Supply chain analysis and design individual case study

Supply Chain Analysis and Design OMGT 2277 SUPPLY CHAIN ANALYSIS AND DESIGN ASSIGNMENT – INDIVIDUAL CASE STUDY COVER SHEET Term Title of Assignment Names and student ID B 2020 Individual Case Study Huynh Kim Son – s3694699 Location SGS Campus Lecturer Hiep P Word Count (Main content without list of references, cover page, etc.) P a g e | 14 Supply Chain Analysis and Design QUESTION INPUTS DEMAND FOR FANCY BAGS Month 3000 Month 5000 Month 2000 Month 1000 WORKERS INVOLVED - Initial number of workers: 20 - Regular wage (per worker): $1,500 - Overtime wage (per hour/ worker): $13 - Maximum standard working time (per worker): 160 hours - Maximum overtime working hours (per worker): 20 hours - Worker hired cost (per worker): $1600 - Woker fired cost (per worker): $2000 PRODUCTION INVOLVED - Initial stock: 500 bags - Number of hours required to produce bag: hours - Raw material cost (per bag): $15 - Inventory holding cost (per bag): $3 DECISION VARIABLES P a g e | 14 Supply Chain Analysis and Design TOTAL COST = Change-In-Workforce-Level costs + Total Regular-Time Wages + Total Overtime Wages + Total Raw Material cost + Total Inventory Holding cost Change-In-Workforce-Level Costs Renova estimates that the cost associated with increasing the workforce level for any month is $1,600 per worker hired A similar cost associated with decreasing the workforce level for any month is $2,000 per worker fired Decision Variables Let Im denote the number of workers hired in month m Let Dm denote the number of workers fired in month m m=1, 2, 3, 4; m=1 refers to month 1, m=2 refers to month 2, m=3 refers to month 3, and m=4 refers to month Change-In-Workforce-Level Costs = 1600I1 + 1600I2 + 1600I3 + 1600I4 + 2000D1 + 2000D2 + 2000D3 + 2000D4 EXTRA: Total Number of Workers (This element depends on the change-in-workforcelevel and NOT considered as a DECISION VARIABLE in Linear Programming However, it is needed in order to conduct Linear Programming in the case given) Renova informs that currently they are having 20 workers available Let Nm denote the total number of workers the company needs in month m N0 = 20 N1 = 20 + I1 – D1 N = N + I2 – D N = N + I3 – D N = N + I4 – D Regular Wages Costs Renova stated that the regular wage per worker of the company is $1,600 per month P a g e | 14 Supply Chain Analysis and Design Total Regular Wages = 1500N1 + 1500N2 + 1500N3 + 1500N4 Overtime Wages Costs Renova pays workers $13 per overtime hour they perform Decision Variables Let Om denote the amount of overtime hours required to sufficiently produce fancy bags to satisfy the demand in month m Total Overtime Wages = 13O1 + 13O2 + 13O3 + 13O4 Raw Material Costs Renova determined that for each fancy bags produced it needs $15 cost of raw material Decision Variables Let Xm denote the production volume in units for fancy bags in month m Total Raw Material Cost = 15X1 + 15X2 + 15X3 + 15X4 Inventory Holding Costs Renova determined that the holding cost for each unit of inventory is $3 Decision Variables Let Sm denote the inventory level for fancy bags in month m Total Inventory Holding Cost = 3S1 + 3S2 + 3S3 + 3S4 OBJECTIVE FUNCTION Minimum Total Cost or P a g e | 14 Supply Chain Analysis and Design z = 1600I1 + 1600I2 + 1600I3 + 1600I4 + 2000D1 + 2000D2 + 2000D3 + 2000D4 + 1500N1 + 1500N2 + 1500N3 + 1500N4 + 13O1 + 13O2 + 13O3 + 13O4 + 15X1 + 15X2 + 15X3 + 15X4 + 3S1 + 3S2 + 3S3 + 3S4 CONSTRAINTS Inventory after Production meets Customer Demand We must guarantee that the production schedule meets customer demand Fancy bags that reach to the customer can come from both this month’s production or last month’s stock Therefore, the demand fulfilment requirement takes the form of: (Ending Inventory from the previous month) + (Production Volume this month) – (Ending Inventory for this month) ≥ This month’s Demand  Given that the Inventory Level at the beginning of Month is 500 units  There are no requirements regarding the compulsory inventory level at the end of any months  The demand for Month 1, Month 2, Month and Month are 3000, 5000, 2000, 1000 respectively Take all elements into consideration, using the production volume variable and inventory level variable, we are able to form the constraints below:  Month 1: 500 + X1 – S1 ≥ 3000 -> X1 – S1 ≥ 2500  Month 2: S1 + X2 – S2 ≥ 5000  Month 3: S2 + X3 – S3 ≥ 2000  Month 4: S3 + X4 – S4 ≥ 1000 Production Capacity meets Production Volume The key element for the whole Linear Programming in the case of Renova is the appropriate workforce level in order to make the number of bags in demand Therefore, the production capacity from the total available working time of workers must be larger or equal to the production volume It could be larger or equal, NOT equal, due to the firing cost occurred in the change-in-workforce level For instance, supposed we are having 50 workers in April but in May we only need 40 workers to produce the required production volume However, if the P a g e | 14 Supply Chain Analysis and Design firing cost of 10 workers are higher than the wages we pay for those 10 excessive workers, it is better that we maintain the same workforce level despite of the excessive capacity Production capacity is calculated by the total amount of available working time, including regular-time and overtime, divided by the time required to make bag Due to the demonstration above, we have the formula: [(Number of Workers this month)*(Maximum Standard Working Time per Worker) + (Total Number of Overtime Hours this month)]/(Time required to make bag) ≥ (Production Volume this month)  Given that Maximum standard working time per worker is 160 hours  The amount of time required to make bag is hours Using these given data, number of worker variable, amount of overtime variable, production volume variable, we have the constraints:  Month 1: (160N1 + O1)/4 ≥ X1  Month 2: (160N2 + O2)/4 ≥ X2  Month 3: (160N3 + O3)/4 ≥X3  Month 4: (160N4 + O4)/4 ≥ X4 Overtime Capacity The total amount of overtime needed in fancy bags’ production schedule is a decision variable Renova has overtime policy in which each worker can only work overtime for maximum 20 hours per month Hence, the total amount of overtime conducted cannot exceed the maximum available overtime of all workers We have: (Amount of Overtime conducted) ≤ (Number of Workers)*(Maximum Overtime per Worker)  Given that the maximum amount of overtime each worker could conduct is 20 hours Using the data given, number of workers variable and amount of overtime variable, we have the constraints:  Month 1: O1 ≤ 20N1  Month 2: O2 ≤ 20N2 P a g e | 14 Supply Chain Analysis and Design  Month 3: O3 ≤ 20N3  Month 4: O4 ≤ 20N4 Decision Variables non-negativity We must guarantee that all of the decision variables, including Number of Workers Hired, Number of Workers Fired, Production Volume, Inventory Level and the amount of overtime, are non-negative because negativity in any of these decision variables would be ineffective and unrealistic Therefore, we have: I1, I2, I3, I4, D1, D2, D3, D4, X1, X2, X3, X4, S1, S2, S3, S4, O1, O2, O3, O4 ≥ Decision Variables Integer There are specific variables that we must guaranteed that their results are integer number, including Number of Workers Hired, Number of Workers Fired, Production Volume and Inventory Level Figure 1: Decision Variables without Integer Constraint As an illustration, without the integer constraint, the results are as Figure Although the result without the integer constraint may have a better objective function, but it is not P a g e | 14 Supply Chain Analysis and Design applicable in real world cases Integer constraint is necessary in this case because we cannot hire 0,33 worker or produced 0,5 product Therefore, we have: I1, I2, I3, I4, D1, D2, D3, D4, X1, X2, X3, X4, S1, S2, S3, S4 = int (REPRODUCE THE MODEL AND SOLVING THE PROBLEM ARE INCLUDED IN THE EXCEL FILE) INTERPRETING THE RESULT QUESTION Investigating the relationship between initial number of workers and the total cost Due to the hiring and firing cost occurred in the change-in-workforce level process of Renova, certainly the initial number of workers has impacts towards the total cost Specifically, supposed the company needs 84 workers to produce enough fancy bags in demand In the situation which they are having 20 workers, they may have to hire 84-20=64 more workers to operate the required production plan, and this is where hiring cost of 64 workers occurs On the other hand, if they already have 80 workers, they only need to hire 84-80=4 more workers, and 60 (64-4) workers hiring cost is saved compared to situation Throughout the example above, we could observe that when the initial number of workers increases, the hiring cost of the company will decrease Hiring cost is accounted in the total cost of Renova (Total Cost Formula in LP model section above), hence a decrease in hiring cost would result in a reduction in the total cost Take all into consideration, it is appropriate to state that the relationship between “Initial Number of Workers” and “Total Cost” is negative, in which an element increases while the other one decreases and vice versa P a g e | 14 Supply Chain Analysis and Design Reproducing Linear Programming and Interpreting the Result The CEO of Renova indicates that “there is an opportunity to begin the process by selecting any initial number of workers between and 200” In the previous Linear Programming provided to Renova, the initial number of Workers play the role of an input (20 initial workers) However, due to the company’s new additional information, we considered it as a decision variable because we not know what the best solution is if we could have any initial number of workers between and 200 The to 200 range now becomes our constraint for the initial number of workers Everything else in the previous Linear Programming does not change STEP 1: CONDUCTING LINEAR PROGRAMMING TO FIND THE BEST SOLUTION Initial Number of Workers Renova addressed that this can be selected between and 200 Decision Variable Let No denote the Initial Number of Workers of the whole period Constraint No ≤ 200 No non-negativity No integer (Everything else in the previous Linear Programming Model stays the same) P a g e | 14 Supply Chain Analysis and Design The integer constraint for the Initial Number of Workers is sill necessary in this case due to the same reason stated in the LP model above – we could not have, for instance, 80.7 initial workers Therefore, in order to figure out the optimal applicable solution when the range of initial workers is between and 200, Integer constraint is required After reproducing the LP model in Excel, we have the results: P a g e 10 | 14 Supply Chain Analysis and Design Figure 2: Optimal Initial Number of Workers in Excel Linear Programming Model As expected, the optimal initial number of workers is 84 This could be explained as the required workforce level for month production is 84 By having 84 initial workers, the Hiring Cost would be and that is the point where Total Cost would be reduced significantly The comparison is below: Figure 3: Costs when Initial Number of Workers is 20 Figure 4: Total Cost when Initial Number of workers is optimal Due to the cost comparison between Figure (20 initial workers) and Figure (84 initial workers), it is observable that every other cost stays the same The only cost that change is P a g e 11 | 14 Supply Chain Analysis and Design the change-in-workforce level cost, which is subjected to firing cost because hiring cost turned to By this, Renova saves $102,400 (774,120-671,720) by eliminating the hiring cost Another perspective to be considered is the Minimum Total Cost between Normal LP and Integer LP Normal LP provides the lower minimum total cost but again, LP in this situation suggest starting with 83.33 workers and certainly it is not applicable in real world circumstance Therefore, it is pertinent to conclude that the optimal applicable solution for Renova is starting the production plan with 84 workers To specifically investigate how the variation in the initial number of workers affects the decision variable and the total cost, we need to observe the sensitivity report provided by Excel solver Nevertheless, when an integer constraint is being set, Excel refuses to provide a sensitivity report Therefore, supposed we already know the optimal initial number of workers is 84 as above, we now assume the company will start with 84 initial workers This action removes the needs for the integer constraint, all others decision variable and objective function maintain the same because it is already optimal, but now we are able to see the sensitivity report and observe the variation STEP 2: ASSUMING THE INITIAL NUMBER OF WORKERS IS THE RESULT OF THE LINEAR PROGRAMMING ABOVE Constraint: - No = 84 - Remove all integer constraint STEP 3: ADDRESSING THE SENSITIVITY REPORT CONDUCTED P a g e 12 | 14 Supply Chain Analysis and Design After conducting the steps above, we get the sensitivity report as below: Subjected to cells $H$80 (last cell in Figure), the allowable increase and allowable decrease of the initial number of workers is ~4.24 and ~0.67 units respectively The shadow price is a positive number, which indicates that there is a positive relationship between the variation of initial workers and the total minimum cost To be clarified, for each unit increase or decrease in the initial number of workers, the minimum total cost would be increase by $705 As long as the constraint R.H.S stays between the allowable range, the shadow price of $705 is applicable If the constraint R.H.S exceeds the allowable range, the whole LP are adjusted, and this sensitivity report cannot be used to assess the variation in the minimum total cost associated with the initial number of workers anymore Allowable range: Lower bound: 84 - 0.67 = 83.33 P a g e 13 | 14 Supply Chain Analysis and Design Upper bound: 84 + 4.24 = 88.24 83.33 ≤ N0 ≤88.24 To be applicable in realistic circumstances, the range should follow an integer value: 84 ≤ N0 ≤ 88 In conclusion, we recommend that Renova should start their production line with the Initial Number of Workers between 84 and 88 in order to get Minimum Total Cost under control with a shadow price of $705 If possible, the optimal applicable solution they could have is starting with 84 workers, in which the Total Cost is minimum with the value of $671,720 P a g e 14 | 14 ... Workers” and “Total Cost” is negative, in which an element increases while the other one decreases and vice versa P a g e | 14 Supply Chain Analysis and Design Reproducing Linear Programming and Interpreting... objective function, but it is not P a g e | 14 Supply Chain Analysis and Design applicable in real world cases Integer constraint is necessary in this case because we cannot hire 0,33 worker or produced.. .Supply Chain Analysis and Design QUESTION INPUTS DEMAND FOR FANCY BAGS Month 3000 Month 5000 Month 2000 Month 1000 WORKERS