Multi-echelon Inventory Control with Integrated Shipment Decisions

Olof Stenius

Research output: ThesisLicentiate Thesis

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Rising fuel prices and increasing environmental awareness emphasizes the
importance of the transportation aspect in logistics. This calls for new improved
inventory control methods that consider the effects of shipment strategies in a
more realistic manner. This thesis, consisting of an introduction and three
scientific papers, studies how shipment decisions can be included in the inventory
control of distribution systems. The systems studied in the papers consist of a
central warehouse that supplies goods to a number of retailers that face stochastic
customer demand.
The first two papers consider a system where shipments from the central
warehouse are consolidated to groups of retailers periodically. This means that
replenishment orders of one or several items from different retailers are
consolidated and dispatched at certain time intervals. By doing so, transportation
cost savings can be realized and emissions can be reduced. This is achieved by
filling the vehicles or load carriers to a higher extent and by using cheaper and
more environmentally friendly, transportation modes.
The first paper explicitly focuses on how to include more realistic
transportation costs and emissions. This is done by obtaining the distribution of
the size of an arbitrary shipment leaving the central warehouse (directly affected
by the shipment frequency). It is thereby easy to evaluate any system where the
transportation costs and emissions are dependent on the size of the shipment. The
paper also provides a detailed analysis of a system where there is an opportunity
to reserve shipment capacity on an intermodal truck-train-truck solution to at least
one of the retailer groups. For this system it is shown how to jointly optimize the
shipment intervals, the reserved capacities on the intermodal transportation modes
and the reorder points in the system. The presented optimization procedure is
applicable in three scenarios; (i) the emissions are not considered, (ii) there is a
fixed cost per unit of emission, and (iii) there is a constraint on the maximum
emissions per time unit.
The second paper extends the analysis of a similar time-based shipment
consolidation system to handle compound Poisson demand (instead of pure
Poisson demand). This system has a simpler transportation cost structure, but the
more general demand structure makes the model applicable for a broader array of
products. The paper also extends the model to handle fill rate constraints, which
further improves the practical applicability. The cost analysis is performed with a
new methodology, based on the nominal inventory position. This variable is a helpful tool for analyzing the dynamics of distribution systems. Another system
where this tool can be used is studied in the third paper.
In this paper all stock points use installation stock (R,Q) ordering policies
(batch ordering). This implies that situations can occur when only part of a
requested retailer order is available at the central warehouse. The existing
literature predominantly assumes that the available units are shipped immediately
and the remaining units are shipped as soon as they arrive to the central
warehouse, referred to as partial delivery. An alternative is to wait until the entire
order is available before dispatching, referred to as complete delivery. The paper
introduces a cost for splitting the order and evaluates three delivery policies; the
PD policy (only partial deliveries are used), the CD policy (only complete
deliveries are used), and the state-dependent MSD policy (an optimization
between a partial and a complete delivery is performed for each delivery). The
MSD policy is proven to perform better than both the PD and the CD policy. In a
numerical study it is shown that significant savings can be made by using the
MSD policy.
Original languageEnglish
Awarding Institution
  • Production Management
  • Marklund, Johan, Supervisor
Print ISBNs978-91-7473-858-2
Electronic ISBNs978-91-7473-859-9
Publication statusPublished - 2014

Subject classification (UKÄ)

  • Transport Systems and Logistics


  • Inventory
  • Multi-echelon
  • Stochastic
  • Shipment consolidation
  • Delivery decisions


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