A two-warehouse multi-item supply chain with stock dependent promotional demand under joint replenishment policy: a mixed-mode ABC approach

Abstract

A multi-item two-level supply chain model under promotional cost sharing is proposed and analysed in this investigation. Here, it is assumed that a retailer purchases different items from a wholesaler under joint replenishment policy and sells the items to its customers. Due to the scarcity of the market place, the retailer uses two rented warehouses to run the business – one with moderate capacity situated at the heart of the market place, namely $R{W}_1$ and another with sufficiently large capacity, a little away from the market place, namely $R{W}_2$. Items are ordered jointly using basic period (BP) policy, initially stored at $R{W}_2$ and transferred jointly to $R{W}_1$ for sale following another BP policy. Demands of the items depend on displayed inventory levels, selling prices as well as the frequencies of the advertisements. Total cost due to the reduced selling prices and the advertisements is considered as the promotional cost. The problem is formulated as a mixed-integer optimisation problem in crisp as well in imprecise environments. To solve such real-life problems, here artificial bee colony algorithm is modified, tested and used. Model is illustrated with some hypothetical test problems and some managerial insights are outlined.

Keywords:

• Two-warehouse
• joint replenishment
• promotional cost sharing
• mixed-mode ABC algorithm

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Nilesh Pakhira

Nilesh Pakhira has graduated from Vidyasagar University, India and completed M.Sc. from I.I.T. Kharagpur, India. His fields of interest are inventory control system, supply chain, fuzzy optimization etc.

Manas Kumar Maiti

Manas Kumar Maiti is an Associate Professor of Mathematics at Mahishadal Raj College. He received his M.Sc. and M.Phil. in Applied Mathematics from Calcutta University, India and M.Tech. in Computer Science from I.I.T. Kharagpur, India and awarded Ph.D. in Applied Mathematics from Vidyasagar University, India. His research interest includes -- Evolutionary Algorithms, Operations Research, Fuzzy Mathematics, Rough Set, etc.

Manoranjan Maiti

Manoranjan Maiti has earlier worked at Indian Institute of Tropical Meteorology, Poona; Structural Engineering Division, Vikram Sarabhai Space Centre, ISRO, Trivandrum; Department of Mathematics, Calcutta University Post Graduate Centre (presently, Tripura University), Agartala; Department of Applied Mathematics, Vidyasagar University, West Bengal. He was also dean, Faculty Council of Science, for a period of 10 years and vice-chancellor (pro-tempore) of Vidyasagar University, for a short period. More than 40 students have been awarded PhD degree in Mathematics under his guidance at Vidyasagar University and NIT Durgapur, West Bengal, as well as several students are doing PhD under him. He has published more than 250 research papers in several international journals. He was associate editor of Applied Mathematical Modelling. His fields of interest are inventory control system, supply chain, fuzzy optimization, transportation, Genetic Algorithm, Ant Colony Optimization, etc.