As two products, Super and Slim Line are on a separate assembly line, we consider only 5 products for our production planning problem.
We find this as a problem of aggregate capacity planning, we will use the labour hours as the unit for our analysis.
As, the week ending Jan 25 has been taken as the base for the calculation of the direct labour index, we go with the assumption that there was a 100% utilisation in that particular week so as to find the total demand in terms of labour hours.
Sum of direct labour index for 1979 = 5430 Approx.
Assuming a week to have 5 working days, with 8 hrs. work shift per day.
Labour Index 100 corresponds to = 4480 labour-hours
Total direct labour hours in 1979 = 243,264 labour-hours
Total production in 1979 excluding Super and Slime Line=90394 units
Avg. Direct labour content per unit = 2.69 labour-hrs/unit
Total demand in 1980 excluding Super and Slim Line= 111,500 units
Total Direct labour hours required in 1980 = 300,063 labour-hours
Option 1: Level Production
For further analysis, the yearly demand is distributed to various months based on the shipment data available for 1979 as that represents the actual quantity demanded for a particular month in 1979.
The graph below shows the variation of cumulative demand for different months of the year.
Required production for a particular month has been obtained using an opening stock of 6189 units.
Required Production = (Cumulative Demand – 6189*2.69) / Month Number
The figure below shows the variation of required production along the course of the year.
From the above graph we observe that the maximum production is required in the month of July and so that needs to be the rate of level production in order to meet the demand for all the months.
Level Production = 25,117.05 labour-hours/month
Taking 25117.05 as the production rate, the table below shows the inventory levels at the end of each month.
Total inventory held in 1980 = 650,380 labour-hours.
Inventory Holding Cost = 650380 * 30 / (12*2.69) = $ 604,442
For 25,117 labour hours/month we need 2 hours over-time in addition to 8 regular hours for 20 days in a month with 112 workers.
Labour cost= $ 1,774,080
Thus, total cost for the level production method is $ 2,378,522.
Option 2: Demand Chase
In case of demand chase production, the following table summarises the no. of workers needed to meet the demand.
In case of the demand chase strategy, there is no inventory cost as we meet the demand in each month.
Total Labour cost = $1,800,000
There is a lot of hiring of new workers involved which comes with a cost of $284.50 per new worker so the hiring cost is going to be pretty high.
As it is the labour cost in case of demand chase is more than that in level production in addition to which there is a high hiring cost due to which it is not feasible to go with the demand chase strategy.
Conclusion
Having performed the numerical analysis, we find that there is a significant cost involved in the demand chase strategy with the hiring of new workers. Though comparatively, the level production strategy has a lower cost associated with it but even in that case the labour usage is pretty less. Therefore, we suggest that it is best to use a hybrid strategy wherein we use the level production strategy until July and then resort to the demand chase strategy after July. This way we would be able to get the benefits of both the strategies.
