Title: A fuzzy collaborative supply chain inventory model with controllable setup cost and service level constraint for imperfect items

Authors: Nughthoh Arfawi Kurdhi; Sri Maria Puji Lestari; Yuliana Susanti

Addresses: Department of Mathematics, Faculty of Mathematics and Natural Science, Sebelas Maret University, Surakarta, 57126, Indonesia ' Department of Mathematics, Faculty of Mathematics and Natural Science, Sebelas Maret University, Surakarta, 57126, Indonesia ' Department of Mathematics, Faculty of Mathematics and Natural Science, Sebelas Maret University, Surakarta, 57126, Indonesia

Abstract: This paper presents a fuzzy collaborative vendor-buyer production-inventory model under service level constraint. The vendor's production process is imperfect and an order lot may contain a certain number of imperfect items with a known probability density function. This article assumes that setup cost and lead time can be reduced at an investing cost and at a crashing cost, respectively. The fuzzy total joint cost under fuzzy average demand is also considered. In this study, we consider two cases of lead time demand that are normal distribution and distribution free. The objective is to simultaneously optimise the lot size, lead time, reorder point, setup cost and number of shipment in one production cycle, constrained on a service level, such that minimise the total joint cost. In distribution free case, we apply a minimax distribution free procedure to determine the optimal solution. Numerical examples are used to illustrate the benefits of integration.

Keywords: fuzzy set theory; imperfect processes; signed distance; collaborative supply chains; supply chain management; SCM; inventory modelling; setup costs; service level constraints; imperfect items; lead times; lot sizes; reorder points; number of shipments; production cycles; supply chain collaboration.

DOI: 10.1504/IJAMS.2015.069265

International Journal of Applied Management Science, 2015 Vol.7 No.2, pp.93 - 122

Received: 08 May 2021
Accepted: 12 May 2021

Published online: 06 May 2015 *

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