VG441 Homework 2 solution


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Problem 1
An company uses 500 tons of steel per day. Suppose that the steel supplier offers the
company a price of $1490 per ton of steel if Q < 1200 tons; $1220 per ton if 1200 ≤
Q < 2400, and $1100 per ton if Q ≥ 2400. Each order incurs a fixed cost of $2250.

The annual holding cost rate, i, is 0.25. (You will need to divide 0.25 by 365 to get the
daily holding cost rate.) Calculate optimal order amount and total cost for the all-units
discount structure and the incremental discount structure.

Problem 2
Suppose there are demands for next 52 periods (demand.xlsx ). Each order palced to the
supplier incurs a fixed cost of $1100. One unit of product held in inventory for one period
incurs a holding cost of $2.40. Find the optimal order quantities in each period and the
optimal total cost.

There are three ways that you can solve the problem:
• Mixed integer linear Programming
• Dynamic programming

• Reformulation as a shortest path problem and use Dijkstra’s algorithm

You can utilize the codes posted on canvas and modify them to suit your need.

both code and result using at least one method, but you are welcome to submit all three.