3.
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of 6 for processors [B], 4 variables instead of 5 for processors [G], 5 variables instead of 10 for processors [C] and 36 variables instead of 80 for sections to use between those levels. Therefore, this approach significantly reduces the number of variables at the time of solution. In the detailed planning of manufacturing networks, such a reduction of problem complexity is essential, considering that data is accumulated in hourly time buckets instead of daily buckets. These models have been solved using the ILOG OPL Studio v.3.0 package. The detailed model representing the numerical example studied here has been formulated as an optimization problem consisting of nearly 40,000 variables and more than 17,000 constraints. This problem was solved on an IBM Pentium IV within less than half a minute.
6. Conclusion This paper introduced a new way to manage flexible manufacturing networks within a supply chain. The complexity of this large-scale scheduling problem has been reduced using a two-stage HPP approach which combines aggregate and detailed mathematical models used for planning and scheduling operations while minimizing travel and production costs. This study indicates that it is possible to generate a detailed plan based on previous aggregate planning results. The proposed approach generates good and feasible solutions to practical problems. The approach that has been presented could help suppliers of a supply chain to manage their flexible networks by simplifying the production planning phase. The aggregate model will allow them to rapidly evaluate their production capacity and identify which processor nodes should be utilized. The detailed model provides a precise plan for better control of operations. Using the aggregate plan information as input for the detailed model considerably reduces problem formulation effort. In this way, the precision level of the detailed model can be increased without making the problem too complex, and it becomes possible to solve realistic size problems within a reasonable computational time.
References Anderson, C. R., & Paine, F. T. (1975). Managerial perceptions and strategic behavior. Academy of Management Journal, 18, 811– 823. D’Amours, S., Montreuil, B., Lefranc¸ois, P., & Soumis, F. (1999). Networked manufacturing: The impact of information sharing. International Journal of Production Economics, 58, 63 – 79. D’Amours, S., Montreuil, B., & Moke, J. (1999). Contract-based tactical planning of a supply chain, July. Glasgow: FUCAM. D’Amours, S., Montreuil, B., & Soumis, F. (1996). Price-based planning and scheduling of multi-product orders in symbiotic manufacturing networks. European Journal of Operational Research, 96, 148– 166. Goldman, S. L., Nagel, R. N., & Preiss, K. (1995). Agile competitors and virtual organizations. New York: Van Nostrand Reinhold/Division of International Thomson Publishing. Hax, A. C., & Meal, H. C. (1975). Hierarchical integration of production planning and scheduling. Studies in Management Science, 1, 53 – 69. Hurtubise, S (2001). Contribution au de´veloppement d’outils de planification de production dans un contexte de syste`mes manufacturiers agiles pour la conception de chaıˆnes d’approvisionnement, Master’s thesis, De´partement de Ge´nie de la production automatise´e, E´cole de technologie supe´rieure, Universite´ du Que´bec, Montre´al, Que´bec. Hurtubise, S., Olivier, C., & Gharbi, A. (2000). Conceptual framework for management of manufacturing networks (2000). POM 2000 world conference on production and operations management, Seville, Spain.
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Jagdev, H. S., & Browne, J. (1998). The extended enterprise—A context for manufacturing. Production Planning and Control, 9(3), 216– 229. McKay, K. N., Safayeni, F. R., & Buzacott, J. A. (1995). A review of hierarchical production planning and its applicability for modern manufacturing. Production Planning and Control, 6(5), 384– 394. Miles, R. E., & Snow, C. C. (1978). Organizational strategy, structure and process. New York: McGraw-Hill. Miles, R. E., Snow, C. C., & Charles, C. (1992). Causes of failure in network organizations. California Management Review, 34(4), 53 – 70. Miltenburg, J. (2001). Production planning problem where products have alternative routings and bills-of-material. International Journal of Production Research, 39(8), 1755– 1775. Montreuil, B., Lefranc¸ois, P., Ramudhin, A., & D’Amours, S. (1992). A conceptual introduction to symbiotic manufacturing networks. Proceedings of CEMIT 92/CECOIA 3 conference, 505– 508. Nahmias, S. (2001). Production and operations analysis (4th ed.). New York: McGraw-Hill/Irwin. Olivier, C (1998). Me´thodologie d’e´valuation des ame´nagements d’usines organise´es en re´seaux de processeurs agiles, unpublished PhD thesis, Faculte´ des sciences de l’administration, Universite´ Laval, Ste-Foy, Que´bec. Olivier, C., Montreuil, B., & Lefranc¸ois, P. (1996). A conceptual framework for planning and control of virtual manufacturing networks in agile production context. Proceedings of Rensselaer’s fifth international conference, Grenoble, France, pp. 154– 159. Olivier, C., Montreuil, B., Lefranc¸ois, P., & Maley, J. G. (1994). Evaluating layouts for mass customizing factories. Proceedings of 10th ISPE/IFAC international conference on CAD/CAM, robotics and factories of the future, Ottawa, Ontario, Canada, pp. 862– 869. Ramudhin, A., Montreuil, B., & Lefranc¸ois, P. (1994). Scheduling project activities in a distributed environment. European Journal of Operational Research, 78(2), 242– 251. Snow, C. C., Miles, R. E., & Coleman, H. J. (1992). Managing 21st century network organizations. Organizational Dynamics, 20(3), 5 – 19.
Planning tools for managing the supply chain Ste´phanie Hurtubise*, Claude Olivier, Ali Gharbi Design and Control of Production System Laboratory, Automated Production Engineering Department, E´cole de technologie supe´rieure, Universite´ du Que´bec, Montre´al, Que., Canada H3C 1K3 Available online 26 June 2004
Abstract In this paper, we introduce a new way to manage the supply chain. The proposed solution reduces the problem’s complexity using a two-stage hierarchical production planning method and is applicable to realistic transportation optimization problems. The approach is based on planning and operations scheduling models, and is designed to minimize travel and production costs within a flexible organizational network. In the aggregate planning phase, a mathematical model involving an aggregation of products, demand and time periods is solved. It is at this initial stage that the size of the problem is reduced and its output is used as input to the detailed phase in order to improve resolution time. The second stage produces a detailed schedule. It is shown that the proposed approach generates good and feasible solutions to practical problems within a reasonable computational time. q 2004 Elsevier Ltd. All rights reserved. Keywords: Flexible manufacturing networks; Networked manufacturing; Supply chain management; Hierarchical production planning; Scheduling of manufacturing systems
1. Introduction Today’s manufacturing enterprises face enormous competitive pressures stemming from the current dynamic and open business contexts. Global competition and market demand for customized products, delivered ‘just in time’, exert real stress on manufacturers. Recently, new production paradigms, such as the extended enterprise, as well as agile, virtual and networked manufacturing, have appeared in response to the increasingly dynamic conditions of the marketplace (Goldman, Nagel, & Preiss, 1995; Jagdev & Browne, 1998). These new concepts prompt geographically dispersed manufacturers to build alliances with their suppliers and customers in order to work more closely with them. They need to work to build manufacturing networks which bridge large sections of the supply chain. * Corresponding author. Tel.: þ1-514-396-8806; fax: þ1-514-396-8595. E-mail addresses: [email protected] (S. Hurtubise), [email protected] (C. Olivier), [email protected] (A. Gharbi). 0360-8352/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.cie.2004.05.018
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Planning the supply chain is a very complex task. Supply chain managers are responsible for, among other things, the planning activities relevant to products, manufacturing processes, technology selection, material flows and control systems. They have to enter into agreements with many players and they orchestrate their operations through exploitation of the capabilities offered by other manufacturers and by their suppliers. Their services and logistics departments are responsible for coordination of production, transportation and storage activities (D’Amours, Montreuil, Lefranc¸ois, & Soumis, 1999). Managers initially have to choose suppliers from among a large number of intervening parties—or processors—and these are flexible, which is what makes the decision complex. Managers have to schedule jobs on these processors in order to make the network operational and to minimize operating costs, while dealing with a multi-enterprise, multi-product and multi-machine environment, as well as demands which fluctuate over time. This gives rise to a large-scale scheduling problem of the job shop type which is really difficult to solve. Efficient supply chain management requires solution of complex and difficult planning problems. Because of their combinational nature, these large-scale system planning problems are usually too large to solve using standard mathematical programming approaches, but can be handled using hierarchical production planning (HPP) (Hax & Meal, 1975), where the production planning problem is organized into a hierarchy of subproblems. HPP is widely used in the production planning literature (Miltenburg, 2001). Subproblems are solved sequentially starting at the top of the hierarchy with the solution of one subproblem imposing constraints on the following one. The aim of this paper is to introduce a new way to manage flexible manufacturing networks in a supply chain. Because this large-scale scheduling problem is too difficult to solve using standard approaches, our first task is to reduce the problem’s complexity. The proposed method for doing so uses a two-stage HPP approach which combines aggregate and detailed mathematical models for planning and scheduling operations, while at the same time minimizing travel and production costs within a flexible network organization. At the end of the 1980s, pioneers like Anderson and Paine (1975), Miles and Snow (1978), Miles, Snow and Charles (1992), Snow, Miles, and Coleman (1992), and many others, started working on the network organization, defining concepts and systemic approaches. More recently, with the arrival of e-commerce, supply chains and manufacturing networks have become a prolific research area. The Network Organization Technology Research Center1 and Production System Design and Control Laboratory2 had developed approaches and tools to address various aspects of this question. Montreuil, Lefranc¸ois, Ramudhin, and D’Amours (1992), for example, introduced the concept of symbiotic manufacturing networks. Then, Ramudhin, Montreuil, and Lefranc¸ois (1994) studied the problem of distributing a set of activities, with precedence constraints in the form of an assembly tree, among a set of competing firms with the objective of minimizing total cost. As well, Olivier (1998), and Olivier, Montreuil, Lefranc¸ois, and Maley (1996, 1994) proposed an approach for evaluating, from cost and flow perspectives, alternative layouts for manufacturing systems organized within an agile network. They also introduced concepts for planning and control of virtual manufacturing networks (VMNs). Hurtubise (2001) contributed to the development of production planning tools for supply chain planning in the context of an agile manufacturing system. D’Amours, Montreuil, Soumis, and Moke (1999, 1996) presented a network model to optimize design and operation decisions for the make-to-order case, 1 2
Affiliated with Universite´ Laval, Que´bec (Que´bec), Canada. Affiliated with E´cole de technologie supe´rieure, Universite´ du Que´bec, Montre´al (Que´bec), Canada.
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minimizing a cost-time trade-off under standard manufacturing constraints. Optimization models have also been developed to address the planning process of the supply chain. An efficient way to manage the planning of a supply chain is through a network approach. Because they are part of the extensive process of supply chain design and management, aggregate planning at the bidding level and then detailed planning for actual production can be efficiently modeled with networks. We have already introduced a conceptual framework for the management of manufacturing networks (Hurtubise, Olivier, & Gharbi, 2000), which integrates various tools in order to quantitatively evaluate networked manufacturing and to efficiently manage it. The framework is used to determine which firms will make up a particular manufacturing network, as well as to control their activities. In order to reduce the complexity of the supply chain planning problem, this paper proposes a solution which uses a two-stage HPP method. The approach combines the aggregate and detailed planning models introduced in our conceptual framework. In the aggregate planning phase, a mathematical model involving an aggregation of products, demand and time periods are solved. In the detailed planning phase, the output of the first-level model imposes constraints on a second model which produces a detailed schedule. Linear programming models are used by suppliers of a supply chain for evaluating their production capacity and for assigning a precise time-phase workload to shop-floor machines. The conceptual framework is summarized in Section 2. Next, the aggregate and detailed models are explained in Section 3. Then, data flow exchange between models is illustrated in Section 4 using a numerical example. Finally, the resulting production plans are compared and analyzed in Section 5.
2. Framework for the management of manufacturing networks Network design is an iterative process which begins with a networking firm wishing to carry out a production program through the exploitation of a network: its supply chain. The process of the framework for network management requires four steps. The first step is the identification, by the networking firm, of potential suppliers capable of executing different tasks for each program activity. After identifying these potential suppliers, the firm invites them to bid on specific aspects of the chain. In order to respond to the offer, bidding firms must prepare an aggregate production plan to evaluate their production capacity within a given time fence. Different approaches can be used. The model developed by Olivier et al. (1994) is one of several. This approach considers individual pieces of equipment—or processors—as nodes in a network, making it possible to find the appropriate subset of processors from a whole set that will meet the job’s requirements. If the bidding firm has enough capacity, the model will yield the production delay required and identify which processor nodes should be utilized. The model for the generation of an aggregate production plan is presented in Section 5. Once the bids have been collected, the networking firm plans its supply chain and manages it dynamically according to demand variation over time. This second step can be achieved with the D’Amours et al. (1996) approach, by which the network suppliers, subcontractors, business units and transporters are identified who should be chosen in order to make the network operational and to minimize operating costs. The bidding firms are then informed as to whether or not their tender has been successful. The third step is the generation of a detailed production plan by all firms whose offers have been accepted. This can be done based on the best potential equipment identified during the aggregate production planning phase. A precise time-phase workload is then assigned only to processor nodes
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identified in the aggregate plan. The latest model developed by Olivier (1998) is used to generate detailed production plans. The functionality of a model developed for this task and integrated with the model for aggregate production is presented in Section 3. Finally, the fourth and last step is the control loop. The networking firm carries out an operations control task by comparing its production plan with the suppliers’ production reports and making the necessary corrections to ensure on-time delivery of the final product. In such manufacturing networks, the nodes can be internal to a given organization as well as external businesses from around the world (D’Amours et al., 1996). The generic term ‘supplier’ may thus apply to internal work cells, departments, factories and divisions, as well as to external businesses.
3. Methodology The proposed approach is aimed at managing the supply chain. First, the best suppliers, or processors—those that will make the network operational, have to be chosen. Second, jobs have to be scheduled on these processors in such a way that operating costs within a realistic production plan are minimized. This generates a very complex production planning problem which is really very difficult to solve. In order to arrive at a feasible detailed schedule, therefore, the complexity of the problem must first be reduced using aggregate planning. The approach proposed here is presented using the example of a flexible manufacturing system (FMS) associated with one supplier in a supply chain. The difficulty in planning for a large-scale FMS is addressed using the HPP paradigm. The essential philosophy of HPP is to make use of the time line to control the amount of detail and of aggregation with the higher levels of aggregation focusing on the longer time horizon while providing guidance to lower levels which are concerned with shorter time intervals (McKay, Safayeni, & Buzacott, 1995). This approach is based on the aggregate and detailed planning models developed in the conceptual framework. Common mathematical models developed to generate aggregate production plans can handle a large quantity of variables, often more than 20,000, and can be solved very quickly. An aggregate plan is optimal, but, in such a plan, data is usually accumulated in daily periods, i.e. manufacturing systems have daily time ‘buckets’, which is what makes the plan difficult to execute because there is no indication as to how the work will be scheduled. Moreover, the temporal sequence of production tasks is not embedded in aggregate planning models; only daily capacity is supported. Fig. 1a shows a Gantt chart showing an aggregate schedule. In the context of scheduling operations in a network, time buckets should be much shorter so as to result in an accurate plan. Unlike an aggregate plan, a detailed plan incorporates the temporal sequence of production tasks and does give indications about how the work will be scheduled. Fig. 1b shows a Gantt chart showing a detailed schedule. In this paper, a detailed planning model able to schedule production in hourly periods is used, and yields feasible schedules which may be used to simplify execution and control of real operations. But, since a problem’s size rapidly increases when precision level is increased, the problem’s complexity has to be considerably reduced in order to generate a precise plan within a reasonable resolution time. To do so, an approximation is carried out: for each product, the detailed planning model will consider only the variables and constraints that concern work centers identified by the aggregate plan and sections between these work centers. All other nodes will be withdrawn from the initial solution. This approach reduces the number of possibilities to evaluate.
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Fig. 1. Differences between an aggregate and a detailed schedule.
The solution will not be optimal, but the fundamental objective here is not to achieve optimality, but to rapidly identify a good, feasible solution. In this way, the detailed model may resolve problems of realistic size within a reasonable time. At the first hierarchical planning level, therefore, the production model developed by Olivier et al. (1994) is used to generate the aggregate plan for evaluating the supplier’s capacity. The detailed planning model developed by Olivier (1998) is then used at the second hierarchical planning level in order to assign a precise time-phase workload to shop-floor machines, based on the best potential nodes specified at the first level by the aggregate plan. 3.1. Aggregate planning At the first stage of the bidding process, a supplier must prepare an aggregate production plan to evaluate its production capacity. This includes selection of the equipment that will be assigned to that job, routing of parts in the production system, estimation of the capacity and manpower required, and, obviously, estimation of the cost involved in the whole operation. Introduced by Olivier et al. (1994),
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VMNs integrate most of this information. For instance, when individual pieces of equipment, or processors, are considers as nodes in a network, it is possible, using the model, to find the right subset of processors from a whole set that will fulfil the job’s requirements. Hence, a supplier first applies the aggregate planning model (Olivier et al., 1994) to evaluate its capacity to respond to an offer. Then, a general LP model involving an aggregation of products, demand and time periods is solved (see e.g. Nahmias, 2001). The global approach of this process is based on a multi-commodity, multi-flow linear optimization model. The objective is to minimize multi-product manufacturing costs and the total interworkstation handling costs subject to constraints on capacity, while meeting total demand for products. Fig. 2 presents a diagram showing the data flow through the aggregate planning model. The input parameters required are the supplier’s production and capacity parameters and the potential processor nodes. The supplier’s production and capacity parameters contain demand requirements from clients, operating costs, capacity requirements and availability, bills of operations (routings), etc. The information generated by the aggregate model makes up the aggregate production plan, which does not take into account temporal aspect and operations sequencing. The aggregate plan includes workflow patterns, workload distribution among processor nodes and the planned utilization of those nodes. A workload pattern can be defined as the pattern of tasks planned to be accomplished by each processor in a given time slot. In aggregate planning, there is only one time slot—or time bucket. This pattern includes the specific groups of products to be processed on each processor in this time period. The workflow pattern expresses the planned routings of items between processors. If the supplier who wants to bid has enough capacity to respond to one or more offers, the model identifies which processor nodes should be utilized at the time of production plan processing. Based on these initial results, a supplier sends its bids to the networking firm. Bids contain available capacity and quotations for specific time periods.
Fig. 2. Data flow diagram for the aggregate planning process.
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3.2. Detailed planning A supplier uses the detailed planning model (Olivier, 1998) for generating its detailed production plan. Like the aggregate planning process, it is based on a linear optimization model which minimizes production, material handling and storage costs subject to constraints on capacity, while meeting total demand. However, this model takes into account temporal aspects and operations sequencing, and generates detailed production patterns. Time bucket length depends on the desired level of accuracy. Given the considerable number and diversity of potential processors, it would not be easy, or even realistic, to generate a detailed production plan using all the flexibility available in a manufacturing facility. For this reason, the complexity of the problem needs to be reduced. Hence, this approach uses the aggregate production plan as an input to the detailed planning model. In the first step of hierarchical planning, the best potential processors are chosen for each family of products, through the aggregate model. A family includes products with the same routing. The output of the first level, i.e. workload and workflow patterns, are used to determine one VMN for each family of products. For each family, the right subset of processors that will fulfil the job’s requirements while minimizing travel and production costs is identified. At the detailed planning phase, those VMNs impose constraints on the planning model of the second step of hierarchical planning, which will produce a detailed schedule. In this second stage, the detailed model assigns a precise time-phase workload only to processor nodes which were identified at the first stage of the process. Using the aggregate plan as input to the detailed model, only a part of the information is retained, making it possible to take into account the temporal aspects with many fewer constraints, while maintaining a good range of flexibility. Even if this approach does not generate the optimal solution, it will produce a very good, feasible, detailed production plan, and this plan will be generated within a reasonable time. Fig. 3 presents a diagram showing the data flow through the detailed planning model. The data flow is similar to that of the aggregate planning model, the difference mainly being the size of the time buckets, long on aggregate planning but much shorter on detailed planning, and work scheduling specifications which are not available with aggregate scheduling, but specified in a detailed plan. In addition to the supplier’s production and capacity parameters, input parameters now include the potential processor nodes (VMNs) that may process each family of products. Those VMNs were identified at the first stage, as previously mentioned. The detailed planning model is used individually by each supplier to generate its detailed production plan. The information generated by this model makes up the detailed production plan. In addition to workflow and workload patterns, the plan also includes buffer levels. In detailed planning, buffers are currently required to balance flow between processors. Based on these results, suppliers may forward delivery schedules, operations reports and job status to the networking firm. Fig. 4 shows the supply chain management process and highlights the approaches that are used here.
4. Numerical example The use of the aggregate and detailed models, as well as the data flow exchange between them, is demonstrated here. The case used as an example concerns a firm which makes and assembles dashboards
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Fig. 3. Data flow diagram for the detailed planning process.
for the automotive industry. The manufacturing system is composed of agile processors in a flexible network. The product line has been aggregated to six dashboard families. In the same way, routing has been aggregated to four levels. Dashboards are made up of three to four indicators, which are speedometers, revolution counters and general gauges for fuel and temperature level. Some components may come from external suppliers and are then not processed by the current manufacturing system. Fig. 5 shows product routing and network layout, while Table 1 presents the data corresponding to the numerical example, i.e. product composition, processing time, processor capacity and demand. Workstations in the last level of the routing are for final assembly. They are named type [C] processors. The third level is made up of assembly processors for speedometers [S], revolution counters [T] and general gauges [G]. A two-component assembly processor makes speedometers and revolution counters. These components are named [AS] and [BS] for [S] indicators as well as [AT] and [BT] for [T] indicators, and are made at the second level of the routing. The first level is made up of processors for coil fabrication [B] which is required for the assembly of the [BS], [BT] and [G] components. Machines process components one at a time. When a component is processed, it is directly transferred to a buffer next to the machine. There is one buffer for each processor. Components wait in the buffer until they are required at the subsequent processor. Costs represent real traveling expenses and these include labor and equipment expenditures. In order to limit quantity of data, traveling costs are not listed here. However, these costs are proportional to the distance between processors; e.g. it costs 0.025$ to move one component from processor G1’s buffer to processor C2, and it costs 0.2125$ to move one component from processor G1’s buffer to processor C10. Since buffers are just next to their processors, there is no cost associated with moving a component from a processor to its buffer.
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Fig. 4. Supply chain management process.
The aggregate planning model is used first, to identify which processor nodes should be utilized at the time of production plan processing. In aggregate planning, data is usually gathered in daily or weekly periods. As can be seen in the aggregate schedule shown in Fig. 1a, the model identifies how many products are processed by each processor for that one time period. Hence, an aggregate plan does not consider delays produced by transfer of products from one routing level to another. It is thus important to limit work center utilization in the aggregate plan so as to keep a safety margin of time in order to accommodate delays and keep the detailed plan feasible. The detailed planning model is then executed, based on the best potential nodes specified in the aggregate plan. In this example, planning models are used arrive at a daily production plan in which a precise timephase workload to shop-floor machines is assigned, while traveling costs are minimized and total demand for all products, considering the limited capacity of processors, is respected. The aggregate model uses a daily time bucket, and work center utilization is reduced by 15% to keep a safety margin of time, as explained above. The detailed model uses hourly time buckets and then generates the 24 production plans required for an entire production day, i.e. one plan for every hour. The latter model automatically considers delays generated by product transfers due to routing. Actually, products made at the first routing level during the first hour (the first time bucket) may not be in transit
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Fig. 5. Product routing and network layout.
before the second hour and may be assembled at the second level work centers only from the third hour, thereby introducing delays into the schedule. Let us look again at Fig. 1. Knowing that the aggregate model planned for 2290 component Bs from family F to move to processor B6, we can determine that this represents 19.1% of this work center’s capacity, as demonstrated by the second bar in Fig. 1a. As it has been stated before, an aggregate plan does not give any indication about work scheduling because the temporal sequence of production tasks is Table 1 Data for numerical example Component, sub-assembly or product
Composition
Component B Component AS Component AT
– – –
Sub-assembly Sub-assembly Sub-assembly Sub-assembly Sub-assembly
1 1 2 1 1 2 1 2 1 1 2
Product Product Product Product Product Product
BS BT G S T
family family family family family family
A B C D E F
Each processor’s capacity
Demand
7.2 5.6 6.3
24 h ¼ 86,400 s 24 h ¼ 86,400 s 24 h ¼ 86,400 s
– – –
B B B AS; 1 BS AT; 1 BT
2.85 2.14 11.76 23.5 25.2
24 h ¼ 86,400 s 24 h ¼ 86,400 s 24 h ¼ 86,400 s 24 h ¼ 86,400 s 24 h ¼ 86,400 s
– – – – –
G; 1 G; 1 G; 1 G; 0 G; 1 G; 0
26.1 26.1 26.1 26.1 26.1 26.1
16 h ¼ 56,600 s 16 h ¼ 56,600 s 16 h ¼ 56,600 s 16 h ¼ 56,600 s 16 h ¼ 56,600 s 16 h ¼ 56,600 s
1512 3349 5625 713 532 5424
T; 0 S T; 0 S T; 1 S T; 1 S T; 1 S T; 1 S
Processing time (s)
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not embedded in aggregate planning. However, a detailed plan does incorporate the temporal sequence. Fig. 1b gives an example of how work is scheduled on work centers by a detailed plan. All the empty spaces correspond to delays introduced into the schedule by routing and product transfers. Hence, the 15% margin of time kept in the aggregate plan makes it possible to take account these delays in the detailed plan. As a result, work center availability does not have to be reduced in a detailed planning model, and it is set to 100%.
5. Results Traveling costs for both production plans are presented in Table 2. Results show that the cost of the aggregate plan, where work center utilization is reduced to 85% is 11.5% higher than the cost of the optimal aggregate plan. Since work center utilization has been reduced to keep a margin of time, some workload has to be assigned by the aggregate model to processors located on more expensive sections when work centers on the most economic sections are saturated, resulting in a more expensive plan. Table 2 results also show that the cost of the detailed plan is 8.5% higher than that of the optimal aggregate plan. The detailed plan costs less than the aggregate plan with reduced availability because its work center availability is not reduced. In the detailed plan, work centers on the most economic sections may be used up to 100%, while they may only be used up to 85% in the previous aggregate plan. Workflow patterns for whole families of products are summarized in Figs. 6 and 7. Fig. 6 shows a section of flow patterns produced by the aggregate planning model. Each flow includes flows for all six families of products. In order to simplify representation, only flows between workstations of type [B] and [G] and between workstations [G] and [C] are shown, because the complexity of the flows and their spreading patterns are the same for the other levels. Workflow patterns between G1 and C2 for each product processed by these work centers are exploded in the lower right corner of Fig. 6. Fig. 7 shows a section of flow patterns produced by the detailed planning model on nodes identified by the aggregate plan. In Fig. 7, each flow includes the flows for all the 24-hourly production plans. The flow patterns shown in Figs. 6 and 7 demonstrate that the least expensive sections between routing levels are well patronized until work centers on these sections are occupied to full capacity. Flow patterns for the aggregate plan are a little more spread out than for the detailed plan, and the least expensive sections are less occupied. That is because work center utilization has been reduced in aggregate planning to keep a margin of time, as explained above. As desired, workflow patterns for the detailed plan follow those of the aggregate plan. In Fig. 6, no processor is used at more than 85% of its capacity, as was specified for the aggregate model. However, in Fig. 7, many processors of type [C] are now used at 100%, since this is allowed in the detailed plan. Table 2 Traveling costs for detailed and aggregate plans Scenario
Cost
Difference
Aggregate plan with 100% availability of work centers Aggregate plan with reduced availability of work centers Detailed plan on nodes identified by aggregate plan
$5039.04 $5617.05 $5467.28
– 11.5% 8.5%
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Fig. 6. Workflow patterns for the aggregate plan with reduced work center availability.
Patterns for product families A and F are summarized in the following figures. These figures are presented in order to explain the use of VMNs as input to the detailed planning model. Fig. 8 shows sections of flow patterns produced by the aggregate planning model for family A, and Fig. 9 shows sections of flow patterns produced by the detailed planning model on nodes identified by the aggregate
Fig. 7. Workflow patterns for the detailed plan on nodes identified by the aggregate plan.
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Fig. 8. Workflow patterns for aggregate plan for product family A.
plan for product A (family A only contains one product). Demand for product A is [1512]. In the aggregate plan, all final products are assembled at processor C2 and the general gauges required for final assembly are all assembled at processor G1. Coil production is split between two processors of type B, i.e. [644] at B1 and [2380] at B2. Then, the VMN for family A retains only those processors identified in the aggregate plan and discards the others. This VMN is shown in Fig. 8. The detailed planning model may only process product A through processors included in its VMN. Fig. 9 demonstrates that this condition is respected. Moreover, in the detailed plan, coils required for product A are now all made by processor B2 and none are made by B1. As shown in Fig. 6, B2 was used at its maximum allowed capacity of 85% of that in the aggregate plan; the remaining components had to be processed at B1, even though it was more expensive to move the components from B1 to G1 than
Fig. 9. Workflow patterns for detailed plan for product A.
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Fig. 10. Workflow patterns for aggregate plan for product family F.
from B2 to G1. In the detailed plan, B2 may now be used up to 100%, and it has enough capacity to totally hoard B1’s production. Hence, in order to minimize travel costs, all components assigned to B1 in the aggregate plan were assigned to B2 in the detailed plan. In the same way, Fig. 10 shows sections of flow patterns produced by the aggregate planning model for family F. This family includes three products [F1, F2, F3] for which demand is [2712, 904, 1808], respectively. Figs. 11– 13 show sections of flow patterns produced by the detailed planning model on nodes identified by the aggregate plan for disaggregated products F1, F2 and F3. Again, Figs. 10 – 13 demonstrate that workflow patterns for the detailed plan for products F1, F2 and F3 follow those of the aggregate plan for family F and that the least expensive sections between routing levels are well patronized until work centers on these sections are occupied to full capacity. Flow patterns for the detailed plan are still less spread out than for the aggregate plan because processors located on the least expensive sections are more occupied.
Fig. 11. Workflow patterns for detailed plan for product F1.
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Fig. 12. Workflow patterns for detailed plan for product F2.
When solving the aggregate plan, the optimization model has to consider all processor nodes and all sections between processors. For each family, that represents 6 alternatives for type [B] processors, 5 alternatives for type [G] processors, 80 alternatives for type [C] processors, 30 alternatives for workflow between levels [B] and [G] and 50 alternatives for workflow between levels [G] and [C]. After solving the plan, if we consider family A, the aggregate plan uses 2 processors [B], 1 processor [G] and 1 processor [C] from among the sets. In the same way, if we consider family F, which includes three products, the aggregate plan uses 4 processors [B], 4 processors [G] and 5 processors [C] from among the sets. Remember that, in this initial production plan, data is accumulated in daily time buckets. These results are then used as input to the detailed model. Actually, for product A, the detailed model has to consider 2 variables instead of 6 for processors [B], 1 variable instead of 5 for processors [G], 2 variables instead of 10 for processors [C] and 3 variables instead of 80 for sections to use between those levels. Similarly for products F1, F2 and F3, the detailed model has to consider 4 variables instead
Fig. 13. Workflow patterns for detailed plan for product F3.
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of 6 for processors [B], 4 variables instead of 5 for processors [G], 5 variables instead of 10 for processors [C] and 36 variables instead of 80 for sections to use between those levels. Therefore, this approach significantly reduces the number of variables at the time of solution. In the detailed planning of manufacturing networks, such a reduction of problem complexity is essential, considering that data is accumulated in hourly time buckets instead of daily buckets. These models have been solved using the ILOG OPL Studio v.3.0 package. The detailed model representing the numerical example studied here has been formulated as an optimization problem consisting of nearly 40,000 variables and more than 17,000 constraints. This problem was solved on an IBM Pentium IV within less than half a minute.
6. Conclusion This paper introduced a new way to manage flexible manufacturing networks within a supply chain. The complexity of this large-scale scheduling problem has been reduced using a two-stage HPP approach which combines aggregate and detailed mathematical models used for planning and scheduling operations while minimizing travel and production costs. This study indicates that it is possible to generate a detailed plan based on previous aggregate planning results. The proposed approach generates good and feasible solutions to practical problems. The approach that has been presented could help suppliers of a supply chain to manage their flexible networks by simplifying the production planning phase. The aggregate model will allow them to rapidly evaluate their production capacity and identify which processor nodes should be utilized. The detailed model provides a precise plan for better control of operations. Using the aggregate plan information as input for the detailed model considerably reduces problem formulation effort. In this way, the precision level of the detailed model can be increased without making the problem too complex, and it becomes possible to solve realistic size problems within a reasonable computational time.
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