Acme Inc. sources a key component used in its product from ABC Enterprise. Based on Acmes production

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Question:

Acme Inc. sources a key component used in its product from ABC Enterprise. Based on Acme’s production schedule they require the component in the following quantities over the next 6 months.

1 2 3 4 5 6

Items Required 1,850 1,550 1,475 1,800 1,360 1,860

ABC ships this component in 3 standard cases with discounts offered on larger cases.

Items/Case Unit Cost Case Cost

Small 50 10.00 500

Medium 100 9.50 950

Large 250 9.00 2250

- In addition to the purchase cost ABC incurs a holding cost for the inventory items left over at the end of the month of $10 per unit. The on-hand balance of the item is currently 0. A material planner for ABC is attempting to develop an ordering plan for this item that minimizes total costs. Do the following:

- Download the shell for this model from Canvas.

- Complete the descriptive model
- Calculate the number of items ordered by multiplying the number of cases ordered by the case size.
- Calculate the purchase cost by multiplying the number of cases ordered by the case cost.
- Calculate the carrying cost on inventory by multiplying the ending balance by $10.

- Formulate the decision problem as an LP relaxation (i.e. a problem without integer constraints) with the following constraints

- Order quantities are non–negative.
- Monthly ending balance is greater than or equal to 0

- Solve the model and report the following
- Average on hand balance
- Total # of cases ordered by size (small, medium, large) Purchase cost, holding cost, and total cost

- Now apply integrality restrictions by manually rounding the order quantities in each month. Work from month 1 to 6, round down when you can but make sure that a non-negative balance is maintained. (Only round non-zero items.) Report inventory, ordering, and cost information from your manual solution.

- Now apply integrality constraints on the model and use Solver to solve the integer program. Report inventory, ordering, and cost information from your solution.