cat.edu/bbcswebdav/pid-2937343-dt-content-rid-21137564.2/courses/ISEN430001.2018
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cat.edu/bbcswebdav/pid-2937343-dt-content-rid-21137564.2/courses/ISEN430001.201810/ISENA Project Question Bob's Custom Trucks has demand over the next six months shown in the table below. Currently, Bob employees 264 full-time workers. Cost to hire a new worker is $400 and to fire a worker is $1000. Inventory holding cost is $300 per car per month. Over the last six months, it takes an average of 10 worker-days to make one car. Currently, there are 180 cars in stock. Bob wants to make sure that at least a 20-car buffer at the end of each month. Bob says he will not using outsourcing or overtime. What is an optimal production plan over next 6 months that minimizes the total cost for production and workforce change? MonthDemand Working day/rmonth November December January February March 510 558 732 1056 1040 960 20 21 20 21 April Project Requirements (1) Formulate the problem as an LP or ILP model, and then use What'sBest to solve it. (2) Write a project report that explains how you formulate the problem, presents your LP or ILP model, and reports and interpret the optimal production plan found using What'sBest. (3) Submit your project report and your What'sBest model through the Blackboard (4) The project will be graded using the following rubric.Explanation / Answer
The decision variables are the number of workers say Wi employed in the ith month and Pi is the production level in the ith month. Let Ii is the opening inventory for ith month and Ei is the ending/ closing inventory for ith month.
As per given conditions Ei >= 20 for all i=1,2,3,4,5,6
The parameters are given as Demands and number of days for each month, say Di, and di for ith month
One car needs 10 worker-days and there are 180 cars in stock or I1=180
Ei = Ii+Pi-Di and Pi <= Widi/10
The formulation requires Objective function as Minimization of Cost of workers change (hire and fire cost) and inventory carrying cost
Solution using excel solver is as follows:
Total minimum cost as per the conditions and parameters is $140,200
Month November December January February March April Total Demand 510 558 732 1056 1040 960 4856 WorkingDays 22 20 21 22 20 21 126 No.workers-W 271 279 348 480 520 520 Production-P 354 556 730 1056 1040 960 4696 Max.Prod. 596.2 558 730.8 1056 1040 1092 Intial Inventory-I 180 24 22 20 20 20 Ending Inventory-E 24 22 20 20 20 20 Min.Ending 20 20 20 20 20 20 No. hired 7 8 69 132 40 0 No. fired 0 0 0 0 0 3.88E-11 Hiring cost@400 2800 3200 27600 52800 16000 0 Firing cost@1000 0 0 0 0 0 3.88E-08 Holding cost@300 7200 6600 6000 6000 6000 6000 Total cost 10000 9800 33600 58800 22000 6000 140200Related Questions
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