Functions & Formulae

Each applied formula has its own function page, with a signature, implementations, and tests.

Capacity utilisation of a health service with plant capacity measured on a frontier

g(E_F, E_V) = PI

Maps a health service's use of its capacity to a capacity utilisation figure. The simple measure in the article, capacity used over capacity available in the same units and period times 100, is a plain proportion of the form of the first part of HE-FM-PR-001, P_1 = a / (a + b), with a the capacity used and b the spare capacity, and of HE-FM-PDC-001, so it is not restated. Its bed form, occupied over available bed-days, is the occupancy o defined in HE-VR-ALOS-006 and used in HE-FM-ALOS-002, HE-FM-BTO-003 and HE-FM-BTO-004, and the empty bed-days of a period are the numerator of HE-FM-BTO-002. The fixed cost of a bed spread over the patients it served is HE-FM-BTO-005, the break-even volume of a service with fixed costs is HE-FM-BEA-002, annualised capital cost is HE-FM-COST-003 and HE-CF-ANLS-001, and the utilisation of a single-server queue is rho in HE-FM-ARRP-005. The average cost form AC = F / Q + v of the article belongs to the average-cost concept. HE-FM-CAPU-001 is plant capacity utilisation in frontier analysis, which divides the output efficiency of a unit when only its fixed inputs constrain production by its output efficiency when all inputs do, so that technical inefficiency (HE-FM-EFF-001) is set aside before unused plant capacity is measured. It is built like scale efficiency HE-FM-EFF-003 but compares a different pair of frontiers. Notation follows the Capacity Utilisation article, which describes the plant capacity measure in words, with the symbols of Valdmanis and colleagues.

  • Plant capacity utilisation from output efficiency with fixed inputs and with all inputs

    PI = E_F / E_V

    Divides the output efficiency score of a hospital or other unit measured with only its fixed inputs, such as beds and rostered staff, constraining output and its variable inputs unrestricted, by its output efficiency score with all inputs constraining output, both from one data envelopment analysis under constant returns to scale. The all-input score E_V carries the technical inefficiency of the unit, so dividing by it leaves the part of the shortfall from capacity output that is due to unused plant, the Johansen definition of plant capacity that Valdmanis and colleagues adopt. A value of 1 means that the unit, once on the frontier, could not raise its outputs in proportion without more fixed inputs, and a value below 1 shows unused plant capacity that could treat proportionately more patients. In 68 Thai public hospitals in 1999 the mean was 0.954. Unlike a bed occupancy ratio, the measure sets outputs against what the fixed inputs could produce.

Capacity Utilisation — Functions & Formulae | HealthEconomics.wiki