Optimal policy for a dynamic multi‐echelon inventory model

Abstract

A general multiperiod multi-echelon supply system consisting of n facilities each stocking a single product is studied. At the beginning of a period each facility may order stock f r o m an exogenous source with no delivery lag and proportional ordering costs. During the period the (random) demands at the facilities are satisfied according to a given supply policy that determines to what extent stock may be redistributed fromfacilities with excess stockto those experiencing shortages. There a r e storage, shortage, and transportation costs. An ordering policy that minimizes expected costs is sought. If the initial stock is sufficiently small and certain other conditions a r e fulfilled, i t is optimal t o order up t o a certain base stock level at each facility.The special supply policy in which each facility except facility 1 passes its shortages on to a given lower numbered facility called i t s direct supplier is examined in some detail. Bounds on the base stock levels a r e obtained. It i s also shown that if the demand distribution at facility j is stochastically smaller ("spread" l e s s ) than that at another facility k having the same direct supplier and i f certain other conditions a r e fulfilled, then the optimal base stock level ("virtual" stockout probability) at j is less than (greater than) o r equal to that at facility k.

A Survey of Multiattribute/Multicriterion Evaluation Theories

“…Various results for this case have been obtained by Strassen (1965) and Veinott (see Bessler and Veinott, 1966), and more recently by Levhari et al ( 1975) , Peleg (1975) and Brumelle and Vickson (1975) . The basic theorem in this area ( Strassen , 1951;Brumelle and Vickson, 1975) says that if X is bounded with ~ and ~ the random vectors for Vickson , 1977).…”

A fuzzy dynamic multi-objective, multi-item model by considering customer satisfaction in supply chain

“…Clark [9] started the studies on a two-layer SC in 1960. Veinott and Bessler [10] developed this model in another study. Goyal [11] presented the joint optimization concept for both vendors and buyers.…”

A Taxonomy for Supply Chain Management Literature

“…(i) multi echelon inventory models {Clark and Scarf (1960,1962), Chen (1998), Chen and Zheng (1994, Erkip et al(1990), Bessler and Veinott(1966), Graves (1985), Lee and Moinzadeh (1987a,b) };…”