The operations manager for a local bus company wants to decide whether he should purchase a small, medium, or large new bus for

Question

1 month ago

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The operations manager for a local bus company wants to decide whether he should purchase a small, medium, or large new bus for

his company. He estimates that the annual profits (in $000) will vary depending upon whether passenger demand is low, moderate, or high, as follows:
(a) If he uses the maximin criterion, which size bus will he decide to purchase?
(b) If he uses the minimax regret criterion, which size bus will he decide to purchase?
(c) If he feels the chances of low, moderate, and high demand are 30%, 30%, and 40% respectively, which size bus will he decide to purchase and what is the expected annual profit for this option?

Bus size Demand
Low Medium High
Small 50 60 70
Medium 40 80 90
Large 20 50 120

Business

1 answer:

Scilla [3.2K] · Answer 1 · 2026-02-26T18:18:20+03:00

Answer:

a) the small bus

b) the medium or large bus

c) the small bus

Explanation:

a) using the maximin criterion, the manager aims to maximize the least possible profit (a pessimistic approach), which results in the following profits:

Bus size Demand

Low Medium High

Small 50 60 70 → minimum profit = 50

Medium 40 80 90 → minimum profit = 40

Large 20 50 120 → minimum profit = 20

Thus, the optimal choice yielding the highest minimum profit is the small bus.

b) applying the maximin criterion, the manager will seek to minimize potential maximum losses, determining losses based on the best profit scenario:

Bus size Demand

Low Medium High

Small 0 -20 -50 → maximum loss = -50

Medium -10 0 -30 → maximum loss = -30

Large -30 -30 0 → maximum loss = -30

Hence, the option that bears the least maximum loss is either the medium or large bus.

c) for calculating the expected value of each option:

small = 30/100*50 + 30/100*60 + 40/100*70 = 61

medium = 30/100*40 + 30/100*80 + 40/100*90 = 72

large = 30/100*20 + 30/100*50 + 40/100*120 = 69

The small bus turns out to be the best choice, as it has the highest expected profit.