Flexible serial capacity allocation with intensive care application

Abstract

Serial delay structures are of natural and practical interest, as in production, communications and health care. Flexible service allocation might well be beneficial, particularly to handle overflow. The availability of bed capacity for Intensive Care (IC) provision was prominent in hospitals during the corona period. By integrating an Intensive Care Unit (ICU) with a flexible Step Down Unit (SDU) for intensive care overflow, IC availability might be greatly enhanced. This will lead to an unsolvable system that has to be evaluated by numerical computation (or simulation). First, as an approximate modeling and from a computational point of view, it is shown that by an artificial capacity flexibility principle, related to a principle known for parallel structures within telecommunications, an analytic so-called product form expression can be obtained for a flexible serial structure, such as an ICU-SDU complex. The principle will be referred to as serial repositioning (SR). The analytic form appears to be of both theoretical and computational interest. Theoretical as the closed form expression under this principle seems new for a serial structure. For indistinguishable intensive care at the ICU and SDU it is also proven to be insensitive, i.e. to only depend on the IC service by its mean. Computational as it provides easily computable estimates and bounds. For distinguishable overflow services, in contrast, insensitivity is numerically shown not to hold. Nevertheless, from a practical point of view, the insensitivity appears virtually true. Throughout numerical support is provided for small and realistic scale. It shows that the result •provides a reasonable first order of magnitude approximate,•supports an intuitive notion of bounds,•strongly reduces computational times and leads to qualitative results. For example, it shows that full flexibility for overflow service might be most useful but not necessarily required. A reallife academic hospital case is numerically studied. It illustrates that just a small number of flexible beds can well be beneficial. The results can be seen as representative for ICU-SDU dimensioning itself as well as for possible application to other serial structures, such as in flexible manufacturing.