Supply total cost optimization

This transportation problem is an example of an important class of LPs called network flow problems Find a set of values for the flow of a single commodity on the arcs of a graph (or network) that satisfies both flow conservation constraints at each node (i.e., flow in equals flow out) and upper and lower limits on each flow, and maximize or minimize a linear objective (say, total cost). There are specified supplies of the commodity at some nodes and demands at others. Such problems have the important special property that, if all supplies, demands, and flow bounds are integers, then an optimal solution exists in which all flows are integers. In addition, special versions of the simplex method have been developed to solve network flow problems with hundreds of thousands of nodes and arcs very quickly, at least ten times faster than a general LP of comparable size. See Glover et al. (1992) for further information. 

This model can be solved by dynamic programming (DP). Let be the optimeil cost-to-go in period k, that is, the total cost to supply the demand in periods k through period n, following the optimal lot-sizing decisions. Then Vj is the desired solution, which we ctm derive through the DP recursion as follows. 

Build strong financial supply chain processes to know total supply chain costs. Help the internal organizations within supply make trade-offs to reduce total costs, not optimize the costs within the silo. 

Same as in level 1, but in addition there is an attempt to increase overall supply chain efficiency through integration of different functional areas, in order to minimize total supply chain cost, instead of isolated functional area optimization. 

In this section we describe a way for finding the pair of safety-stock parameters 7 and 7, that minimize the long-run average total supply chain cost. We assume that installation-based policies are used. The extension of the discussion to echelon-based policies is relatively easy, given the observations made in 6.1.2. We refer to a supply chain in which these optimal safety stocks are used, as a coordinated two-level inventory system. We assume that h < and set = 0. Aviv (2002b) shows the following ... 

The supply chain configuration is established by selecting the most appropriate routes and contract conditions for delivering products. It is optimized to minimized total costs (Eq. 14.1). The total costs consist of purchasing costs (Eq. 14.2), handling costs (Eq. 14.3), supplier setup cost (Eq. 14.4), and fixed cost (Eq. 14.5) ... 

In Example 11-9, DO picks the lot size of 6,325 with an objective of minimizing only its own costs. From a supply chain perspective, the optimal lot size should account for the fact that both DO and the manufacturer incur costs associated with each replenishment lot. If we assume that the manufacturer produces at a rate that matches demand (as assumed in Example 11-9), the total supply chain cost of using a lot size Q is obtained as follows ... 

The optimal lot size (Q ) for the supply chain is obtained by taking the first derivative of the total cost with respect to Q and setting it equal to 0 as follows (see worksheet Example 11-9) ... 

Observe that if DO orders a lot size of 9,165 units, the supply chain cost decreases to 9,165 (from 9,803 when DO ordered its own optimal lot size of 6,325). There is thus an opportunity for the supply chain to save 638. The challenge, however, is that ordering in lots of 9,165 bottles raises the cost for DO by 264 per year from 3,795 to 4,059 (even though it reduces overall supply chain costs). The manufacturer s costs, in contrast, go down by 902 from 6,008 to 5,106 per year. Thus, the manufacturer must offer DO a suitable incentive for DO to raise its lot size. A lot-size-based quantity discount is an appropriate incentive in this case. Example 11-10 (see worksheet Example 11-10) provides details of how the manufacturer can design a suitable quantity discount that gets DO to order in lots of 9,165 units even though DO is optimizing its own profits (and not total supply chain profits). 

Mathematical planning models can be employed to select and schedule processes and partners such that the overall supply chain is by design robust to internal and external stimuli. In particular, portfolio optimization models commonly applied in finance can be used to select a portfolio of suppliers such that the total supply chain cost variability and the consequences fi om supplier non-performance are within manageable limits, as demonstrated in the later sections of this paper. In addition, recent work in the area of robust optimization can also be used to generate supply chain solutions that maintain their optimality under minor deviations in environmental conditions. 

Strategic-level Deviation Management Model. Given the expected costs and variability (deviation) of costs for all suppliers, the first problem relates to the selection of an optimal group of suppliers such that the expected cost of operating the entire supply chain and the risk of variations in total supply chain costs is minimized. 

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