Optimal Production Planning in Wiring Harness Assembling Process Using Mixed Integer Linear Programming

Optimal Production Planning in Wiring Harness Assembling Process Using Mixed Integer Linear Programming

Donatus Feriyanto Simamora

Magister Management Technology Program Institut Teknologi Sepuluh Nopember Surabaya, Indonesia

Suparno

Magister Management Technology Program Institut Teknologi Sepuluh Nopember Surabaya, Indonesia

Abstract This study propose a real case of production planning in industry to face the uncertainty demand by optimizing the available resources to minimize the cost of production in wiring harness assembling process. Aggregate production planning is a tool to balancing uncertainty demand and available resources in short-medium term planning horizons. CV. XYZ is a subcontract company which engaged in wiring harness assembling process. Wiring harness is the wiring and power distribution system for the transmission of electric power and signal in automotives. This study use Mixed Integer Linear Programming (MILP) as a tool process to optimize the production plan. MILP is a method of mathematic program to achieve the optimal goal with the limits of available resources. This method allows researcher to optimize the production planning in wiring harness assembling process. Variable work time hour, the amount of man power used and inventory are the focus of this study. Result from this optimation model, by increasing the number of employees, it can minimize the total production cost in wiring harness assembling process by 0.4% from Rp. 2,043,458,430 to Rp. 2,036,236,800 or decrease Rp. 7,221,630 over 12 month planning period

Keywords Production Planning, Optimization, Wiring Harness, Mixed Integer Linear Programming (MILP).

1. INTRODUCTION

   This study is an example of a real case of production planning to minimize the cost of wiring harness assembling process. Wiring harness is the wiring and power distribution system for the transmission of electric power and signal in automotives. The difficulties in wiring harness assembly depends on the number of cables and component required. Each process has a variety of additions process depends on the type of component used.

   Wiring harness orders had fluctuating demand in a certain period, causing an imbalance between orders received and available resources owned by the company. Required the optimal production planning to balance the demand and companys supply by optimizing the available resources.

   The purpose of this study is to create an optimal production planning to minimize the production cost in wiring harness assembling process with variation of man power required, overtime hour and inventory. This study is using Mixed Integer Linear Programming (MILP) as a model formulation to solve this problem.

2. LITERATURE REVIEW

   Aggregate production planning (APP) is a tool process in order to balance uncertainty demand and the available resources in short-medium term planning horizons. APP can minimize the cost of production or increase company revenues in their objective function (Chase, et al., 2006). APP can be implemented in various ways with the conditions and situation in the company by doing customer demand quantity analysis, fulfillment schedule, material availability, production capacity as well as other resources. In the management factory, a production manager must take a right decision of production planning for the coming period (Siswanto, 2006).

   Buxey (2005) described that in APP there are some strategies can be done to meet customer demand and companys supply. Labor strategic and inventory levels are the most frequent choices taken by company. Using labor strategic will cause low inventory levels, make inventory holding cost to be low but the labor cost is higher. Liu & Tu (2008) described that by increasing inventory levels can balance customer demand and avoiding loss of sales, but inventory cost may increase. Reversely, if the company doesnt have or lack of inventory, will cause service to the customer not optimal.

   Various methods have been developed in the previous aggregate production planning. Tang, et al. (1981) proposed a study of aggregate planning in the heavy equipment industry by using basic model of linear programming to minimize the production cost. Vercellis (1991) proposed model simulation scenario strategies can be done in APP. Production levels, inventory levels, or the combination of both strategy has been simulated to minimize the production cost. Nam & Longendran (1992) tried to classified any APP models into 2 group model, these are optimal model and near optimal model. Optimal model is a model that use exact mathematic programming to solve APP. Near optimal model is approach model based on Opinion Companys top management or an expert. Takey & Mesquita (2006) explained that in APP, mathematic model has important role in balancing supply and demand as to help managers take production planning decisions.

   In a competitive competition, industry players must make their operation efficiency in allocation their available resources. Liu & Tu (2008) developed stockout model to balancing demand and supply in limited inventory integrated

   with algorithm polynomial time complexity model. Leung & Chan (2009) formulated goal programming model to increase company revenues with limited available resources. In Goal Programming, these are more than one objective functions to be achieved by giving weight to the each objectives. These weights mean that every objectives have a priority to be achieved. Leung & Chan (2009) provides first objective is to increasing sales profit, second objectives minimize maintenance cost, and last priority objective is to optimizing machine utilization. Al-e-hashem, et al. (2011) developed robust optimization models integrated with integer programming for multi product which had production in different places. In the same year Aghezzaf et al. (2011) also developed robust optimization model for the product which has 2 stages of production, where the first product or semi finish product is a product that has a relatively stable demand, and the second product or finish goods is a product which has fluctuating demand. More complexity of customer demand which had flexibility in delivery time studied by Al-e-hashem et al. (2013), he developed stochastic model integrated with linear programming for the multi product which has production in different places. Gansterer (2015) developed APP model to increase service level in Make to Order (MTO) industry.

   so it should go beyond the regular working time 21 working days within one month, it will make overtime increased. To anticipated the problem, CV. XYZ make overtime strategy to meet the exceed demand in certain months, and trying to allocate resources to help groups that had a exceed demand.

   The imbalancement between the orders and the availability of the resources in certain periods led the company to improve their production planning as to improve their corporate profitability. It required balancing the customer demand and companys supply by optimizing the availability of existing resources. Overtime hours, the amount of labor (workforce) needed and stock (inventory) are the focus in this study, where the combination of these strategies will be compared with the company current strategy, which only using the strategy of working hours (overtime). This purpose is to obtain the optimal strategy to minimizing the cost of production in the assembling process.

   IV. METHODOLOGY

   1. Research Framework

      Problem Identification

      In this research, the first step is to identifying the problem and to undesanding all the constraint in the company. The flow research is illustrated in figure 1 as attached below.

3. PROBLEM DESCRIPTION

   CV. XYZ is a subcontract company which engaged in wiring harness assembling process that will be supplied to the Automotives industry in Indonesia. Wiring harness is the wiring and power distribution system for the transmission of electric power and signal in automotives. The company was located in Bekasi, West Java. The company product is a component of wiring harness which is each type of product had different processing time and different amount of employees required in the assembling process.

   As informed before that the products had a different processing time and amount of employee required, caused by orders received had a different process. To anticipate this problem, CV. XYZ had 2 plant where the first plant is to perform the assembling process, and the second plant is devoted to the process cutting and crimping. CV. XYZ divided their employees into several group based on the similarity of the use number employees needed. CV. XYZ had 4 group to perform the assembling process. Group A, B, C had a particular specialization in the assembling part number variants. While group D, is a special group to cut the wire which had a specific length.

   As an assembly company, CV. XYZ is highly depend on the availability of their human resources in the assembling process. Appendix 1 is the CV. XYZ Monthly Delivery Realization. From the Appendix 1, by dividing the quantity with daily production capacity, we got the total working day needed of each group followed by the availability working days in each month.

   For example in July 2016, the entire production in group A can only be resolved in 10 days, which meant that group A only had the effective 10 working days from 21 normal working days in a month. While the 11 rest days, they will be off. Of course this leads to the waste of resources. But in other months, working hour group A exceed the regular time,

   Data Collection & Tabulation

   1. Data Collection

      • Type of Products

      • Historical Orders

      • Cost of Assembling Process

      • Production Demand

   2. MILP Model Development

   3. Data Tabulation

   Analyzing & Conclusion

   1. Analyzing Result of Tabulation

   2. Conclusion

   Figure 1. Research Flowchart

   All data in this study were obtained from the company's books and also from doing interviews with the employees. These data have been specified as follows:

   1. Types of Product

      There are 12 kind of main products CV. XYZ will be the subject in this study. Nine product is an assembly product, 3 product is a cutting product. Any products had different employee needed and different processing time.

   2. Cost of Assembling Process

      The cost of assembling process in this study is the operational cost and inventory cost. Operational cost including packaging cost, administration cost, transportation cost, labor cost, and monthly cost (water & power bills). These costs are very influence into the operational performance of the wiring harness assembling process. As a subcontracting company, CV. XYZ doesnt have cost of raw materials. Cost of raw materials are charged to the customer.

   3. Assets Cost

      Assets cost is the cost of covering aspects of the equipment and the property. This cost is also a critical. Without assets cost, production activities cannot be performed. Assets cost include the cost of buildings and equipment cost.

   4. Demand / Production Needs

      Production demand was generated from the historical data during previous 9 month production. These data then processed into the companys production targets for next 12 month planning. This production demand is adapted to company production target as to input for next 12 month planning.

      Parameters

      : Demand product i in t period (unit).

      : Operational & overhead cost except labor cost product i (rupiah per unit).

      : Cost of holding product i (rupiah per unit).

      : Cost of labor in reguler time product i (rupiah per man- hour).

      : Cost of labor in overtime product i (rupiah per man- hour).

      : The box ability to store product i (unit).

      : Available / Maximum box allowable due to limited space constraint (unit).

      : Cost of hiring new employees (rupiah per man).

      : Cost of firing employees (rupiah per man).

      : Processing time for each product i (man-hour per unit).

      : Available reguler time hours in t period (hour).

      : Avaialble overtime hours in t period (hour).

      : Allowable total man power used (man).

      Objective function:

   1. Model Development

   The selection model is taken based on the companys problem and constraint. This model adapted from Takey & Mesquita (2006) which is using Mixed Integer Linear Programming (MILP) as a model to generated APP. This model had a variation in overtime hour, workforce, subcontract and inventory. These variables have a similarity with the companys problem. Bit development model in this research is the model formulation in the requirement of working hour employees, where the process of assembling wiring harness had different process time and employees needed, deep formulation in inventory model where the component of wiring harness stored in a box, each box had the ability to store a components due to the size of the part number of components. And also elimination of subcontract strategy, because CV. XYZ is a subcontract company.

   Index

   i : Types of Product (12 part number) t : Periods (12 Bulan)

   Decision Variables

   : Quantity of product i during reguler time hours in t period (unit).

   : Quantity of product i during overtime hours in t period (unit).

   : Amount of inventory product i in t period(unit).

   : Reguler time hours needed for product i in t period

   Constraint:

   (man-hour).

   : Overtime hours needed for product i in t period (man- hour).

   : Amount of man power hired in t period (man).

   : Amount of man power fired in t period (man).

   : Total of man power used in t period (man).

   The objective function (equation 1) is to minimize the production cost of wiring harness assembling process include product operational cost (regular and overtime), product inventory cost, workforce cost (regular and overtime), hiring and firing cost.

   Equation 2 to 13 is a constraint of mathematic model, where the equation 2 is a material flow balance that inventory is equal to the amount of products in regular and overtime, plus inventory in previous month, minus the demand during t period.

   Equation 3 determine that product i stored in box cannot exceed the allowable maximum box. Due to limited space available.

   Equation 4 determine the worktime hour needed for product i under regular time by multiplying processing time and amount of product i under regular time condition.

   Equation 5 determine the worktime hour needed for product i under overtime by multiplying processing time and amount of product i under overtime condition.

   Equation 6 determine the total of worktime hour under regular hours time cannot exceed the available reguler time hours during t period. Equation 7 determine the total of worktime hours under overtime hours cannot exceed the available overtime hours during t period.

   Equation 8 balancing the number employees used in each month, considering the hired and fired worker. Equation 9 restrict the uses of man power used cannot exceed the allowable man power used.

   Equation 10 indicated that during planning, amount of man power used is a integer. And equation 11 indicated that amount product in regular and overtime hour, inventory, hiring and firing are nonnegatives.

   1. RESULT

      The data was generated with software lindo 6.1. In this study, researcher did a comparation between current company strategy (overtime and fixed man power used) compare to alternative strategy (overtime, flexibility of man power used, and inventory) to obtained the best strategy to minimize the production cost of wiring harness assembling process.

      Summary output from lindo programming can be seen in Appendix 4. The output show that the alternative strategy resulted in lower production cost than the company current strategy. Production cost is decline by 0.4% from Rp. 2,043,458,430 to Rp. 2,036,236,800 or decrease Rp. 7,221,630 over 12 month planning period.

      Figure 2. Wiring Harness Production Cost during Planning Horizon

      As from the Figure 2, the production cost increase along the longer periods time, because the increased demand led to rise in production cost. In the early period, the company current strategy had a lower production cost than the alternative strategy. But after demand increase, alternative strategy generate lower production cost.

      Figure 3. Production Units under Regular Time

      Figure 4. Production Units under Overtime Hour

      In the Figure 3 & 4, it can be seen that alternative strategy can minimize the production cost by maximizing amount of production during regular time. This is because the labor cost on regular working time is relatively lower than labor cost in overtime. The alternative strategy had 6.7% greater in amount production unit during regular time compared to the company current strategy, where the production unit in company current strategy amounted to 3,372,913 units, while the alternative strategy had production unit in regular working hours amounted to 3,599,356 units or greater 226,453 units

      Figure 5. Regular Working Hour Needed (Man-Hour / Month)

      Figure 6. Overtime Hour Needed (Man-Hour / Month)

      Figure 5 show the regular working hour needed between all the strategies. The company current strategy had lower availability of regular working time compared with alternative strategies. This is because the company current strategy, using a fixed number of 43 employees. While the alternative strategy had the flexibility in man power used. When demand increased, working hour need is increased too. So when the working hour need exceed the availability of regular working hours, it will cause overtime hours. As seen from the Figure 6.

      Figure 7. Inventory unit during Planning Horizon (Unit)

      From figure 7 that the current condition of the company's strategy has inventory in the second period until sixth month of period. This is because in that period, the need of regular working hours under the availability of regular hours so it can be optimize the amount of production in regular working hours which can be increased to create inventory to anticipate the needs of working hour in the next period. Meanwhile, after the seventh and eighth periods, the company current strategy has no inventory because the needs of regular working hours had reached the limit availability. Diverted by using overtime, in the ninth period until the end of the period (see figure 5 & 6).

      The conditions of alternative strategies as shown in figure 7, to avoid the use of overtime hours, the company maximize regular working hours when demand increased to make inventories to anticipate the needs of the working hour in the next period.

      The optimation result also performed a sensitivity analysis to determine changes of the parameters to the optimal solution. This sensitivity analysis is intended to test the reliability of the model. Some of the parameters to be analyzed is operational cost, labor cost, inventory cost and demand.

      Table 1. Sensitivity of Parameter Change to the Optimal Solution

      Parameter Change	Optimal Solution Change in Percentage
      	Operational Cost	Labor Cost	Inventory Cost	Hiring & Firing Cost	Demand
      -10%	-6.0%	-4.0%	0.0%	0.0%	-10.2%
      -5%	-3.0%	-2.0%	0.0%	0.0%	-5.1%
      Fixed	–	–	–	–	–
      5%	3.0%	2.0%	0.0%	0.0%	5.1%
      10%	6.0%	4.0%	0.0%	0.0%	10.2%

      Table 1 show the sensitivity analysis for every changes in all parameters to the optimal solution. As seen from the table 1, that in this model the most vulnerable parameter affects to the optimal solution is the parameter of demand from the customers. Where when customer demand decrease or increase by 10%, it will affects the optimal total production costs by 10%. This means that every 1% change in demand, will give a 1% impact on total cost of wiring harness assembling process. And for the sensitivity of cost parameter, the operational cost had the most cost sensitivity to affects the optimal solution by 6%, and labor cost affects the optimal solution by 0.4%. While inventory cost and hiring and firing cost, not too influential to the optimal solution.

   2. CONCLUSIONS

This research was conducted on a subcontracting company wiring harness. The study compared two strategies in aggregate production planning to minimize the production cost in wiring harness assembling process. The first strategy is the company current strategy using fixed amount of employees used and overtime used. The second strategy is an alternative strategy, which strategy to use flexibility in the number of employees.

From these results, that the alternative strategy can minimize the total production cost in wiring harness assembling process by 0.4% from Rp. 2,043,458,430 to Rp. 2,036,236,800 or decrease Rp. 7,221,630 over 12 month planning period. The alternative strategies can minimize the production cost by maximizing the amount of production in regular time and avoiding overtime labor costs.

This study is an applicative research and expected to be used for the similar problems. This research only used integer variables on amount of man power used. Given that is impossible to the company to produce a product with real number, it is suggested to the next researcher using integer on product and working hour variables. This research is expected to be used as a suggestion for CV. XYZ to minimizing the cost of their production by considering the changes in customer demand which is very vulnerable parameter to changes optimal solutions wiring harness assembly production costs.

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APPENDIX 1. CV. XYZ HISTORICAL MONTHLY DELIVERY REALIZATION

APPENDIX 2. INPUT DEMAND FOR 12 MONTH PLANNING

APPENDIX 3. DATA INPUT FOR AGGREGATE PRODUCTION PLANNING