An algorithm portfolio based solution methodology to solve a supply chain optimization problem

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Abstract

This paper introduces the algorithm portfolio concept to solve a combinatorial optimization problem pertaining to a supply chain. The supply chain problem is modeled with capacity constraints and demand variations over different time periods to minimize the total supply chain configuration cost. The algorithm portfolio is implemented over various problem instances to inspect and alleviate the computational expensiveness of a solution strategy. A bunch of five algorithms are utilized hereby viz. AIS, GA, Endosymbiotic Optimization, PSO and Psychoclonal algorithm. The observations reflect the appropriateness and effect of algorithm portfolios over the adopted supply chain, and viability over other optimization problems.

Introduction

The supply chain configuration is comprehended differently with reference to different problem context. For instance, it can be defined in terms of the selection of an optimal product family (Lamothe, Hadj-Hamou, & Aldanondo, 2006) or supplier option selection (Graves & Willems, 2005). A common issue in supply chain management is to minimize the supply chain configuration cost (Ganeshan, Jack, Magazine, & Stephens, 1999). However, the globalization and enlarged product variety in a supply chain leads to product proliferation (Chong, Ho, & Tang, 1998) which complicates the supply chain structure and raises the cost. To compromise over price-premium and manufacturing cost, modular strategies (He & Kusiak, 1996) and delayed differentiation (Lee, Robertson, & Ulrich, 1998) are utilized. Meanwhile, component commonality and differentiation determining cost and revenue are to be pertinently realized by standardizing one/some of the components while differentiating others for different market products. A product platform is generally referred to the common components, parts, subassemblies or assets shared across a product family (Sawhney, 1998). Platform based product development (PPD) obviously alleviates the costs and time to market and in addition to that it is a vital strategy for manufacturing mass customized product (Salvador, Forza, & Rungtusanatham, 2000). Moreover, as evident from the supply chain and product development literature, the inventory levels of common modules, in case of PPD, are highly reduced what is known as ‘risk pooling’ effect and is an outcome of component commonality. Various supply chain problems have been solved in the literature to obtain the minimum supply chain configuration cost like product cycle time and product variety (Piramuthu, 2005), uncertainties in supply and demand (Kwon, Im, Kun, & Lee, 2007), integration of manufacturing/distribution planning decision (Liang & Cheng, 2008), scheduling problems (Chan, Chung, & Chan, 2005), logistical operations and reduction of bullwhip effect (Zarandi, Pourakbar, & Turksen, 2008).

This paper researches a supply chain problem entangled with product development implications; however, it strives more to present a renovated solution methodology to promptly and economically resolve the supply and manufacturing decisions. Precisely, it addresses the inexorable quest to develop a versatile, prompt and efficient solution device to boldly tackle the noise and variations in a given supply chain issue that may arise from time to time and situation to situation which has been barely attended in supply chain contexts. For this purpose, it adopts a combinatorial cum integer supply chain optimization problem pertaining to raw material vendor selection, manufacturing process selection and transportation mode selection in a supply chain. The undertaken problem is pretty similar to Graves and Willems (2005) who employed deterministic solution methodology viz. Dynamic programming for one instance of the problem but overlooked the promptness, versatility and computational cost issues for the problem particularly for large size variants of the problem. Huang, Zhang, and Liang (2005) considered the same problem; solved it by a random search algorithm viz. GA with appreciable promptness for one problem instance, however, ignored the establishment of its performance over diverse problem instances and nor did they adjudged other competing stochastic algorithms. Akcay and Xu (2004) employed a combination of two deterministic heuristics to resolve similar problem but pertaining to optimal base stock policy and component allocation. However, the computational time involved in solving the problem will be large at the cost of exact optimality of solution (as is the case with deterministic algorithms), particularly in case of large and complex variants of the problem. Moreover, these algorithms possess not much flexibility when the problem complexity and nature is varied substantially.

As reflected from the above discussion, most of the previous works have either utilized algorithms based on the performance over a few similar problem instances or lack a sophisticated performance evaluation strategy. At the same time, they do not allow a negotiated consideration of computational cost, solution quality and versatility. Particularly, the deterministic algorithms are associated with large computational cost and effort; while, on the other hand, the run time of the stochastic algorithms varies for the same problem instance (from run to run) as well as for different problem instances. Obviously, the performance is not similar with different problem instances of the same problem. Thus, the related literature on supply chain has sparse attention on overall performance evaluation, performance consistency maintenance and the algorithm selection issue. Though few attempts to optimize the overall performance of the algorithms such as Dean and Boddy (1988) are found in the literature but seldom have these or other overall performance based strategies been harnessed in supply chain optimization problems. However, recently, an audacious strategy viz. algorithm portfolio – “a collection of different algorithms and/or different copies of same algorithm running on different processor” Gomes and Selman (1997) – has been proposed by Gomes and Selman (2001) to analyze complexities of the results of computationally hard problems that may lead to better amelioration in terms of overall performance. This paper resolves and inspects a supply chain optimization problem through algorithm portfolio conceptualization with statistical and experimental evaluations over various problem instances with different problem complexities. The undertaken problem is mainly a combinatorial cum integer supply chain problem in which raw material vendor selection, manufacturing process selection and shipping mode selection issues juxtaposed with product platform considerations and service time decisions are addressed. The model is formulated to optimize the total supply chain configuration cost for a product family with and without product platforms.

In order to overcome the above-mentioned shortcomings of usual optimization algorithms and their performance evaluation strategies, this paper inspects several algorithms bunching them into portfolios based on cumulative performance over various problem instances of the underscored problem. Summarily, the paper focuses on following implications (i) algorithm performance improvement in terms of computational cost and a quality deviation from the expected solution (ii) exploitation of the performance diversity of multiple algorithms (iii) minimization of the overall risk associated with the use of an algorithm (iv) ranking the portfolios based on its overall performance (v) provide the supply chain decision maker with a tool to evaluate and ensure promptness and reliability of the solution methodology (vi) an efficient strategy and algorithm kit for taking supply chain decisions in stipulated time frame.

Section snippets

Platform product development and the supply chain: an example

The product family must possess adequate product variety to address functional, physical or process demand diversity (Lamothe et al., 2006). This paper attends physical product diversity for product development and focuses on the determination of an optimal configuration of supply chain by making optimal supplier selection, manufacturing process and shipping decisions. For this purpose, a specific example from Graves and Willems (2005) or Huang et al. (2005) is taken for study. In this example,

Mathematical formulations

A multi-period model formulated hereby possesses scope of studying of PSC, ISCs and other evaluation means such as AOH inventory, WIP inventory, time to market etc. The necessary assumptions made are as under (1) immediate processing of any arriving order; (2) small values of average back orders; (3) restricted capacity at each stage; (4) number of options, production cost and processing times vary over different time periods; (5) demand distribution of end-products varies with the time period

Designing the algorithm portfolio

Addressing the performance variations and risk of various algorithms is a cumbersome job (Gomes & Selman, 1997) prominently for computationally hard problems. Moreover, the “winner takes all” strategy for the algorithm selection for a problem cannot maintain an efficient performance over different problem instances (Rice, 1997) of a supply chain problem.

Motivated by these adversities, this paper enquires for a viable and insightful perspective to an optimization problem via algorithm portfolios

Results and discussions: graphical and statistical insights

The data for the first problem instance is taken from Huang et al. (2005) and that for the rest of two are appropriately simulated which is available on the URL www.geocities.com/salik_nifft/data_portfolio. This section presents results observed as the costs implications in the supply chain followed by themes and inferences drawn for the portfolios.

Conclusions and future research

This paper introduces the algorithm portfolio concept to obtain an optimal supply chain configuration for a firm producing a platform based product. An extended optimization model is harnessed for this purpose making vendors, manufacturing process and product delivery mode selections at various stages of the supply chain. The problem is resolved through a platform and an independent supply chain (PSC and ISC, respectively) approaches where the lower cost is incurred in the PSC. As supply chain

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