The model is developed for a regional blood bank that would receive scheduled demand from affiliated hospitals. Using linear programming formulation to optimize the number of collected units to meet the daily demand. The model assumes the collection and demand are for whole blood units, for all eight types of blood; scheduled demand also is assumed to be of equal urgency to all hospitals and across all blood types. The constraints compel the model to keep the collection rate adequate to prevent the inventory from falling below a certain minimum level while taking into consideration storage capacity and compelling the collection not exceed this capacity. The objective function is designed to minimize the overall costs and wastage.
Other assumptions were also decided upon to help in guiding the formulation. For example, the initial inventory is set to be null. FIFO policy is assumed to be implemented to keep the inventory fresh, the shelf life of whole blood units is set to expire after 35 days (approximately five weeks) which is the assumed time horizon of the model. We also considered the unit cost includes the cost of collection, handling and storage. As it has been indicted before, not all collected samples are registered in the inventory; some samples are deemed invalid after collection. We assume that only 90% of collected units are to be included in the inventory. The feed to the blood bank is assumed to be available at certain quantities available for each blood type, from regular donors. The time horizon will span over five weeks; the collection is made daily based on scheduled weekly demand, collection proportion will vary based on demand for each blood type, week by week. We assume the weekly demand is about 700 blood units in total for all blood types, based on information received from the regional blood bank in Abu Dhabi.
Variables are denoted by indices that help in tracking the time when the collected unit is registered to the inventory; the first index (i) is used to denote the blood type, second index (t) is used to assign the week during the planning horizon period, and the third index (b) is used to indicate the day of the week. We also consider all variables to be of a positive value.
For each index, the range will be as the following :
\(i\ \in\left\{1,2,3..8\right\}\) since there are eight types of blood
\(t\ \in\ \left\{1,2,3..5\right\}\) since the planning horizon is five weeks
\(d\ \in\left\{1,2,3..7\right\}\) since there are 7 days in each week