She has been asked to submit an production plan for the next calendar year. Each year Marl’s marketing and sales department produces a forecast of appliances by month for the next year, which the production planning department uses to plan production. The first step in the planning process is to construct an aggregate production plan, which consists of the planned gross production by month for the year but does not indicate numbers of specific appliance types, sizes or models to be made each month but is an aggregate as each type of appliance requires roughly similar materials and labor resources.
As the production periods approach later in the year, master production plans will be remunerated which would be specific regarding appliance type, model number etc. Linda therefore needs to make a decision on what would be the most suitable plan to keep costs at a minimum but also taking into consideration the feasibility of the plan. Primarily, the plan should involve keeping the total cost (equal to the sum of hiring costs, layoff costs, inventory costs and both regular and overtime labor costs) as low as possible.
It should also take into account other factors such as the fact that firing staff and hiring and training new employees brings its own headaches, especially in a emitted labor market such as exists in Stratford, as well as affecting union relations and employee morale. In addition, excessive overtime might lead to lower efficiency and restricted production could lead to poor work habits and low morale.
The plant has the physical capacity to produces only 13,000 appliances per month and currently employs 160 workers who work 40 hours a week and are expected to have an annual output of about 480 appliances next year. The monthly cost of employment to MR., including fringe benefits, is around $2,400 per month per worker and a worker-month of overtime costs them about $3,300. Additionally, the personnel department estimates that hiring, training and related expenses would amount to $1 ,800 per worker, whereas severance and other layoff expenses would cost a total of $1,200 per worker.
MR. also expect to have 240 finished units in inventory on to hold an appliance in inventory for a month during the next year. 2. 1 . Assumptions As we will be using a linear mathematical model that is a idealization of real life to obtain recommendations, we will explicitly state the simplifying assumptions and approximations made to allow us to use the model. A. We assume that the parameter values are know with certainty.
We assume that the following data are correct for every possible situation: ; The annual output per worker will be 480 appliances per year and no appliances need to be discarded ; The shipment forecast for every month is precise and reliable and the company will therefore not lose potential clients due to unexpected demand changes ; The master production plan is formulated correctly and has no additional implications for the aggregate plan ; There is no storage limit for the inventory ; There will be 240 units in inventory in the beginning of the next calendar year
The cost for storage will be $8 a month for each appliance ; The wage cost will be $2,400 for each worker ; The total hiring costs to employ a new working will be $1,800 for each new worker ; The total layoff costs will be $1,200 for each laid off worker ; A worker-month of overtime costs the company $3,300 ; There will be 160 workers employed at the start of the calendar year ; Workers will work 40 hours a week ; There will be no additional costs to take into account, such as fines, legal fees or time lost due to external or internal factors such as strikes. Potential new workers re available to the extent needed ; The required raw materials are readily available from regional resources on short notice ; No workers quit or miss work for extended lengths of time b. We assume that the returns to scale are constant We also assume that the returns to scale are constant within the range of possible values for the decision variables. The output of each worker is always 40 units per month, irrespective of hiring and layoffs ; A worker-month of overtime also yields 40 units every time, irrespective of other factors We assume that, although a different product mix will me made at different times of he year, there is no cost saving or extra cost involved due to product mix variations. In addition, we assume that overtime, hiring and firings do not affect performance or influence catheter in any way. 3. 1 .
Solution Approach We obtained three possible solutions, discussed further on, which are based on different approaches but not combining them. Therefore we should calculate the optimal solution, using certain constraints which we decide ourselves, in Excel using the solver and the Simplex ALP method. 4. 1. Results Three possible solutions were already suggested by Linda Metzger. In the first one (Exhibit 1), production level and workforce are held constant throughout the year at a level sufficient to meet the peak demand period.