3. Model and Notations
3.1 Description of the model
This research is focused on an IPDSP with a single product, single machine, multiple customers and batch delivery.
All customers are geographically distributed and every period (e.g. one day) has a fixed working time horizon (e.g. 8
hours). Every customer has a deterministic demand in each period and the plant must fulfill the customer demands
within the time horizon - backorders are not allowed. The plant has a fixed and sufficient capacity to satisfy the
demand in each period. The products have a constant lifetime, they are delivered after production without keeping
intermediate inventory and the delivery must be completed before the lifetime is exhausted. There is a truck fleet to
handle the distribution. Each truck starts its routes from the plant and fulfills all customers’ demand in the routes and
then returns to the plant. Spilt delivery is not allowed which means that every customer’s demand must be satisfied
by one truck on one stop. The capacity of each truck is fixed and if time allows, trucks can be assigned multiple
routes within the time horizon. Our objective is to satisfy all customers’ demand on time and minimize the total
transportation cost. This means determining the fleet size, each vehicle’s routes and plant’s production schedule