Heuristic policies

Remark. A different type of approach to study forecasting issues in inventory management is that taken, e.g., by Chen et al. (1999). In their models they assume that the decision-makers are not aware of the exact characteristics of the demand process, and hence they resort to popular forecasting mechanisms such as the moving-average technique when making replenishment decisions. Chen et al. also propose heuristic policies that are very similar in their nature to those proposed in this paper. 

Table 2.8 presents heuristics for two reactants involved in series/parallel reactions. First, the hypothesis of complete consumption of the reactant that could raise separation problems should be investigated. However, the recycling of both reactants should be envisaged when high selectivity is the aim. The optimization should examine both reactor design and recycle policy. 

To implement such near optimal control algorithms would require considerable space and time on a process minicomputer because of the severe nonlinearities in the process, and therefore it is prdbaUy impractical in most situations. However, off-line simulations of this control policy shows some upper-limits as to what could possibly be accomplished and the nature and magnitudes of the feedrate manipulations that are necessary. This can then lead to the development of simpler heuristic-type control algorithms which capture the impextant aspects of the optimal control but are more easily implemented on-line. 

To handle the complexity of the plant and to still achieve the overall goal, a control hierarchy has been developed and used for many years. This architecture gets the company policy (several weeks time resolution) and refines it to the current action to be applied on any actuator of the plant (ms-sec resolution time). The procedure is to observe the state of the plant through thousands of sensors and evaluate the next action for any resolution time. Implicit, explicit, heuristic and first principles models are used in order to generate the adequate action. The common process control architecture has four control levels. The lower level of the architecture is the basic regulatory control, this control is achieved by single decentralized loops. Most of these loops are controlled by standard PID controllers. The actuating horizon at this level is just one. 

So the optimal solution is the path 1-3-5-7. Lot sizing policy is ordering 105 in the first period, 105 in the third period and 109 in the fifth period. As seen in the results before, heuristics also found the optimal solution for this example. 

We can attain the optimal transshipment policy using the dynamic program. However, the calculation of dynamic program is time costly and difficult to implement. Since the transshipment decision has to be decided upon frequently in the digital age, in the next section we propose three heuristic decision rules that can be easily implemented by practitioners. 

Some variations of the basic model are also studied in the literature. Unlike the basic model and most models considered in this area where the objective is to minimize a total system-wide cost, Lu (1995) considers a model with the objective of minimizing the vendor s total cost subject to the maximum cost the buyer may be prepared to incur. Both the case with a single vendor and a single buyer and the case with a single vendor but multiple buyers under both policies (b) and (c) with identical delivery quantities are considered. The single-vendor-single-buyer problem is solved optimally by closed-form formulas, while a heuristic is proposed for the single-vendor-multiple-buyer problem. 

Golhar and Sarker (1992) and Jamal and Sarker (1993) consider the basic model under policy (a) with the assumption that the conversion rate from raw material to final product is one to one. Two cases are considered (i) Imperfect matching - production uptime and cycle time are not exact integer multiples of finished product delivery cycle (ii) Perfect matching the above numbers are integers. An iterative heuristic is used to solve the problem. Sarker and Parija (1994) consider exactly the same problem except that the conversion rate from raw material to final product is not assumed to be one to one. An exact algorithm is proposed. 

Extensions of the basic model with multiple types of raw materials needed for producing a single product are studied by Sarker and Parija (1996) and Sarker and Khan (1999, 2001). Sarker and Parija give a closed-form solution for the problem under policy (b) and with the assumption that the production cycle time is an integer multiple of the pre-specified finished product delivery cycle. Sarker and Khan propose a heuristic for the problem under policies (a) and (c) and the assumption that delivery of final product to the customer is carried out in the end of the whole production lot. 

Shang, K. and J. Song. 2003. Newsvendor bounds and heuristic for optimal policies in serial supply chains. Management Science. 49(5) 618-638. 

Srinagesh, G. 2001. An efficient heuristic for inventory control when the customer is using a (s,S) policy. Operations Research Letters, 28, 187-192. 

Lot Sizes and Costs for Ordering Policy Using Heuristic... 

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