The Value of the Multi-period Solution revisited: When to model time in capacitated location problems

Abstract

Location decisions are often long-lasting and multi-period models have received considerable attention. The price to pay for the increased flexibility in decision-making is an increase in complexity. When facilities are capacitated, multi-period models impose additional restrictions regarding when to use resources. The value of the multi-period solution (VMPS) was introduced to quantify the benefit resulting from shifting to a multi-period model by setting its objective value in relation to that of a static counterpart. As the latter is not uniquely defined, different types of VMPS are reported in the literature. In the present study, we show that different static counterparts require different interpretations and evaluate different aspects of the aforementioned trade-off. We discuss which characteristics of the problem data result in decision-makers benefiting from the added flexibility of multi-period modeling. Thereby, we show that rather than the degree to which the problem parameters change over time, the degree to which the multi-period model allows to reduce relevant cost components determines the value of a multi-period approach.