What is the best ordering policy for a warehouse to minimize cost, while meeting demands? | ||||||||

The warehouse has a limited storage capacity of 50000 cubic meters (m3) and a budget of $30,000. | ||||||||

Holding Cost | Storage Space per unit (m3) | Demand per month | Ordering cost per order | Price per unit | ||||

Product 1 | $25 | 440 | 200 | $50 | $200 | |||

Product 2 | $20 | 850 | 325 | $50 | $300 | |||

Product 3 | $30 | 1260 | 400 | $50 | $275 | |||

Product 4 | $15 | 950 | 150 | $50 | $400 | |||

Storage Capacity | 50000 | Budget | $30,000 | |||||

Quantity to order each month | Cost of holding | Space | ||||||

EOQ | and ordering | used (m3) | ||||||

Product 1 | 25 | 28.28427 | $713 | 5500 | ||||

Product 2 | 25 | 40.31129 | $900 | 10625 | ||||

Product 3 | 25 | 36.51484 | $1,175 | 15750 | ||||

Product 4 | 25 | 31.62278 | $488 | 11875 | ||||

Cost of products | $29,375 | Total | $3,275 | 43750 | ||||

Problem | ||||||||

This model continues to build on the first inventory policy model. We expand the model by giving the warehouse a | ||||||||

budget for buying new products. In other words: A warehouse sells 4 products with a different demand for each | ||||||||

product. Each product has a different holding cost and requires a certain amount of space. What should the ordering | ||||||||

policy for the warehouse be, given its limited storage capacity and limited budget? | ||||||||

Solution | ||||||||

The variables are exactly the same as in the first model. So is the objective, and the way it is calculated. The | ||||||||

difference is that we have an extra constraint which keeps us within the budget. This new constraint is expressed as: | ||||||||

Cost_of_products <= Available_money and we also have | ||||||||

Space_used <= Available_space as before | ||||||||

We still have Quantities >= 0 via the Assume Non-Negative option. This time, we also require integer quantities: | ||||||||

Quantities = integer | ||||||||

Remarks | ||||||||

Once again, we have calculated the EOQs as discussed in the first inventory policy model. If we would give a | ||||||||

unlimited budget and unlimited storage space, the Solver would find exactly those values. | ||||||||

There is one more change we made in this model compared to the one on worksheet Invent1. This time we | ||||||||

required the variables to be integers. Whether this is a valid assumption would depend completely on the type of | ||||||||

product that is dealt with. If a model is trying to determine how many cars, airplanes or other such articles to buy, it | ||||||||

could be very important to use integer variables. If the model, on the other hand, is giving an indication how much | ||||||||

sugar to buy, for example, it would not be appropriate to use integer variables. | ||||||||