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    Linear Programming Problem - The EnergyBoat Company

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    The Background

    The EnergyBoat, Inc. produces and distributes high quality motor boat with highly seasonal demand. To handle this seasonality, the company has several options for its supply chain aggregated planning purposes: hiring an additional workers during peak seasons, outsourcing part of the demand to a third party manufacturer, building up inventory during the slow months, or backorder the demand which will be delivered in the following month.

    To determine how to best use these options, the vice president of production and distribution started with the demand forecast over the next six months, as shown in the following table:

    Month Demand forecast
    May 2,000
    June 3,200
    July 4,000
    August 5,200
    September 2,500
    October 2,500

    EnergyBoat sells each product to retailer for $900. The company has a starting inventory at the beginning of May of 1,200 units. At the beginning of May the company has a workforce of 200 employees. The plant has a total of 20 working days in each month, and each employee earns $30 per regular hour. Each worker works 8 regular hours a day, if they work overtime, their hourly wage is $45/hour. The capacity of the plant is determined by the total labor hours worked. Therefore, machine capacities and raw materials do not limit the capacity of the production operation. Due to the labor rules, no employee will work more than 8 hours of overtime per month. The various costs are shown in the following table:

    Item Cost
    Material cost $120/unit
    Inventory Holding cost $20/unit/month
    Marginal cost of backorder $60/unit/month
    Hiring & Training $2000/worker
    Layoff cost $5000/worker
    Labor hours required 15 hours/unit
    Regular labor cost $30/hour
    Overtime labor cost $45/hour
    Cost of subcontracting $760/unit

    EnergyBoat has no limits on subcontracting, inventory storage and backorder. All backorders are supplied from the following months' production. Inventory costs are incurred based on the ending inventory of each month. The supply chain manager's goal is to obtain the optimal aggregate plan that allows EnergyBoat to end October with at least 1800 units in inventory.

    The Questions

    1. The optimal aggregate plan is the one that results in the highest profits over the six-month planning period. Given EnergyBoat's desire to maintain high customer service, all demands must be satisfied. Formulate the optimization problem and solve it.

    2. While the optimal production plan can be obtained, the vice president is concerned about several issues. One issue is the over-time labor cost, the union is considering raising the over-time wages from $45 to $47 in the coming contract. Given this becomes true, the vice president is wondering its impact on the optimal plan and the optimal profit, will the original optimal plan be still optimal? How much does the optimal profit change?

    3. The second issue is demand forecast which is generated by actual sales of the past several years. From previous experience, the forecasts are subject to errors, the vice president wants to know the impact of the forecast errors on the optimal profits, i.e., suppose the actual sales is slightly higher (lower) than the forecast, how will the optimal profit change? And in what range of the forecast error the rates of changes are valid?

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    https://brainmass.com/math/algebra/linear-programming-problem-the-energyboat-company-34286

    Attachments

    Solution Preview

    Hi see the attached file. Thanks

    1. The optimal aggregate plan is the one that results in the highest profits over the six-month planning period. Given EnergyBoat's desire to maintain high customer service, all demands must be satisfied. Formulate the optimization problem and solve it.
    The Problem is formulated in Excel and solved.

    2. While the optimal production plan can be obtained, the vice president is concerned about several issues. ...

    Solution Summary

    This problem solves the EnergyBoat Company case using linear Programming model in Excel using Solver add-in. The optimal solution and sensitivity analysis is presented.

    $2.19

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