The Horn Shoe Company

The Horn Shoe Company, a firm primarily producing women’s shoes in several factories throughout the country, is adding temporary workers to produce its new Fall line of shoes. The company projects that it will need 200,000 additional pairs of shoes for May, 300,000 for June, 270,000 for July, and 150,000 for August. Horn can hire both experienced and novice workers on a temporary basis. After one month with appropriate training on the job novice workers are classified as apprentices; after two months, they are considered “experienced” workers. Cost and productivity estimates for temporary workers are as follows:

Novice Apprentice Experienced

Costs of:

Hiring$200 — $500

Training $ 800/month $ 100/month —

Salary $1000/month $1200/month $2000/month

Termination $ 250$ 500 $ 700

Productivity

Pair of shoes400/month 600/month 800/month

The hiring of a temporary worker takes place at the beginning of a month, and the termination at the end of a month. All temporary workers must be terminated by the end of August.

Each month, for the purpose of training and to help in supervision, management requires that at least 20% of all workers will be experienced; however because of market supply this number cannot exceed 50% of all the workers (each month).

Assignments:

a.Formulate a linear programming that helps find an optimal hiring/termination policy over the four month period which minimizes Horn’s total costs while meeting the additional production requirements.

Formulation Hint: Define the following variables for each month:

• Number of novices hired for the month

• Number of experienced workers hired for the month

• Total number of apprentices during the month

• Total number of experienced workers during the month

• Total number of novices terminated at the end of the month

• Total number of apprentices terminated at the end of the month

• Total number of experienced workers terminated at the end of the month

Be sure to include constraints for each month expressing:

(Total experienced workers in month i) =(Number of experienced workers hired in month i)+(Experienced workers carried over from month i–l)+ (Fill in the blank… from month i–l)

and

(Total Number of apprentices in month i) =Who becomes an apprentice in month i?

These are not the only constraints.

  1. Prepare a report that summarizes your recommendations for the hiring/termination plan, and details the various costs for each month.
  2. Include an analysis of the effects several changes might have on the total costs and the optimal plan. Follow the guidelines provided:

a)Management is interested in the insight you can provide about the effect adding training to apprentice workers might have on your recommended plan. You are asked to consider each month separately. This analysis should show the changes in total cost as a function of the training costs each month. You can draw graphs of Total cost vs. Training cost. Management is especially interested in the answers to the following questions:

  1. Would you change your recommended hiring/termination plan if at any given month $100 will be spent on training each apprentice? Answer without re-running if possible.
  2. If $100 per apprentice are spent on training apprentices in any given month,in which month do you recommend it is done from total cost point of view alone,without changing the recommended optimal plan? Answer without re-running the model.

b)Management expressed a desire to check the re-allocation of the hiring costs for novices and experienced workers.The plan is to spend $25 less on hiring a novice, and $25 more on hiring an experienced worker in all months.

  1. If all these changes are implemented at the same time would you change your optimal hiring/termination plan? (You need to consider them all together). Do not re-run the model if possible.
  2. Management has raised an interesting question. If the amount saved on hiring a novice is spent on hiring an experienced worker every month, and if indeed the current recommended plan should stay, is $25 really the maximum trade-off amount? If not then what is the maximum amount that can be traded-off between the hiring costs of novices and experienced workers that will keep the current solution still optimal?

c)One more concern was the demand for shoes. Management realizes that deviationsfrom the projected demand are not unusual. One possible scenario management is asking you to analyze is that the demand in the months May through August oscillates around the current figures. Specifically, in May the demand will be 2000 pairs below the one currently projected, in June 2000 above, in July 2000below, and in August 2000 above. What will be the total cost of the new optimal plan? Answer without re-running if you can. Show your work.