Multi-echelon Inventory Control with Integrated Shipment Decisions

Författare

Olof Stenius

Summary, in English

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.

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