A Piecewise Objective Probabilistic Optimization Approach as Decision Making for Supplier Selection and Inventory Management With Price Discount

Introduction

Manufacturing industries are continuously struggling to optimize operational costs to gain more profit due to the existence of several cost components such as procurement and inventory during the industrial manufacturing process. Procurement cost is incurred during the process of purchasing raw materials or products while inventory cost is required in the warehouse to store raw materials and products. However, without loss of the generality, all kinds of materials handled in this problem were referred to as products. A manufacturer commonly has several suppliers with different requirements such as the product price, transport cost, maximum capacity to supply the product in a time, product defect rate, and late delivery product rate (Ware et al., 2014). This means it is possible to optimize the procurement cost by selecting the optimal supplier or, in more advanced technique, determining the optimal product volume to be ordered from each supplier. Meanwhile, inventory cost can be optimized by storing only the minimal product volume to satisfy demand in the warehouse. However, in some cases, the decision-maker may prefer to set inventory at some “secure” or “target” level and this means there is the need to determine the preference level which can be termed as the inventory tracking control problem (Ignaciuk & Wieczorek, 2019; Mahmoud et al., 2010).

The effort towards obtaining the best supplier and control the inventory have been reported by several case study researches conducted in different industrial fields such as automotive manufacturing (Jamil et al., 2013), banking (Onut & Tosun, 2014), electricity and power plant (Alam et al., 2012; Tan et al., 2014; Tsui & Wen, 2014), blood distribution (M. Kumar & Kumar, 2018), medicine (Fazli-Khalaf & Nemati, 2018), steel (Oroojeni Mohammad Javad et al., 2020), humanitarian and disaster logistics (Ghorbani & Ramezanian, 2020; Olanrewaju et al., 2020), petrochemical industries (Mohseni et al., 2019), and several others. Moreover, the progress of mathematical modeling in the supplier selection problem and inventory management from the simple to recently developed ones is discussed in the literature review section of this paper. However, these problems were solved separately without any integration, for example, the supplier selection was addressed in (Alhourani & Saxena, 2019) without considering inventory management. The use of one decision-making model for some simple cases i.e. without discount works has also been reported in past researches (Sutrisno, Widowati, & Solikhin, 2016; Sutrisno & Wicaksono, 2015). Therefore, this article focused on the problem with the discount.

In this paper, a new approach involving the use of decision-making tools to solve supplier selection and inventory management problems containing price discounts and probabilistic parameters is developed. This involves the application of a mathematical optimization model in a class of probabilistic programming with a piecewise objective function after which computational experiments were conducted to assess the proposed model and determine the optimal decision.