A steel company operates a foundry. The foundry casts three types of steel rolls

Question

A steel company operates a foundry. The foundry casts three types of steel rolls that are machined in its machine shop. Machined rolls are used by other companies in their mills to manufacture various products. At the beginning of each quarter, the companies prepare their monthly needs of steel rolls and submit them to the foundry. The foundry manager then draws a production plan that is essentially constrained by the g capacity of the shop. The foundry can directly purchase the rolls at a premium price from outside sources. A comparison between the cost per roll when acquired from the foundry and its outside purchase price is given in Table 1. Unit shortage cost is shown in Table 1 as well. The processing time for each roll type is shown in Table 2. The estimated demand for the rolls is shown in Table 3. Table 1. Steel RollRegular Time Over Time CostOutsourcing Cost Shortage Cost Holding Cost ($ per roll) ($ per roll per Cost ( per roll) (S per roll) per rol month 90 130 180 100 135 188 108 145 194 90 130 180 4 2

Explanation / Answer

If there is a limit to the inventory that the factory can hold, say x units, then we have to put an additional constraint in our formulation which restricts the inventory to exceed x units. Rest of the formulation remains as it is.

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