Question

You do not need to get solution. Please indicate and explain all relevant information/assumptions explicitly.An international company aims to make the production, inventory and workforce plans for one of its production facilities. They obtained the following demand data for their system in a unit of tons during last 6 months. Month Demand Forecast Production Days 1 260 20 2 290 25 3 420 20 4 230 15 5 250 19 6 230 15 In their planning process, they will use three ahead moving average method (N=2) to predict the future demand data for next 6 months. There are currently 100 workers employed at the company. It is observed that, over a period of 30 working days, 20 workers produced 120 tons. The cost of hiring up to 25 workers is $750, and after 25 hires cost decreases to $600. Firing a worker costs $550. Inventory holding cost is $40 per ton per month. At the beginning of the planning period, the company has no materials in the stock. The company wants to have at least 100 ton in inventory at the end of 2nd month and plans to start 6th month with 150 tons in the stock. Some of the demand can also be allowed not to be satisfied for next 6 months. If company can not satisfy its customers, cost of this situation will be $45 per ton. a) Please write down an open - f orm mathematical model to get optimal solution for this problem.

Answer 1

You need to have a step by step approach to this question.

Here is the relevant information you'll need to get a solution to this question-

Step 1- Find out the Forecasted monthly demand using the three ahead moving average.

Step 2- Now when you have forecasted the production, then -

Add 100 ton to the forecasted production of 2nd month (since the company wants to have inventory of same amount at the end of 2nd month).

Add 150 ton to the forecasted production of 5th moth (since company wants to start 6th month with 150 ton inventory, thus it shall be produced in 5th month).

Step 3- Now calculate that how much you can produce with the given no. of workforce of 100 workers.

Since 20 workers produce 120 tons in 30 working days, therefore, 1 worker produce in 1 working day = = 0.2 tons

So in month 1, there are 20 workin days. so with 100 workers you can produce =(0.2)*(100)*(20)= 400 tons

Step 4- Now since you are having a demand as well as production data, use it to make an optimised solution for the company.

Calculate Cost to the company at various level. Compare it Demand. Calculate holding cost for the company. Decide using this comparison what is the optimal no. of workers that needs to be employed with the company.

With Step 1 & 2, production and inventory plans would be completed. Further with step 3 & 4, workforce plan as well as an optimised solution would also be achieved.

It would be difficult if you try to solve workforce plan first. So it is advised to be on approach.