A fuzzy chance-constrained programming model for integrated planning of the wheat supply chain considering wheat quality and sleep period: a case study

Abstract

Wheat is a staple food in many countries, and as a result, the first most cultivated crop worldwide. Since wheat is a vital product in terms of food security, its supply chain needs to be studied and planned carefully. This paper proposes a mixed-integer linear programming model for integrated planning of imported and domestically-produced wheat that addresses supplier selection, order planning, transportation, storage, and distribution problems at the same time. Specifically, this model focuses on the wheat quality and wheat sleep period. Moreover, differentiation of long-term and short-term storage facilities and consideration of intra-layer flows between storage facilities are other characteristics of this model. A fuzzy chance-constrained programming approach is employed to cope with the uncertainties associated with domestic supply, demand, and global wheat prices. Applicability and advantages of the developed model are demonstrated using real data from the wheat supply chain of Iran. Results show that the current status of the wheat supply chain of Iran is far from being optimal, and there are many opportunities for improvement.

Green Design of Regional Wheat Supply Chains under Uncertainty

“…Tables (6) and (7) show the optimal amount of rain-fed and irrigated wheat to be produced in each province in each period, respectively. Irrigated wheat is produced from current irrigated farms.…”

“…Constraint (5) express that all produced wheat from rain-fed and irrigated farms is transported to silos by road and rail transportation modes. Restriction (6) states that the amount of wheat in domestic silos in current period is equal to the amount of wheat left over from the previous period, plus the amount of wheat shipped from the farms to the silo, plus the amount of wheat that is transshipped from lateral silos to the silo in the current period, minus the amount of wheat that is transshipped from the silo to other silos, minus the amount of wheat sent from the silo to domestic customers. Restriction (7) is the same as restriction (6), except that it reflects the balance of inventory in import-export silos.…”

“…Restriction (7) is the same as restriction (6), except that it reflects the balance of inventory in import-export silos. In other words, the amount of import and export are added to restriction (6). Constraint (8) states that safety stock in silos should be maintained according to the needs of each province.…”

“…Pourmohammadi et al [6] presented a mixed integer linear programming (MILP) model for integrated planning of wheat supply chain. Their model determines the optimal values for the decisions such as supplier selection, order planning, transportation, storage and distribution under uncertainty.…”

A stochastic-fuzzy multi-objective model for the last-mile delivery problem using drones and ground vehicles, a case study

“…Usually when dealing with the uncertain constraints involving possibilistic or fuzzy data in their left and/or right-hand sides, the possibilistic chance-constrained programming (PCCP) approach is utilized [45]. This method has been applied in a vast variety of studies (e.g., [45] - [47]). In this method, a minimum confidence level of satisfaction as a safety margin can be set by the decision-maker (DM) to control these uncertain constraints' confidence levels.…”