Customer Information Driven After Sales Service ... - RePub

typically observed in spare parts logistics situations.
4.3 Problem Formulation
4.3. Problem Formulation
In this section, we introduce our notation and provide a more formal problem description.
Next, we present an MDP formulation for the current problem setting.
4.3.1 Problem Description and Notation
In accordance with figure 2.7 in Section 2.7.1, we consider a two tier inventory network
with one supplier in the top tier and n FSLs of finite capacity in the bottom tier. Figure
4.1 depicts a schematic diagram of the inventory system with three FSLs and a
supplier. At regular intervals (agreed upon between the supplier and service provider),
the part shipments from the supplier arrive. The service provider uses these parts to
replenish its FSL locations. The stocked spare parts at FSLs are further utilized to fulfil
incoming demand requests. Between two regular shipment arrivals from the supplier,
the service provider can also request an emergency part shipment from the supplier, albeit
at an emergency shipment rate. In the current execution scheme, these emergency
shipments are only ordered when the FSL network is out of stock (see Section 2.7.1 for
details). We however attempt to relax this assumption in our approach.
All of the customers are dispersed at various geographical locations. The demand
follows an independent Poisson process requesting one part at a time. Note that
the part may represent a kit of spare parts fit for satisfying (generic) customer
requests. A demand arrival can be fulfilled from any of the FSLs at regular transportation
costs. The regular transportation costs are linearly increasing in distance
with a fixed cost component. Upon demand fulfillment, each customer is charged a
price as per their contractual agreement. The notation for the above setting is as follows:
Notations
Sets
N = Set of customers (indexed by j)
M = Set of source locations (indexed by i, withi = 0 for supplier and i ∈{1, 2, 3,...}
for FSLs)
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