Q1. Hayes Electronics stocks and sells a particular brand of personal computer. It costs the firm $450 each time it places an order with the manufacturer for the personal computers. The cost of carrying one PC in inventory for a year is $170. The store manager estimates that total annual demand for the computers will be 1,200 units, with a constant demand rate throughout the year. Orders are received within minutes after placement from a local warehouse maintained by the manufacturer. The store policy is never to have stockouts of the PCs. The store is open for business every day of the year except Christmas Day. Determine the following:
The optimal order quantity per order
The minimum total annual inventory costs
The optimal number of orders per year
The optimal time between orders (in working days)
Q2. Hayes Electronics in Problem 1 assumed with certainty that the ordering cost is $450 per order and the inventory carrying cost is $170 per unit per year. However, the inventory model parameters are frequently only estimates that are subject to some degree of uncertainty. Consider four cases of variation in the model parameters: (a) Both ordering cost and carrying cost are 10% less than originally estimated, (b) both ordering cost and carrying cost are 10% higher than originally estimated, (c) ordering cost is 10% higher and carrying cost is 10% lower than originally estimated, and (d) ordering cost is 10% lower and carrying cost is 10% higher than originally estimated. Determine the optimal order quantity and total inventory cost for each of the four cases. Prepare a table with values from all four cases and compare the sensitivity of the model solution to changes in parameter values.
Q4. The Western Jeans Company purchases denim from Cumberland Textile Mills. The Western Jeans Company uses 35,000 yards of denim per year to make jeans. The cost of ordering denim from the textile company is $500 per order. It costs Western $0.35 per yard annually to hold a yard of denim in inventory. Determine the optimal number of yards of denim the Western Jeans Company should order, the minimum total annual inventory cost, the optimal number of orders per year, and the optimal time between orders.
Q6. The Simple Simon Bakery produces fruit pies for freezing and subsequent sale. The bakery, which operates 5 days per week, 52 weeks per year, can produce pies at the rate of 64 pies per day. The bakery sets up the pie production operation and produces until a predetermined number (Q) of pies has been produced. When not producing pies, the bakery uses its personnel and facilities for producing other bakery items. The setup cost for a production run of fruit pies is $500. The cost of holding frozen pies in storage is $5 per pie per year. The annual demand for frozen fruit pies, which is constant over time, is 5,000 pies. Determine the following:
The optimal production run quantity (Q)
The total annual inventory costs
The optimal number of production runs per year
The optimal cycle time (time between run starts)
The run length, in working days
Q12. The purchasing manager for the Atlantic Steel Company must determine a policy for ordering coal to operate 12 converters. Each converter requires exactly 5 tons of coal per day to operate, and the firm operates 360 days per year. The purchasing manager has determined that the ordering cost is $80 per order and the cost of holding coal is 20% of the average dollar value of inventory held. The purchasing manager has negotiated a contract to obtain the coal for $12 per ton for the coming year.
Determine the optimal quantity of coal to receive in each order.
Determine the total inventory-related costs associated with the optimal ordering policy (do not include the cost of the coal).
If 5 days of lead time are required to receive an order of coal, how much coal should be on hand when an order is placed?