تجزیه و تحلیل تنگنا برای برنامه ریزی تولید کل در زنجیره تامین

Global competition has made it imperative for the process industries to manage their supply chains optimally. The complexity of the supply chain processes coupled with large computational times often makes effective supply chain management (SCM) difficult. Production system is an important component of a supply chain. This paper introduces a novel approach for aggregate planning of production in supply chains. The approach derives inspiration from pinch analysis, which has been extensively used in heat and mass exchanger network synthesis. By representing demand and supply data as composites, it gives planners greater insight into the SCM process and thus facilitates re-planning and quick decision-making. Two case studies are solved, one involving a single product and another involving multiple products on a single processor. For the first case study, optimal production plans are obtained and matched with the results obtained by solving equivalent optimization problems in GAMS®. For the second case study, an algorithm is proposed to determine the sequence of production of the multiple products. The initial guess obtained by following the algorithm reduces the computational time to one-sixth of the time otherwise taken by the solver. It may be concluded that plans obtained by pinch analysis provide either the best aggregate plans or excellent starting points to reduce the computational time for solutions by mixed integer programming formulations.

Supply chain for a business consists of all the stages involved directly or indirectly in fulfilling demand from a customer. Production planning, scheduling and distribution are some of the operations performed in a supply chain. In most cases, a planning model is developed and an equivalent optimization problem is solved using standard optimization algorithms (McDonald & Karimi, 1997). One of the difficulties faced with discrete mathematical programming is combinatorial complexity, which increases dramatically with the size of the problem. The aim of this work is to introduce the approach of pinch analysis in aggregate planning within the overall framework for optimization of supply chains. Aggregate planning (Chopra & Meindl, 2001) aims at maximizing profit over a specified time horizon while satisfying demand. Pinch analysis has been extensively used in chemical engineering for the optimization of various resources such as energy and water (Linnhoff & Hindmarsh, 1983, Shenoy, 1995 and Wang & Smith, 1994). Pinch is defined as the most constrained point in the process. The proposed approach determines an aggregate plan taking the pinch into consideration through graphical representation. At the pinch, the material flows in a supply chain are balanced and problem decomposition is possible. The method helps in setting targets, i.e., predicting optimal performances based on fundamental principles prior to actual scheduling of processes.

Pinch analysis, proposed as a graphical procedure involving production and demand composites, is shown to provide not only a good qualitative understanding of the production planning problem but also optimal to sub-optimal solutions. In the case of production planning problems following chase strategy, the approach can be shown to provide optimal solutions as it ensures minimal inventory. Since cost factors are not explicitly incorporated in pinch analysis, it cannot always guarantee cost-optimal solutions for other cases. In the case of level strategy with no stockout, the cost influences are incorporated implicitly in the disposition of the demand and production composites. Depending on the cost data and demand profile, the solution can be either optimal or sub-optimal. This is also true for the stockout case. For multiple products, the approach can solve the product-sequencing problem when all product demands are at the terminal time and product changeover effects (time and cost) can be neglected. Pinch analysis helps in achieving targets by minimizing inventory for a given strategy. A hybrid approach, where pinch analysis provides a good starting guess, can assist considerably to reduce the computational time for optimizations during planning in SCM. Pinch analysis brings in the much-required flexibility into quick re-planning. It enables the manager to make quick and correct decisions related to warehousing requirements, acceptance of new orders, minimum level of safety stocks, effect of machine breakdown, and actual inventory costs. For minor changes, the resulting effects can be observed on the composites without running mathematical formulations thus saving on computational time (Singhvi, 2002). This paper has focused on only one stage (namely, production) of the supply chain. The supply and distribution stages have not been explicitly included in the analysis. In a complete supply chain scenario, the aggregate planning process may be applied repeatedly with the demand from one stage becoming the supply to the next stage. Future work needs to extend the simple pinch analysis approach proposed here to capture all the variables and tradeoffs that may exist in a complex supply chain planning problem.