فرایند شبکه تحلیلی و یکپارچه سازی برنامه ریزی آرمانی چند دوره ای در تصمیمات خرید

This paper presents a multi-period inventory lot sizing scenario, where there is single product and multiple suppliers. By considering multi-period planning horizon, an integrated approach of Archimedean Goal Programming (AGP) and Analytic Network Process (ANP) is suggested. This integrated approach proposes a two-stage mathematical model to evaluate the suppliers and to determine their periodic shipment allocations given a number of tangible and intangible criteria. In the evaluation stage, the suppliers are evaluated according to 14 criteria that are involved in four control hierarchies; benefit, opportunity, cost and risk (BOCR). In the shipment stage, a multi objective mixed integer linear programming (MOMILP) model is described to solve the order allocation problem. This MOMILP model is suggested to achieve target values of periodic goals: budget, aggregate quality, total value of purchasing (TVP) and demand over the planning horizon, without exceeding vendor production capacities. This multi-period model is solved by using AGP. Finally some computational experiments are conducted to test the performance of the proposed method.

Companies need to work with different suppliers to continue their activities. In manufacturing industries the raw materials and component parts can equal up to 70% product cost. In such circumstances the purchasing department can play a key role in cost reduction and supplier selection is one of the most important functions of purchasing management (Ghodsypour & O’Brien, 1998). Several factors may affect a suppliers’ performance. Dickson (1966) identified 23 different criteria for vendor selection including quality, delivery, performance history, warranties, price, technical capability and financial position. Hence, supplier selection is a multi-criteria problem which includes both tangible and intangible criteria, some of which may conflict. Basically, there are two kinds of supplier selection problem. In the first kind of supplier selection, one supplier can satisfy all the buyer’s needs (single sourcing). The management needs to make only one decision; which supplier is the best. In the second type (multiple sourcing), no supplier can satisfy all the buyer’s requirements. In such circumstances management wants to split order quantities among suppliers for a variety of reasons including creating a constant environment of competitiveness. Several methods have been proposed for single and multiple sourcing problems in the literature (Aissaoui, Haouari, & Hassini, 2006). First publications on vendor selection can be traced back to the early 1960s. Although, the problem of supplier selection is not new, quite a few researchers treat the supplier selection issue as an optimization problem, which requires the formulation of an objective function (Wang, Huang, & Dismukes, 2004). Since, not every supplier selection criterion is quantitative, usually only a few quantitative criteria are included in the optimization formulation. To overcome this drawback, Ghodsypour and O’Brien, 1998 and Wang et al., 2004 proposed integrated approaches. They are achieved in two phases. At first, a supplier evaluation is elaborated using a multi-criteria tool. In these studies, the Analytic Hierarchy Process (AHP) method was applied to make the trade-off between tangible and intangible factors and calculate a rating of suppliers. The second stage of these global approaches consists of effectively selecting the suppliers and allocating orders using mathematical programming to take into account the system constraints. Thereby in the study of Ghodsypour and O’Brien (1998), calculated ratings are applied as coefficients of an objective function in a linear program such that the total value of purchasing becomes a maximum. This single period single item model was constrained by the demand, capacity and quality requirements. They used ε-constraint method to solve the problem. In addition to a goal that maximizes the total value of purchase (AHP ratings input), Wang et al. (2004) considered a second goal that minimizes the total cost of purchase. The resulted preemptive goal programming (PGP) determines the optimal order quantity from the chosen suppliers considering as constraints vendor capacities and demand requirements. Demirtas and Ustun (2005a) combined ANP and MOMILP model to solve order allocation problem by using a Reservation Level Driven Tchebycheff Procedure. They minimized total defect rate and total cost of purchasing, and maximized TVP. On the other hand, none of these integrated approaches considered a multi-period planning horizon. Several researchers combine supplier selection and procurement lot-sizing by considering a multi-period planning horizon and defining variables to determine the quantity purchased in each elementary period (Bender et al., 1985, Buffa and Jackson, 1983, Tempelmeier, 2002 and Basnet and Leung, 2005). Buffa and Jackson (1983) presented a schedule purchase for a single product over a defined planning horizon via a GP model considering price, quality and delivery criteria. It included buyer’s specification such as material requirement and safety stock. Bender et al. (1985) studied a purchasing problem faced by IBM involving multiple products, multiple time periods, and quantity discounts (the type of quantity discount was not mentioned). The authors described, but not developed, a mixed integer optimization model, to minimize the sum of purchasing, transportation and inventory costs over the planning horizon, without exceeding vendor production capacities and various policy constraints. Contrary to single period models dealing with any form of price discount, by considering inventory management in a multi-period horizon planning, Tempelmeier (2002) incorporates a trade-off between ordering larger quantities to get a reduction on purchasing costs and maintaining low inventories to minimize holding costs. Basnet and Leung (2005) balance ordering and holding costs in a multi-item model by considering a multi-period scheduling horizon. They proposed an uncapacitated mixed linear integer programming that minimizes the aggregate purchasing, ordering and holding costs subject to demand satisfaction. The authors proposed an enumerative search algorithm and a heuristic to solve the problem. Although they considered multi-period planning horizon, neglected intangible criteria. Both of multi-period planning horizon and intangible criteria can not be neglected in real life problems such they are working on. To eliminate this drawback, Demirtas and Ustun (2005b) have also used ANP and GP approach for multi-period lot-sizing. In this paper, an integration of ANP and multi-period MOMILP is proposed to consider both tangible and intangible factors for choosing the best suppliers and define the optimum quantities among the selected suppliers. This two-stage mathematical model is proposed to evaluate the suppliers and to determine their shipment allocations given a number of tangible and intangible criteria. In the evaluation stage, the suppliers are evaluated according to 14 criteria that are involved in four control hierarchies; BOCR. It will be useful to determine priorities by ANP, a new theory that extends the AHP. With the ANP it is recognized that there is feedback between the elements in different levels of the hierarchy and also between elements in the same level, so the decision elements are organized into networks of clusters and nodes. ANP deals systematically with all kinds of feedback and interactions (inner and outer dependence). When elements are linked only to elements in another cluster, the model shows only outer dependence. When elements are linked to the elements in their own cluster, there is inner dependence. Feedback can better capture the complex effects of interplay in human society (Saaty, 2001). Using pairwise comparison, a more accurate scoring method that has been applied on supplier selection are the AHP and ANP approaches. Barbarosoglu and Yazgaç, 1997, Yahya and Kingsman, 1999, Masella and Rangone, 2000, Tam and Tummala, 2001, Lee et al., 2001, Handfield et al., 2002 and Colombo and Francalanci, 2004 propose the use of AHP to cope especially with determining scores. In a recent study, Liu and Hai (2005) presented the voting analytical hierarchy process (VAHP) that is a novel easier weighting procedure in place of AHP’s paired comparison. The analytical network process (ANP), a more sophisticated version of AHP, was also applied for vendor selection by Sarkis and Talluri, 2000 and Sarkis and Talluri, 2002. In the shipment stage, a MOMILP model is described for a multi-period inventory lot sizing scenario, where there are multiple suppliers and single product. It is suggested to achieve target values of periodic goals such that budget, aggregate quality, TVP and demand over the planning horizon, without exceeding supplier production capacities. This multi-period model is solved by using AGP and some computational experiments are conducted to test the performance of the proposed method. GP is an analytical approach devised to address decision-making problems where targets have been assigned to all the attributes and where the decision maker (DM) is interested in minimizing the non-achievement of the corresponding goals. In other words, the DM seeks a Simonian satisficing solution (i.e., satisfactory and sufficient) with this strategy (Romero, 2004). Buffa and Jackson, 1983, Sharma et al., 1989, Chaudhry et al., 1993, Karpak et al., 1999 and Wang et al., 2004 used GP method in purchasing decisions. In these studies, only Wang et al. (2004) proposed an integrated approach for single period.

Although, supplier selection problems are not new, quite a few researchers treat the supplier selection issue as an optimization problem, which requires the formulation of the objective function. Several mathematical models have been proposed for single and multiple sourcing supplier selection problems in the literature but, not every supplier selection criterion is quantitative, so only a few quantitative criteria are included in the optimization formulation in these studies. To overcome this drawback, some authors have suggested new models that integrate multi-criteria decision making techniques and the mathematical models with single or multi objectives for single period. Being different from previous studies, this paper presents an integration of ANP and AGP approach in multi-period inventory lot sizing scenario, where there are multiple suppliers and single product. A two-stage mathematical model was proposed to evaluate the suppliers and to determine their shipment allocations given a number of tangible and intangible criteria. In the evaluation stage, the suppliers were evaluated according to 14 criteria that are involved in four control hierarchies; benefits, opportunities, cost and risks (BOCR). Although AHP and ANP are the multi-criteria decision making techniques which provide to consider both tangible and intangible factors, AHP is not sufficient to catch the effects of the same level criteria on themselves and the effects of the alternatives on the criteria. To overcome the drawbacks of AHP, the priorities of suppliers were calculated by ANP although an increase in the number of pairwise comparisons and more complex calculations. Real data was used for the quantitative criteria in comparisons to improve the system consistency. These priorities obtained by ANP are used to calculate TVP, the third goal of shipment stage. In the shipment stage, to find the optimal order quantities and inventory levels, a multi-period AGP model was built to minimize unwanted deviations. It is conducted more computational experiments to test the performance of the proposed method. The sensitivity analysis of the AGP model was also performed for different levels of periodic budget, quality, TVP and demand. Sensitivity analyses can be enlarged with capacity levels and priorities of suppliers and different weights of goals for long term planning activities.