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Wagner and Whitin (1958) develop an algorithm to solve the dynamic Economic Lot-Sizing Problem (ELSP), which is widely applied in inventory control, production planning, and capacity planning. The original algorithm runs in O ( T 2 ) time, where T is the number of periods of the problem instance. Subsequently, other researchers develop linear-time algorithms to solve the Wagner-Whitin (WW) lot-sizing problem; examples include the ELSP and equivalent Single Machine Batch-Sizing Problem (SMBSP). This paper revisits the algorithms for the ELSP and SMBSP under WW cost structure, presents a new efficient linear-time algorithm, and compares the developed algorithm with equivalent algorithms in the literature. The developed algorithm employs a lists and stacks data structure, which is a completely different approach than that of the comparable algorithms for the ELSP and SMBSP. Analysis of the developed algorithm shows that it executes fewer different actions throughout and hence it improves execution time by a maximum of 51.40% for the ELSP and 29.03% for the SMBSP.

With the increase of salinity, shrimp monoculture is a typical production system on many global coasts. They are thus inviting commercially valuable exotic shrimp species that threaten the population of natives and causing alteration of ecosystem function. This intentional introduction and redistribution of shrimp species is an Anthropocene feature of the global coast. Therefore, we investigated how the coastal system breaches a freshwater system leading to more saline-friendly production. Spatiotemporal mapping showed the scope of diversified coastal livelihood that illustrate the coexistence of saline and sweet water-based production system in Bangladesh with a mean accuracy of 89% (kappa statistics 0.86). In many parts, the once agriculturally dominated landscape has transformed into aquaculture to produce shrimp, crab, fish, and salt. Continuous Change Detection and Classification (CCDC) algorithm also depicts the breakpoint in time series of normalized difference vegetation index (NDVI) data due to coastal land-use change. This dynamism includes the strong presence of mixed rice-shrimp culture in Assasuni (west coast) and Chakaria (east coast), as well as salt panning in Chakaria and paddy rice production in Kalapara (mid-coast). Thus those areas are more resilient because many other coastal communities primarily depend on shrimp or aqua monoculture, having limited or no alternative production system. Due to semi-intensive shrimp cultivation, biotic depletion, disease, pollution like antibiotics, nutrients, and organic matter loads are also less than the global coast's intensive aquaculture area. This study revealed the need for a blended fresh and saline-based production system. The findings can be used as a reference in the formulation and implementation of sustainable coastal management policies.

This paper addresses the multi-period inventory lot-sizing problem with supplier selection and inventory shortage, and it considers both all-units and incremental quantity discounts. A unique preprocessing approach is introduced that transforms discount quantity intervals into newer ones, revealing the supplier that has the minimum total ordering, purchasing, and transportation costs. This transformation changes the lot-sizing problem with multiple quantity discount models into a problem of a single quantity discount schedule. The problem is formulated as a Mixed Integer Non-Linear Programming (MINLP) model. Since the problem is intractable, a hybridized search method is developed, where both an Evolutionary Algorithm (EA) and a Linear Programming (LP) driven local search are combined. For initialization, Wagner-Whitin (WW), back-shifting and relaxed LP approaches are used. Finally, for validation and justification purposes, test cases from the industry and literature are used.