The MAX function of equations 2 and 3 ensures that bed acquisitions and orders are constrained to be nonnegative. Generally, hotel managers cannot simply add new beds to a hotel as they wish. Acquiring new beds involves time lags and delays, and requires resources. Hotel construction, for example, requires labour and equipment. If it assumed that there is ample process capacity, then the only delay in acquiring new beds entails an acquisition lag, the acquisitions rate depends on the supply chain (SC) that has been ordered but not yet received and the acquisition lag.
The stock to be controlled by hoteliers, hotel Bed Capacity (Eq. 4), is the accumulation of the acquisitions rate (Eq. 3) less the depreciation rate. For simplicity, the stock of beds is assumed to depreciate at a constant rate (Eq. 5).
Bed Capacity (t) = Bed Capacity (t – dt) + (acquisitions – depreciation)*dt where Depreciation = Bed Capacity / average bed life
Decision rules for the SCM Sector In the decision rules structure, hoteliers and hotel managers place orders to replace depreciated hotel beds (Eq. 5) as wells as any discrepancy between desired bed capacity and actual BC (Eq. 7). Where desired bed capacity is a function of the target bed-to- tourist ratio and the annual number of stopover visitors (Eq. 9). The acquisition lag forces them to maintain an adequate supply of unfilled orders, so that bed acquisitions are close to desired acquisitions (Eq. 6). Hence, the orders rate represents an anchoring and adjustment process (Eq. 7). Similarly, the suppliers of beds to hoteliers must adjust their Supply Chain analogously to how hoteliers adjust their bed capacity. They must also set their desired supply chain (SC) according to the expected acquisitions lag, which could generally differ from the actual acquisition lag.
Desired Acquisitions = MAX (0, depreciation + adjust BC)
Adjust BC = (desired bed capacity – Bed Capacity)/ bed capacity adjustment time