Amelioration of Capacity Constraints in Manufacturing Systems Using Alternate Production Sequence

Today’s market is in a constant flux of demand changes. Due to this the product demand and the product mix continuously change from one time-period to the next. For a company to be profitable and competitive, it has to ensure that all of its resources are optimally utilized. These resources include facility layout, material handling, and production system. Previous research has shown that the system state has to be identified prior to increasing capacity to mitigate the constraint. As the demand and product mix change, a facility layout that was efficient can soon become inefficient or the cost of production and material handling increase. This research evaluates usage of alternate part sequence as a means to eliminate or reduce production system constraints. It focuses on reducing machine usage when the selected process sequence leads to production capacity constraints.


Introduction
One of the ways to improve the competitiveness of manufacturing systems is to incorporate efficient facility layouts in the organization.A logically designed facility layout will be able to accommodate new products to the system, operate at low cost, by delivering the products at right time and respond to demand variations in the system.Thus facility design plays an important role in an enterprise for the smooth flow of work, material and information flow throughout the system.Material handling cost can contribute 20-50% of the manufacturing cost of a product and designing efficient layouts can reduce 10-30% of these expenses (Tompkins et al., 2010).
Facility layout problems can be classified broadly into Static Facility Layout Problems (SFLP) and Dynamic Facility Layout Problems (DFLP).Static facility layout problem models are used when the product demands are static and do not change from period to period.Optimization approaches that are used to model static facility layout problems are quadratic assignment problem and mixed integer programming.Researchers have used heuristic approaches such as genetic algorithms (GA), simulated annealing and tabu search for solving these problems (Meller andGau, 1996 andAzadivar andWang, 2000).A static facility layout model cannot be used when there are fluctuations in product demand and product mix.When new products are introduced or existing ones removed from the system the material handling requirements and cost changes.Maintaining a dynamic facility layout requires continuous assessment of product demands, the flow between departments, and evaluation of the layout to determine the time at which a redesign should be performed (Benjaffar and Sheikzadeh, 2000).
Dynamic facility layout can be solved by two approaches; the first approach is to develop a robust layout for a multi period scenario.Kochhar & Heragu (1999) proposed a methodology to develop an agile manufacturing layout which satisfies all variability for a production requirement.Kouvelis and Kiran (1999) addressed the primary approach, in which multiple demand scenarios are utilized for determining the optimal robust layout for a particular period under consideration.They proposed a dynamic programming approach which gives an optimal solution for a multi-period scenario.The second approach assumes that the layout will be subjected to changes from time to time.Conway and Venkatramanan, (1994), and Balakrishnan and Cheng, (2000) proposed genetic algorithms for solving the DLP.Optimization approaches over multiple periods have been proposed by Yang and Peters (1998), where both the rearrangement and material handling cost are reduced.Baykasoglu and Gindy (2001) used simulated annealing approach to solve DLP problems.Urban (1993) proposed a descent pair-wise exchange to reduce material handling cost in DFL scenario.This approach was further modified by Balakrishnan, Cheng, and Conway (2000) in which a backward pass pair-wise exchange for each period has been added.Krishnan, Cheraghi, and Nayak (2006) classified approaches to solving dynamic facility layout problems into four major categories: Robust layouts that address multiple production scenarios (uncertainties) for a single period, robust layouts for multiple time periods, redesigned layouts for various time horizons based on changes in production requirements, and multiple layouts for various time horizon that are robust to address multiple production scenarios (uncertainties) for each time period.
For achieving competitive manufacturing performances, parameters such as facility layout, material handling system, process routing & production plan should be considered.In the presence of production and capacity constraints, earlier research has focused on identifying and improving facility layouts and by addition of material handling and production capacity.However, an alternate approach to mitigating production and material handling capacity constraints is to use alternate sequences for production, which will allow for use of non-bottleneck machines more effectively and for easing the usage of bottleneck machines.
Process sequence is the series of operations that are necessary to transform the raw material to its final geometry.For alternate sequences to be considered as an alternative to mitigate production capacities, a facility must have machines that are capable of performing the necessary operations.However, this may incur increased costs.Elleuch, Bacha, Masmoudi and Maalej (2008) proposed grouping of machines temporarily to form virtual cells which leads to the intercellular transfer of parts to a secondary machine during the breakdown of the primary machine.The results obtained showed an improvement in cell availability with the use of intercellular transfer.Jabalameli, Arkat and Sakri (2008) take into account machine reliability and alternative process routes and developed a mathematical model which minimizes the intercellular movement costs and machine breakdown costs in addition to maximization of machine reliability and solved them using heuristics.Ameli, Arkat & Barzinpour, (2008) proposed a bi-objective linear integer programming model which considers alternative process routes and machine reliability for the generalized cell formation problem to minimize total costs along with the total time.The results obtained showed that total movement costs increase while the total costs and total time decrease with machine reliability consideration.Ameli and Arkat (2008) proposed a linear programming model by taking process sequence of parts and production volumes into account for the formation of machine cells.Furthermore, the proposed model has been considered with alternate process routes and machine reliability.The results show that there were increased intercellular movements and reduced overall costs when machine reliability was considered.Diallo, Pierreval and Quilliot (2001) presented an effective methodology for the configuration of cells when the part process plans were changed due to the machine breakdowns.The reconsideration of process plans helps to overcome the disturbances caused due to the machine failures.The results obtained shows that the total number of parts transferred between cells was less in case of the configuration obtained by proposed methodology than the configuration without reliability consideration.Jeon, Leep and Parasaei (1998) proposed a cell configuration procedure which consists of two phases.In phase 1, the possible number of alternative routes during machine failure was found by a new similarity coefficient and part families were formed by the use of p-median model.In phase 2, a mathematical model which takes into account the operational and scheduling aspects when a machine failure occurs was considered and their effects on machine utilization was observed.The main aim of the proposed methodology was to form machine cells by minimizing the penalty cost for early or late finishing, cost of holding inventory, cost of operation and machine investment.Jeon, Broering, Leep, Parsaei & Wong, (1998) extended this approach further by developing a software for the implementation.

Research Objective
The objective of any manufacturing facility is to maximize profit by providing a quality product within the demanded time.The facility has to operate within its capacity constraints, namely, capacity and logistic constraints.Capacity constraints can further be classified into production capacity and material handling capacity constraint.This research focuses on meeting the demands on the manufacturing system and increasing the profitability within the defined constraints by evaluating alternative sequences and alternate facility layouts that can be used to manufacture a part.

Methodology
Earlier research by Dhuttargoan, Krishnan, and Shah (2017) developed methods for identifying the state of a system.This paper explores the use of alternate process sequences to alleviate the impact of logistics and production constraints.The process sequence is a series of operations through which the raw material is transformed to its final shape, fit, and form.For a part, there may be a single unique process sequence or it may have more than one sequence depending on the type and quantities of machines available in the facility.The process sequence provides details regarding the machines and the time required for production of each part on the machine it needs to be processed on.Process sequence thus can be used to determine the required production capacity.The ability of a production facility to meet demand is a function of production capacity, material handling capacity, facility layout, and process sequence.
The failure to meet demand could be due to one or more of the following factors: a) Logistic and production constraints, b) Inefficiency of layout, and c) Process sequence.As product demands change, the manufacturing system may fail to meet demand due to logistic or production capacity constraints.To meet demand, the facility may have to add production or material handling capacities or a combination of both.Production capacity restrictions can be alleviated by adding new machines with higher capacities (faster processing) replacing the existing lower capacity machines.Alternatively, adding machines with similar capacity as the bottle neck machine, could also help in improving production capacity.If the demand cannot be met due to material handling capacity constraints, the facility can add more material handling units.Material handling constraints can also be improved by changing speed of material handling.If a facility is in transition state, then there would be a need to add both production capacity and material handling capacity.
Another possibility for failure to meet demand is inefficiency in facility layout.Under that situation, the facility has an alternative to modify the facility layout.Changing facility layout involves fixed and variable cost.A given layout may work fine for one product mix with given demands in a given time period, but may not work for the next product mix due to demand changes.However, facility design changes can be expensive.
Failure to meet demand can also be due to the process sequence.If demand cannot be met, an alternate process sequence may be used, if capacity is available on the alternate machines.Using an alternate process sequence can thus be considered as another way of eliminating production constrained state.However, when using an alternate process sequence, the cost of processing may increase.An algorithm showing general procedure for the research is shown in the Figure 1.Is UPS > Threshold?
Identification of system state and details of methods associated with it are described by Dhuttargoan, Krishnan, and Shah (2017).Shah, Krishnan, and Dhuttargoan (2015) developed a genetic algorithm approach to generate a new facility layout.However, the method increases capacity by adding machines at required locations.This paper introduces the concept of using alternate sequence as a method to introduce more production capacity in case of a dynamic facility layout problem.The flowchart for the methodology is shown in Figure 2.

Cost Estimation
Cost of meeting demand is a function of the production sequence selection, facility layout changes and addition of production and material handling capacities as necessary based on the process sequence selection.Costs can be classified into production cost, facility layout cost, and material handling cost.Notations n -machine type; n = 1,…, N, i -machine location; i = 1,…, N, j -machine location; j = 1,…, N-1, p -total number of products, ranges from p = A, …, P, s -total number of sequences, ranges from s = 1, …, S, t -time period under consideration pstp -total number of sequences for product p in time period t t nstp -Time product p takes on machine n in sequence p stp during time period t d pt -demand for product p in time period t U nstp -Average utilization of each machine type (n = 1 to N) for p stp for all product P during time period t TV -Threshold value O n -Operating cost of machine type n H mstp -Percentage utilization of each material handling unit (m = 1 to M) for p stp for all products during time period t ℎ              , 0, ℎ g ijtps -Dynamic flow between departments i and j during time period t for p stp D ijtps -Distance between departments i and j during time period t for p stp Q -Cost of utilizing all machines for a time period R stp -Cost of production using sequence combination cx for time period t C -Cost of carrying a part per unit distance Z t -Total cost of production during time period t M tps -Material handling cost during time period t using p stp F t -Fixed cost of transition to current time period V t -Variable cost of transition to current time period D n(t-1,t) -Distance each machine has to be moved going from time period t-1 to t for p stp Y n -Cost per unit distance of the moving machine from one location to another A t -Cost of adding production capacity in time period t n t -total number of machines of type 'n' that are required in time period t a n -cost of each machine of type 'n' b m -cost of adding one unit of material handling unit B t = Cost of adding material handling capacity in time period t m t = number of MHUs that are required to be added in time period t

Production Cost
The optimal sequence is selected using the methodology in Figure 2. Average utilization of each machine associated with the selected sequence for each product can be calculated as: Cost of production is calculated using the utilizations of the machines and the operating cost of each machine.

Material Handling Cost
Material handling cost is a non-value added cost.As the selection of the machines depends on the process sequence selected, the material handling cost depends on the process sequence selected.Material handling cost depends on the distance between machines and hence the facility layout.The dynamic flow between departments i and j is calculated using Equation 3.

Rearrangement Cost
Rearrangement cost consists of two different cost components: a variable cost component and a fixed cost component.Equation ( 5) shows the calculation for Fixed Cost component: The variable cost (Equation 6) is a function of the cost of the production time lost and the distance through which the machines are moved from time period t-1 to t.The cost of downtime is neglected. (

Cost of Adding Production and Material Handling Capacities
If demand cannot be met, it indicates that the system is in production or material handling constrained state or both.If production capacity has to be increased, the cost of adding production capacity (Equation 7) depends on the type of machine that needs to be added.
( 1) * Similarly, if more material handling capacity is needed, the cost of adding material handling capacity can be calculated as shown in Equation 8.

Total Cost
Total cost of production (Equation 9) for a given time period is given by sum of all costs i.e. sum of production cost, cost of material handling, cost associated with facility rearrangement and cost associated with adding more material handling and production capacities.
The plus or minus sign in the fourth and fifth terms represents the cost of increased or reduced production and material handling equipment cost respectively.Equation 10 shows the total production cost over the planning horizon for the 'T' time periods.

Procedures
The following procedures/flow charts are used in implementing the methodology.They are explained using the case studies later.

Procedure for Process Sequence Analysis and Optimal Sequence Selection
This procedure is used to determine the machines and processing time for each part on the machines, along with the system capacity and constraints (Figure 3).

Procedure for Determining Production Capacity Required
The procedure for determining the additional production capacity is shown Figure 4.

Procedure using Simulation for State System Identification
Procedures for using simulation to determine the production and logistic constraints are described in Dhuttargoan, Krishnan, and Shah, (2017).The procedure can be used to add material handling capacity (one unit at a time) to transition to production constraint state.

Procedure for Facility Layout Changes
As shown in previous literatures, facility layout problems are np-hard and it is easier to solve using heuristics.The GA algorithm used for this approach has been developed by Krishnan, Jithavech and Liao (2009).The parameters of the procedure have been modified with slight changes in the objective function and in fitness function.The GA cost function is provided in Equation 10.The cost function attempts to minimize the material handling cost for the projected demand.

Case Study (7-departments, 5-products, 3-time periods)
In this case study the analysis was done using simulation for the given time period.The product demand data, revenue, and possible sequences for each part is shown in Table 1.The operating cost and processing time is shown in Table 2 and Following assumptions were made for the multi-period seven department case study • Rectilinear distance between machines is 50 feet • All material handling units have equal speed (120 ft/minute) and capacity (1 part) • Material handling units have unidirectional paths • Each department has an input and output buffer with infinite capacities • Product demands are deterministic and known before beginning of each time period • Material handling cost during each time period is $0.10/foot • Cost of moving machines 1, 3, 5, 7, 9 is $50/foot and machines 2, 4, 6, 8 is $45/foot • Cost of buying new machine 1, 3, 4, 5, 7, 9 is $10,000; machine 2, 4, 6, 8 is $12,000 • Cost of buying new material handling unit is $50,000 • Fixed cost of rearrangement for each time period is $1,000 For the simulation a warm-up period of two weeks is used.Data is collected for a 4 week time period.To evaluate if the model is in production system dominant zone or material handling system dominant zone, it was necessary that the source makes right mix of products available at the right time.There are 243 possible combinations of sequences (using Equation 12).Using the utilization of each machine, the production cost for each sequence combination can be calculated.The best sequence is selected by optimizing the objective function using MATLAB.

Seven Department Case Study: Time Period 1
Table 4 lists the optimal sequence for the parts in the time period 1.The utilizations of each machine is calculated using Equation 1 is shown in the Table 5.The production cost for time period 1 is $25,062.60.As machine utilization percentages are less than 100 for all machines, the selected optimal sequences are selected to meet demand for this time period 1.Using sequences A2, B1, C3, D2, E2, and with known demand data for time period t= 1, a from-between chart is constructed.The from-between chart is shown in Table 6.The layout for time period t = 1 generated by GA is shown in Figure 5. Based on simulation results obtained (Table 7), it can be seen that the layout obtained using GA can meet demand for the time period.Thus for this time period no additional machines or material handling resources are necessary.The material handling cost associated with these dynamic flow values for time period t = 1 as calculated by Equation 4is $78,200.There is no fixed or variable rearrangement costs incurred in time period t = 1.Thus the total cost of meeting demand in the time period t = 1 calculated using Equation 10 is 103,262.60.

Seven Department Case Study: Time Period 2
For time period 2, the results indicate that of all the possible sequence combinations, the sequence combination found in time period t = 1 is optimal in terms of manufacturing cost.Analysis of machine utilization shows that the utilization of machine 1 for time period 2 is 115% which means that the production capacity is a constraint.To eliminate this constraint, the choices are to add more production capacity at machine 1 or to consider alternate sequencing.Based on the modified flow chart suggested in Figure 2, alternate sequences were evaluated.Table 8 lists the sequences selected for each of the parts during the time period, when machine capacity constraints were considered.The utilizations (U nstp ) for each machine with an initial value of n t = 1 calculated using Equation 1 is shown in Table 9.The production cost R stp for the selected sequences is $39,714.00.The percentage utilization of all machines is less than 100, and the process sequences selected for time period 2. It avoids adding new machines to alleviate possibility of production constraint.A comparison of the sequences for the two time periods is shown in Table 10.The only process sequence that is changed is for part B. Selecting this alternate process sequence reduced utilization of machine 1 to 77% from 115%.If the same process sequences as in time period t = 1 are used, the production cost would be $38,862.00,but the cost of adding an additional machine would have been $100,000.While using alternative sequence for B the production cost is $39.714.00 which is 2% higher than using sequence combination as in time period 1.To validate this further, the simulation results (Table 11) with data for both time periods has shown that demand can be met.

Sequence id Sequence
As demand is met using layout as in time period t =1 and sequence combination as in time period t = 2, there is no need to evaluate if layout change is necessary.However, it was evaluated for cost comparison purposes.Using the sequences A2, B2, C3, D2, E2, and with known demand data for time period t = 2, a from-between chart can be constructed.The frombetween chart is shown in Table 12.Based on the demand data, the layout generated using the GA for time period t = 2 is shown in Figure 6.The GA cost function primarily attempts to reduce the material handling cost.Thus the layout suggested in time period t = 1, if used for time period t = 2 may have a higher material handling utilization.The results from the simulation with the new layout for time period t = 2, shows that there are no material handling and capacity constraints.Thus there was no need to add production capacity or material handling capacity if we used layout suggested in time period t = 1 or time period t = 2.As demand is met with layout as in time period t = 1, there was no need to change layout as generated by GA for time period 2. Comparison of the average MH utilizations using the layout as suggested by t = 1 and t = 2 are shown in the Table 13.However, both layouts have to be investigated to determine the least cost solution.

Table 13. Material Handling Utilization Comparison
Average material handling unit utilization % H mstp 99.5 98.9

Option1: Keep Old Layout
Table 14 below shows the utilization of each machine using selected sequence combination during t = 2.The total production cost is $39,714.Material handling cost for time period t = 2 is $146,000.As the layout used in this time period is same as in time period t = 1, there is no rearrangement cost.As the production capacities and material handling capacities are adequate, there is no need for additional resources.Thus, the total cost of meeting demand, if same layout as in time period 1 is used along with the new sequence combination selected in time period t =2 is $185,714.

Option 2: Change Layout
Production cost depends on the process sequence and not on the layout and hence is $39,714 as in Option 1. Material handling cost can be calculated using Equation 4; the dynamic flow values are unchanged from option 1, as they depend on the sequence combination selected.However, the distance travelled depends on the layout selected hence the material handling cost calculated based on the new layout for time period t = 2 is calculated to be $114,000.Table 15 below shows the distance each machine has to be moved to configure the new layout.The total cost of rearrangement is $137,500.Besides these two options, we can also use the sequence as suggested in time period 1 which would have resulted in production constraint and a need to add more production capacity.A cost comparison of all the options is shown in the Table 16.Thus during time period 2, we had the following alternatives to meet demand: 1. Use GA layout from t = 1 and sequences from t = 1 (represented as GA1S1) 2. Use GA layout from t = 1 and sequences from t = 2 (represented as GA1S2) 3. Use GA layout from t = 2 and sequences from t = 1 (represented as GA2S1) 4. Use GA layout from t = 2 and sequences from t = 2 (represented as GA2S2) Based on the costs, the best solution is to option 2, i.e. keep same layout for time period 1 and 2, while changing process sequence for time period 2. Thus using alternative sequence, we were able to eliminate production capacity constraint by using alternative sequence in time period 2.

Seven Department Case Study: Time Period 3
The calculations and procedures are repeated for time period 3. Analysis of percent utilizations of each machine indicates that machine 1 is over utilized.Thus adding a new machine of type 1 or alternate process sequences have to be selected.When adding constraint for machine type 1 utilization are used, the process sequence combination used in time period t =2 is the best optimal sequence.However, machine utilization indicates that machine 7 is over utilized.So, to use that process sequences, another machine of type 7 has to be added or alternate has to be used.Machine 7 utilization constraints were also added and resulted in A2, B2, C3, D2, and E2 as the optimal alternative sequence.Table 17 below shows the process sequences selected for each part.

Sequence id Sequence
The utilizations of each machine with an initial value of n t = 1 calculated using Equation 1 is shown in Table 18.The cost of production for the selected sequences is $47,615.As the utilization of all machines are less than 100, these process sequences can be selected to meet demand for time period 3, without the need for adding machines.Thus from time period t = 2 to t = 3, alternate sequences are used and the production constraint limitation is eliminated.The best process sequence combination uses second sequence for products A, B, D, and E; and third sequence for C and demand can be met with existing production capacity.Since layout was not changed in time period t = 2, the layout currently existing is same as in time period t = 1.However, the simulation results (Table 19) using layout from time period t = 1 and parameters from time period t = 3, indicate that demand cannot be met.Thus with the layout as in time period 1, demand cannot be met.According to the modified flow chart in Figure 2, we can check for the material handling utilization and add more capacity if necessary or we can evaluate new layout using GA algorithm.Material handling unit utilization data as obtained from simulation results is shown in Table 20.The utilization data obtained from simulation results indicates that all the material handling units are extensively utilized resulting in an average utilization of 99.9%.
As the material handling utilization is greater than the threshold value of 99.5%, more material handling capacity is needed.An additional material handling unit is added to the system at a cost of $50,000.The simulation results (Table 21) indicate that by adding a material handling unit, demand can be met.As an alternative to adding material handling unit, we could have changed the layout.As we know the demand for the given time period, we can construct a from-between chart show in Table 22.

Sink
The layout for time period t = 3 is shown in Figure 7. Simulation results (Table 23) indicate that demand can be met with the new layout with existing production capacity, and using the sequence as found optimal for time period t = 3 and the original material handling capacity with 3 material handling units.Thus, the demand can be met for time period 3 by adding more material handling capacity and using the old layout or by changing layout while keeping material handling capacity unchanged.Cost analysis was carried out for both options.Table 24 shows the utilization of each machine using selected sequence combination during time period t = 3.The total production cost is $47,615.Material handling cost for time period t = 3 is $176,000.As the layout used in this time period is same as in time period t = 1, there is no rearrangement cost.The cost of increasing material handling capacity is 50,000.Thus the total cost of meeting demand for this option is $273,615.Production cost depends on the sequence selection and not on the layout and hence is $47,615.The material handling cost for time period t = 3 is $126,500.Table 25 shows the distance each machine has to be moved to configure the new layout.The total rearrangement cost is $185,000.Besides these two options, the sequence from time period 1 or time period 2 which would have resulted in production constraint and a need to add more production capacity could also be considered.Thus there are 4 options: 1. Use GA layout from t = 1 and sequences from t = 3 (represented as GA1S3) 2. Use GA layout from t = 3 and sequences from t = 3 (represented as GA3S3) 3. Use GA layout from t = 1 and sequences from t = 1 (represented as GA1S1) 4. Use GA layout from t = 1 and sequences from t = 2 (represented as GA1S2) Cost comparison shown in Table 25, indicate that the most economical option is to consider alternate sequences rather than changing the layout or adding more production capacity.

Conclusion
In this paper, a new procedure for developing dynamic layouts when product demands are changing from one timeperiod to the next has been developed.Traditionally in the development of dynamic facility layouts, the system capacity was assumed to be infinite.Previous research has developed procedures for identifying the capacity constraints that could lead to infeasible facility layouts.The capacity constraints were identified using a simulation based procedure.The capacity constraints were alleviated by adding material handling and production capacity as required and by redesigning the facility layout.However, in this paper use of alternate process plans were identified as a method for overcoming the capacity constraints.The procedure allows alternate process plans to be selected, when current material handling and production capacity restrictions make the production system infeasible.The increased cost of the less efficient process plans are typically offset easily by the savings in material handling equipment and production equipment.

Figure
Figure 1.Redesign Methodology Flowchart

Figure
Figure 2. Modified Redesign Methodology Flowchart

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Figure 3. Flowchart for Part Sequence Analysis and Optimal Sequence Selection

Figure 4 .
Figure 4. Flowchart for Determining Production Capacity Requirement.