12.2 The Silver Lining Creamery is a small boutique ice cream parlor in Rapid City, SD. They produce all of their ice cream on site and, in addition to having traditional flavors like chocolate and vanilla, they create unique flavors like honey lavender and peanut butter-Oreo.

In this chapter, you learned about calculating the Economic Order Quantity (EOQ). This model is also applicable when determining how much to produce at one time or what is called the Economic Production Quantity (EPQ). In the EOQ, the order amount Q is replaced by the production amount Q and the fixed cost of placing an order is replaced by the fixed cost of a production run or batch.

Suppose you run an ice cream parlor that produces its own ice cream similar to Silver Linings.

You are trying to determine how many gallons of chocolate ice cream you should make in one production batch during the summer months.

Each month, your demand will be 100 gallons of chocolate ice cream. You can make up to 100 gallons of ice cream in a production batch; however, once production is stopped, the machine must

be cleaned and a few parts and inputs changed out for the next production batch. It takes one worker an hour to clean the machine and the cost of replacement parts and inputs for each batch is $5. You pay your workers $12 per hour.
You could produce 1 batch of 100 gallons each month; however, there are also some costs associated with storing larger quantities of ice cream.
Each additional gallon of ice cream in inventory costs $0.50 in refrigeration costs. Your firm also has a high quality reputation due to not serving ice cream that is too far past its production date. Approximately 20 percent of ice cream in the freezer must be thrown out or given away to maintain this quality standard. Each gallon of ice cream costs $10 to produce.
Use this information and the template provided to determine the EPQ.

a. Use the given information to put the per gallon carrying costs, per batch production costs, and monthly demand in the template.

b. Start by assuming 1 batch per month (as discussed above) and use a formula to calculate the number of Q (gallons) per batch. Use this number and the formulas provided in Chapter 12 to calculate monthly carrying costs of refrigeration and spoilage in the template. Use the number of batches per month to calculate monthly costs of labor and supplies. Be sure to use cell references in your formulas. Find the total carrying and fixed production costs.

c. Is 100 gallons per production batch the EPQ for this situation? If no, should the EPQ be higher or lower?

d. Increase the number of batches to 5. How many gallons are produced in each batch?
Did total costs increase or decrease by increasing the number of batches?

e. Use Solver to minimize total costs by changing the number of batches per month; be sure to add the constraint that the number of batches must be an integer. What is the EPQ? How many batches per month are needed to attain this EPQ? What are the total costs for this EPQ?

f. Suppose demand for chocolate ice cream decreases to 60 gallons per month because you introduce a number of other new flavors.
Change demand and repeat part e.

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Cost Type 3 Refrigeration Costs 4 Spoilage Costs 1 8 12345670 5 Total Carrying Costs 6 7 B C Carrying Costs Per Gallon Per Production Q Fixed Costs of a Production Batch Cost Type Per Batch Per Number of Batches 9 Post Batch Labor 10 Post Batch Supplies 11 Total Proudction Costs 12 13 14 Total Carrying and Fixed Prodution Costs 15 Monthly Demand 16 Number of Batches Per Month 17 Production (Gallons) Per Batch