Question

The management at Hackney's Southwestern Regional (HSR) are interested in determining the optimal fleet purchase mix for the coming year. There are four types of vehicles that can be purchased: standard, intermediate, compact and subcompact. All cars purchased are depreciated and paid off for over a two-year period, after which they are sold in a secondary market. Table 1 presents the wholesale purchase price and revenues (the second year includes the resale value)

Type	Price ($)	1st yr. ($)	2nd yr. ($)
Standard	20,000	14,000	23,000
Intermediate	15,000	9,000	15,000
Compact	12,000	7,000	13,000
Subcompact	9,000	5,000	9,000

HSR has established a budget of $5 million for funding the purchases this year. It can either pay the entire amount for the cars or make a down payment and pay the remaining balance over a two-year period. The financing company requires at least a 20% down payment and that at least 50% of the purchase price plus interest must be paid by the end of the first year. The financing company is currently charging 8%. HSR uses a 10% discount rate for financial planning. Hackney management estimates that they can rent all of the cars that are purchased. However, in order to meet overall market demand they wish that each vehicle category represent at least 15 percent and no more than 50 percent of the total number of vehicles purchased.

a. Formulate a linear programming model for this problem.

b. Define the basic assumptions associated with this problem.

Answer 1

Please refer calculations below:

d) Given the NPV of various options, for a good mix, we should maximize options giving highest NPVs. Hence mix should be 50% standard, 20% Intermediate, 15% compact and 15% subcompact. This will be the case even if financing charge becomes 6%

e) there seems to be some missing data for this part- otherwise, if 25% is the lease requirement for each car, then it should be standard/intermediate/compact/subcompact- each to be 25%

	Dec-16	Dec-17	Dec-18			Total budget	5000000
	Purchase price	Revenue	Revenue +Resale			Down payment	20%
Standard	20000	14000	23000			Year 1 repayment	50%	of principal+ interest
Intermediate	15000	9000	15000			Y
						Interest rate	8%
						discount rate	10%
Standard car	Dec-16	Dec-17	Dec-18
Downpayment	-4000					Summary of NPV
Principal repayment	0	-8000	-8000			Standard	12159
Interest	0	-1280	-640			Intermediate	5896
Inflows	0	14000	23000			Compact	5361
Net Cash flow	-4000	4720	14360			Subcompact	3174
NPV	12158.68
Intermediate car	Dec-16	Dec-17	Dec-18
Downpayment	-3000
Principal repayment	0	-6000	-6000
Interest	0	-960	-480
Inflows	0	9000	15000
Net Cash flow	-3000	2040	8520
NPV	5895.87
Compact car	Dec-16	Dec-17	Dec-18
Downpayment	-2400
Principal repayment	0	-4800	-4800
Interest	0	-768	-384
Inflows	0	7000	13000
Net Cash flow	-2400	1432	7816
NPV	5361.32
Subcompact car	Dec-16	Dec-17	Dec-18
Downpayment	-1800
Principal repayment	0	-3600	-3600
Interest	0	-576	-288
Inflows	0	5000	9000
Net Cash flow	-1800	824	5112

NPV 3173.88