B. Conceptos Básicos
2. Personas Privadas de la Libertad a. Secuestrados
The four computational experiments show that the six-phase heuristic performs better than the Lagrangian relaxation based heuristics (Robinson and Lawrence, 2004 and Gao and Robinson, 2004) for the capacitated coordinated lot-sizing problem, but its performance drops significantly as the item TBO level increases. On the other hand, the simulated annealing metaheuristic (SAM) not only improves the six-phase heuristic's performance but also provides a good estimate of the optimality gap at higher levels of TBO. The EH
heuristic of Federgruen et al. (2004) provides the best known optimality gap for the capacity constrained coordinated problem but it is not practical to implement in a supply chain planning system, as the computational requirements of this heuristic is highly sensitive to the problem size. In contrast, SAM's CPU requirements are relatively invariant the problem size. We also tested the SAM on one of nation's leading direct (catalogue based) marketers dataset of 239 items and 26 periods and were able to obtain results in less than 14 seconds. These results strongly suggest the potential application of SAM as a highly efficient and effective solver in logistics, operations, and supply chain planning software.
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CHAPTER VII
EVALUATION OF COORDINATED LOT SIZING HEURISTICS
UNDER ROLLING HORIZON
Our experimental design is derived from both the MPS rolling schedule and the coordinated lot-sizing literature, as there is no published research for this class of problem in the rolling horizon literature. The environmental factors are based on Robinson et al. (2006) and Federgruen et al. (2004) while the MPS design parameters are based on Zhao et al. (2001) and the performance metrics are based on the study by Sridharan et al. (1988) and Sahin et al. (2004). In this study, we also introduce additional improvements to the experimental factors and performance metrics.
7.1 Experimental design
The experimental design consists of four basic components; environmental factors, MPS design factors, coordinated uncapacitated lot-sizing heuristics and the simulation procedure.
7.1.1 Environmental factors
Four environmental factors, namely, number of items, major (family) TBO, minor TBO and demand lumpiness are considered for this computational study. The number of items is taken from the set I ∈ {4, 8, 12}. The demand generation follows Robinson et al. (2006) with necessary modifications to suit this computational study. Demand, dit, is generated from a normal distribution and varies by item and time period. The even numbered items have a mean demand of 50 units and a standard deviation of 20 units and odd numbered items have a mean demand of 100 units and a standard deviation of 20 units. The demand density or lumpiness is tested at three levels, DD ∈ {0.50, 0.75, 1.0}. When DD=0.50 only 50% of the time periods experience demand, similarly at DD=0.75 only 75% of the periods experience demand, while the rest of time periods have zero demand. The mean of the normal distribution that generates the non-zero portion of the demand stream is adjusted,
such that they retain the overall average demand. For example, at DD=0.75, the mean
demand of normal distribution for odd and even numbered items are increased to 67 and 133, thereby maintaining the overall average at 50 and 100 units respectively.
The generation of time between orders (TBO) is based on Maes and Wassenhove (1988) and Federgruen et al. (2004). The major TBO
(
2St' hD)
is used to generate the joint setup cost St', where D, is the average demand for the product family and h is the holding cost per unit per time period, which is set at $1.00. The item setup cost sit' isgenerated from the minor TBO
(
2sit' hd)
, where d represents the average demand for the item. Each TBO is evaluated at three levels, {low, medium, high}, whose values are taken from a uniform distribution on the intervals [1, 3], [2, 6] and [5, 10] respectively.7.1.2 MPS design factors
We use two factors, planning horizon length and frozen interval length, to design our MPS scheduling policy. The planning horizon length (PH) is set as an integer multiple, K ∈ {2, 4, 8} of natural order cycle, N, i.e. PH = K*N. The natural order cycle length, N, for the
coordinated lot-sizing problem is calculated using the expression S s hD
I i it t +
∑
=1 ' ' 2presented in Ballou (1998). The frozen interval length, n is defined as a portion F of
planning horizon length, i.e. n = F*PH. It is evaluated at four levels, F∈ {0.25, 0.5, 0.75, 1}. We assume re-planning is done at the end of the frozen interval which provides both lower schedule cost and stability (Sridharan et al. 1990, Zhao and Lee 1996, Zhao and Lam 1997).
7.1.3 Coordinated uncapacitated lot-sizing heuristics
The nine lot sizing procedures considered in this computational study are: Four Forward pass heuristics
FP-E: Forward-pass heuristic using the modified Eisenhut decision criterion FP-E-WR: FP-E with the right-shift improvement routine of two phase heuristic FP-LV: Forward-pass heuristic using the modified LV decision criterion
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FP-LV-WR: FP-LV with the right-shift improvement routine of two phase
heuristic Three FB based heuristics
FB: Fogarty-Barringer heuristic
FB-SK Fogarty-Barringer heuristic with the Silver-Kelle procedure PM: Boctor et al.'s perturbation metaheuristic initialized by FB-SK Two Two-phase based heuristics
TP: Two-phase heuristic
SAM: Simulated annealing metaheuristic initialized by TP The detailed descriptions of these heuristics are provided in Chapter IV.
7.1.4 Simulation procedure
We carry out a full factorial design, resulting in 972 combinations of experimental factors, which include both environmental and MPS design factors. For each combination we generate ten random problems. Each problem is then solved by the nine CULSP heuristics listed in Section 7.1.3, resulting in a total of 87,480 data points for analysis. All the heuristics were coded in C++ and the simulation study is conducted in a laptop running Pentium® M processor at 1.7 GHz. Prior research (Blackburn et al. 1986 and Sridharan et al. 1987) show that experimental run length of 300 time periods eliminates both
initialization and termination effects; in this research we use a run length of 400 time
periods. Figure 7.1 illustrates the rolling schedule policy for two successive planning cycles.