he Wilcox Manufacturing Company produces an item that is subject to wide seasonal fluctuations in sale. The forecasted demand for the next 6 months for the forthcoming year are given below: Jan 3000 Feb 5000 March 8000 April 9000 May 4000 June 2000 The firm must always meet the monthly demand requirements. It can fulfill the demand either by producing the required amount during the particular month or by producing only part of the required amount and making up the difference by using the overproduction (inventory) from previous months. The Accounting Department has estimated that it costs $2.00 to increase output by one unit from one month to the next and $1.00 to reduce output by one unit from one month to another. The monthly cost of storing 1 unit of product is $1.50. The warehouse capacity limits maximum inventory to 5000 units. The production capacity of Wilcox for any month is limited to 7000 units. The production schedule for the month of December in the current year calls for the production of 3000 units and it is estimated that the inventory level on January 1 will be 1000 units. The problem is to determine the optimal production schedule for the Wilcox Company for the forthcoming year. Formulate this as an optimal control problem as follows: Define your variables clearly. Identify the state variables and the control variables. Write down the constraints that must be satisfied each month briefly describing the significance of each. Write down the objective function to be optimized. Show that the optimal control problem can be reduced to a linear programming problem.
The Wilcox Manufacturing Company produces an item that is subject to wide seasonal fluctuations in sale. The
Jan 3000
Feb 5000
March 8000
April 9000
May 4000
June 2000
The firm must always meet the monthly demand requirements. It can fulfill the demand either by producing the required amount during the particular month or by producing only part of the required amount and making up the difference by using the overproduction (inventory) from previous months.
The Accounting Department has estimated that it costs $2.00 to increase output by one unit from one month to the next and $1.00 to reduce output by one unit from one month to another. The monthly cost of storing 1 unit of product is $1.50. The warehouse capacity limits maximum inventory to 5000 units. The production capacity of Wilcox for any month is limited to 7000 units. The production
The problem is to determine the optimal production schedule for the Wilcox Company for the forthcoming year. Formulate this as an optimal control problem as follows:
- Define your variables clearly. Identify the state variables and the control variables.
- Write down the constraints that must be satisfied each month briefly describing the significance of each.
- Write down the objective function to be optimized.
- Show that the optimal control problem can be reduced to a linear programming problem.
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