help with operation management homework

supply chain

A vacuum cleaner manufacturer tries to "plan ahead" in order to effectively address the seasonal variation appearing in the annual demand of its products. A planning horizon of 6 months is used. The monthly demand data Di, where i=1,2,3,4,5 and 6 is given. The manufacturing company currently employs 38 workers. It takes a worker 5 hours to make a unit and workers are paid $15/hour. The company works 20 days a month, 8 hours a day. The material cost is $100/unit. The marginal cost (excluding material cost) of subcontracting is $80/unit. The cost of carrying a unit in inventory from one month to the next is $5/unit. The inventory at the beginning is lo units. The decision variables are defined as follows: W: workforce size for month t,t=1,...,6 Pti number of units produced in month t,t=1,...,6 It: inventory at end of the month t, t=1,...,6 Cti number of units subcontracted in month t, t=1,...,6 1. Assuming no new hires, no layoffs, and no overtime by the policy. No stockout is allowed and the month ending inventory cannot exceed 25% of the demand in that month. 1.a. Formulate the total cost that the company is trying to minimize. Substitute data where applicable. (5 points) 1.b. What are the constraints? (5 points) 2. Assuming the company aims for a chase strategy, the cost of hiring is Ch and the cost of layoff is Ciper worker. 2.a. What decision variables should be added? (4 points) 2.b. What changes should be made in the formulation from part 1 (both objective function and constraints)? (6 points) 3. Due to the uncertainty of the economy, the cost parameters may change over time. They predicted that the labor cost (pay of the workers for the in house option) can either go up by 20% or go down by 10% with an equal chance over the next two ye The cost of subcontracting will remain the same (by contract) over the next two years. Assume the demand will remain stable explain briefly how would the uncertainty change the coefficients of the objective function and the total cost? (5 points)