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Report on Inventory Models

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Mercury Corporation Inventory Decision:
Mercury Corporation manufactures running shoes. The factory is open 250 days a year. Mercury currently buys the laces for its shoes from Ti-Rite Company, but is considering manufacturing the laces in-house. Mercury's contract with Ti-Rite specifies a base price per lace of $0.05. Ti-Rite has offered the following quantity discount schedule: (see attached document for schedule)

Annual demand for laces at Mercury is estimated to be 500,000. The cost to place an order with Ti-Rite is $100. The lead time for delivery is 10 working days. If Mercury begins in-house production of laces, it will incur a production cost of $0.0465 per lace. The setup cost for each production run will cost $600. The annual holding cost for each lace is $0.01.

Managerial Report:
You have been hired as a consultant to analyze the alternatives available to Mercury.
Prepare a report for the management of Mercury Corporation that summarizes your findings. Include the following:

1. Determine the optimal order quantity, reorder point, cycle time, annual holding costs, annual ordering costs, annual purchasing costs, and total annual costs if Mercury purchases the laces for Ti-Rite.
2. Determine the optimal production lot size, length of a production run, cycle time, annual holding costs, annual ordering costs, annual purchasing costs, and total annual costs if Mercury begins producing the laces in-house.
3. Make a recommendation to management as to whether Mercury should begin producing the laces in-house or continue purchasing the laces from Ti-Rite.

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Linear programming model for bicycle manufacturer

A bicycle manufacturer is determining its production schedule for the next 6 months. Assume that it costs this company $150 to manufacture each bicycle. At the end of each month, a holding cost of $35 per bicycle left in inventory is incurred. No more than 40 bicycles can be stored in inventory at any point in time. Monthly demands for bicycles are projected to be as follows: 150 in month 1; 175 in month 2; 165 in month 3; 156 in month 4; 169 in month 5; and 178 in month 6. Assume that at the beginning of month 1, 10 completed bicycles are in inventory. Finally, this company can produce up to 170 bicycles per month. Formulate and solve a linear programming model to find a cost-minimizing production schedule that meets all demands on time.

Answer the following questions:
3.1) Write down the decision variables.

3.2) Write down the optimization statement for the objective function.

3.3) Write down the constaints.

3.4) With Excel Solver, what is the optimal production schedule? (Please hand in a printed copy of the report)

3.5) By Excel Solver, what is the sensitivity report? (Please hand in a printed copy of the report)

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