I am currently working on a project called the supply chain game. We control a factory that produces chemicals. Below is the information we are given to calculate costs. I want to know at what # of barrels currently being held in a warehouse triggers production at our factory. For example when our warehouse gets down to "x" barrels our factory will begin another batch. We currently have a capacity of 70 batches a day. We are also trying to decide how many barrels should be produced in each batch. Also, can you give me a formula that can do forecasting with this information? I don't think I have all the information I need to do farecasting how much inventory I will have in 365 days or how much profit.

Production

A factory can only produce one batch a time. The more capacity a factory has, the faster it produces a batch of a given size. The cost of a factory building is $500,000 regardless of the factory capacity. The cost of factory equipment and fixtures is proportional to capacity: Capacity of one drum per day costs $50,000. For example, the cost to build a new factory with a capacity of 5 drums per day is $500,000 + (5)$50,000 = $750,000. Adding an additional capacity of 2 drums per day later would cost (2)50,000 = $100,000.

It takes 90 days to either construct a new factory or to add capacity to an existing factory. The cost of the factory is incurred as soon as construction begins. Capacity cannot be retired.

Production in factories is carried out in batches, where each batch is an integer number of drums set by you. The cost to produce one batch equals $1500 plus the number of drums in the batch times $1000. For example, the cost to produce a batch of 10 drums is $1500 + (10)$1000 = $11,500.

Warehousing

A new warehouse costs $100,000. There is no practical limit to the number of drums a warehouse can hold. It takes 60 days to build a warehouse and the cost of the warehouse is incurred as soon as construction begins.

Jacobs pays insurance and other out-of-pocket holding costs on chemicals once production is complete. These holding costs for one drum for one year is $100, whether the drum is en route to a warehouse or the drum is physically in a warehouse. There are no such holding costs for work-in-process inventory in the factory.

Transportation

Finished drums are shipped from the factory to the warehouse as soon as production is completed. The drums can be shipped by either truck or mail. One truck can carry 200 drums. If the batch is less than 200 drums, then less than a truckload will be used. The cost of full or less-than-full truckload is the same. If drums are shipped by mail, the shipping cost is proportional to the number of drums being mailed.

Transportation costs are as follows:

Origin and Destination	Cost per Truckload	Cost to Mail One Drum
Same region	$15,000	$150
Different regions on continent	$20,000	$200
Between continent and Fardo	$45,000	$400

Transportation times are as follows:

Origin and Destination	Truck	Mail
Same region	7 days	1 day
Different regions on continent	7 days	1 day
Between continent and Fardo	14 days	2 days

Financial

All customers will pay $1450 per drum. The drum must be shipped within 24 hours of receiving the order or the order is lost. Warehouses may partially fill orders and one order may be filled from multiple warehouses.

All order fulfillment is by mail, so the cost to fulfill an order is:

• $150 per drum if the order is in the same region as the warehouse
• $200 per drum if the order and the warehouse are in different regions on the continent
• $400 per drum if the order is on Fardo and the warehouse is on the continent, or the order is on the continent and the warehouse is on Fardo.

Interest accrues on cash at 10% per year, compounded daily.