Research On Product Mix Optimization Decision Based On Theory Of Constraints

The theory of constraints (TOC) product mix problems that involvesdetermination of the quantity and the identification of each product to make or buy isone of the most fundamental decisions in practical application of a manufacturingenterprise.The TOC product mix optimization decision is extracted from the productionand operations problems as the research object and is resolved further in order to givesupport to production and operations practice through modeling, analyzing, algorithmconstructing, optimizing, simulating, management system developing andimplementing. The main innovative contributions of the dissertation are as follows:1. Mathematical modeling and analyzing for the TOC product mix problemsAccording to various optimization patterns, optimization strategies, and otheroptimization conditions, the TOC product mix optimization model is established,which including 1) the traditional TOC product mix optimization model onlyconsidering self-resources for maximizing system throughput and increasingutilization efficiency on the bottleneck resources; 2) the TOC product mixoptimization model with the extending capacity of outsourcing for maximizingsystem throughput, satisfying demands for the finished products at most, andincreasing utilization efficiency on the bottleneck resources; and 3) the TOC productmix optimization model with the elevating capacity of outside process for maximizingsystem throughput, satisfying demands for the finished products at most, andincreasing utilization efficiency on the whole.In order to simplify the models above, the new definition and classification ofcapacity constrained resource (CCR) and non-CCR is described in the form ofmathematic expression, which is different from traditional TOC approach that can notidentify some non-CCRs from the constraints of TOC product mix optimizationproblems and would mislead TOC product mix decision and worsen the manufacturing performance of the organization. Based on the new identificationmethods, the complicacy is decreased and the impact of the constraints on the modelis lessened through cutting down the restriction of the first-level non-CCR and thesecond-level non-CCR from the constraints of TOC product mix optimizationproblems.Furthermore, these models are analyzed, their maximal throughput is compared,and some theorems are proved, which are 1) the throughput of product mixoptimization using the integrated optimization strategy of make or buy is superior tothe respective optimization strategy, which is the traditional TOC heuristic (TOCh)operational logic, and integrated optimization may eliminate the profit loss resultingfrom traditional TOC product mix decision from another point of view; 2) thethroughput of TOC product mix optimization synthesizing these two outsourcingform simultaneously is more outstanding than the others that optimization with theextending capacity of outsourcing; and 3) the throughput of TOC product mixoptimization considering outside process pattern is more outstanding than thethroughput of TOC product mix optimization considering outsourcing pattern if everyproduct's expenses of aggregate outside process is equal to its expenses ofoutsourcing, and the same optimization strategy is selected. But the conclusion cannot come into existence under different optimization strategy is selected in theiroptimizations. These conclusions lay a foundation for the further algorithmestablishing, and give a principle for decision-making when meeting the product mixproblems.2. Optimization algorithm and simulation for the TOC product mix problemsThe TOC product mix problems is one of most typical combinatorialoptimization problems, which are NP-complete and its running CPU time may requireexponential time in the worst case. An immune algorithm (IA) for TOC product mixoptimization decision is introduced to identify optimal or near optimal product mixfor small or large-scale problem instances under conditions where the original TOChfailed, which is considered to produce non-optimal or infeasible solution owing toidle time left on the bottleneck when facing the single or multiple CCR(s), and toobtain inferior quality solution in reasonable computation times when dealing withlager size product mix problems encountered in practice, the same as integerprogramming (IP).The optimization algorithm based on IA and TOC (IA_TOC)is established forresolving the model mentioned, which includes 1) one variable under one dimension algorithm (IA_TOC_â… ) for the traditional TOC product mix optimization; 2)multi-variable under one dimension algorithm (IA_TOC_â…¡) for the TOC productmix optimization synthesizing these two outsourcing types simultaneously, and somecorresponding alternative solution for the other four models through some parameterssetting; and 3) one variable under two dimensions algorithm (IA_TOC_â…¢) for theTOC product mix optimization considering outside process pattern, especially therevised algorithm (R_IA_TOC_â…¢) for the large-scale problem instances.In addition, when considering outside process pattern, the retrieve,decomposition and assembly operations for bill of material (BOM) is needed. A BOMoperations algorithm is constrficted based on a new designed BOM data structure, andeasily resolve the problem that the common operations of BOM algorithm are difficultfor ransacking algorithm due to the complicacy and low efficiency by using simplelinear arithmetic operators.IA_TOC series algorithms obtain optimal solution through immune evolutionary.Within the immune evolutionary stage, some of the TOC philosophy is transferredinto heuristic information, further, the explicit optimizing process of TOCh isembedded into IA to form immune response mechanism, which ensures that theimmune evolution always moves forward the direction of optimization in feasiblefields. Moreover, the algorithm imitates and accomplishes other immune mechanisms,such as immune selection using antibody's expected proliferation value synthesizingfitness and concentration based on informative entropy, immune self-adaptiveregulation based on antibody's promotion or suppression, vaccination based onvaccine alleviating the undulate phenomenon during the evolutionary process(restraining antibody from degeneration). These immune mechanisms not onlyimprove the searching ability and the adaptability greatly, but also increase the globalconvergence speed evidently.Simulation results for small and large-scale TOC product mix problems showthat the IA_TOC series algorithms are effective in achieving the feasibility solutionsin reasonable times.For smaller size TOC product mix problems, comparing the results of theproposed method in references from revised TOeh, IP, Tabu search (TS),Geneticalgorithm(GA) with the results of the IA_TOC series algorithms, the simulation testsprove that the algorithms can constringe quickly and optimize the problemseffectively to get stated maximum goals. Also, simulation results for large size TOCproduct mix problem show that the IA_TOC series algorithms are more predominant than those of optimal methods, such as TS, GA, in achieving the feasibility solutionsin reasonable times. Therefore, the proposed approach is appropriate for adoption byproduction planners for the product mix problem of manufacturing enterprise.3. Optimization management system for the TOC product mix problemsA reconfigurable TOC product mix optimization management system is putforward for decision-making better in practical management, and its input, output andoperational logic are discussed. Especially, based on the advantages anddisadvantages analysis of traditional five focusing steps(FFS) logic, the newoperational logic of TOC product mix optimization management system is given andadopts their strong, points and restricts their weaknesses at best. Changing thetraditional optimization strategy under which the product priority is the foundation ofproduct mix optimization, the new operational logic optimizes the product mix firstly,plans the execution step of the established decision and improves continuouslysecondly, such as identifies, elevates, and subordinates constraints including themanufacturing priority of the products based on some rule. Moreover, changing theproduct mix decision only according to the plant's own capacity in the traditionalTOC heuristic logic, the extending capacity is considered in the start stage of productmix in advance, which decreases the loss-of only exploit the existing capacity to makedecision of product mix.The function model of optimization management system is designed accordingto the comprehensive investigation of the enterprise's requirement and the principle oftight cohesion within the module and loose coupling between the modules. Theinformation model is built based on IDEF1X methods and is described by ERwin,which is a computer aided modeling tool from Computer Associates (CA). Theinformation integration model with other management system, such as MRPâ…¡/ERP,CAPP, is given and its integration solution is discussed.In the case, the component-based development is selected, and thecomponent-based hierarchy software architecture for the optimization managementsystem is established. Finally, the optimization management system is developedsuccessfully through the assembly of these finished components, especially somecomponents are encapsulated as a large-grained component and can be directlyassembled into other components by the way of reuse-in-the-large, such as privilegecontrol large-grained component, BOM management large-grained component, andTOC product mix optimization large-grained component, which encapsulates themodel, algorithm, and optimization execution for the TOC product mix problems discussed above.Running results in 3 enterprises in China showed that the TOC product mixoptimization management system based on component is feasible, reconfigurable, andcan meet the individual requirements of an enterprise.