Part B: Problem Solving Problems

1. An assembly plant of an auto manufacturer uses parts from many suppliers and is deciding on a policy for the use of TL or LTL transportation for inbound shipping. LTL shipping costs $1.2 per unit. TL shipping costs $1200 per truck plus $80 per pickup. Thus, a truck used to pick up from four suppliers costs $1200+(4×$80)=$1520. A truck can carry up to 2,500 units. The assembly plant incurs a fixed cost of $150 for each order placed with a supplier. Thus, an order with four distinct suppliers incurs an ordering cost of $600. Each unit costs $60, and assembly plant uses a holding cost of 20%. Assume that product from each supplier has an annual demand of 5,000 units. The assembly plant has hundreds of suppliers and must decide on the number of suppliers to group per truck if using TL.

a. Determine the optimal order quantity (round to whole unit),the annual ordering cost, the annual holding cost, the annual shipping cost, and total relevant cost for each supplier if LTL shipping is used.Also determine the time between orders in months. (5)

b. Determine the optimal order quantity(round to whole unit), the annual ordering (including shipping) cost, the annual holding cost, and total relevant cost if TL shipping is used with a separate truck for each supplier.Also determine the time between orders in months. (5)

c. Determine the optimal number of orders, the optimal order quantity (round to whole unit), theannual ordering cost, the annual holding cost and the total annual relevant cost per supplier if TL shipping is used but two suppliers are grouped together per truck. Also determine the time between two orders in months. (5)

d. Determine the optimal number of orders, the optimal order quantity (round to whole unit), theannual ordering cost, the annual holding cost and the total annual relevant cost per supplier if TL shipping is used but five suppliers are grouped together per truck. Also determine the time between two orders in months. (5marks)

2. Weekly demand for breakfast cereals at a grocery store is normally distributed with a mean of 260 boxes and a standard deviation of 80 boxes. The store manager continuously monitors inventory and currently orders 1,000 boxes each time the inventory drops to 600 boxes. The supplier currently takes weeks to fill an order.

a. Determine the safety inventory that the store carries. (4)

b. Determine the cycle service level(CSL)thatthe store achieves as a result of this policy. (4)

c. Determine the fill rate that the store achieves. (4)

d. Assume that the supply lead time from the supplier is normally distributed with a mean of weeks and a standard deviation of weeks. Determine the safety inventory the storeshould carry if it wants to provide a . (4)

e. Determine the required safety inventory when the standard deviation of lead time is reduced from 1.5 weeks to 0.5 weeks. (4)

3. Home Improvementcarries a snow blower in the winter. A snow blower costs $285 and sells for $395. One order is placed at the beginning of the season. Currently, Home Improvement disposes of any unsold snow blowers at the end of the season to outlet stores at $250. It costs $35 to hold a snow blower in inventory for the entire season. Demand for snow blowers has been forecast to be normally distributed, with a mean of 1,800 and a standard deviation of 650.

a. Determine the optimal number of snow blowers thatHome Improvementshould order for the season, assuming a single order. (6)

b. Determine the expected profit from this policy. (7)

c. Determine the expected overstock at the end of the season that will be sent to outlet stores. (7)

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