Single capacitated production facilities where multiple products are produced pose particularly challenging scheduling problems. The traditional economic lot size calculation reflects the optimum production batch size in the light of the tradeoff between inventory carrying costs and order preparation/setup costs. However, these calculations are straightforward only when applied to a single product. When multiple products are produced on the same facility, the production quantities must be translated into a schedule which is within the capacity of the facility and results in the timely satisfaction of demand for each product. Previously published solution procedures directly address the capacity issue. A far less tractable issue is the stockout concern. This issue has previously been addressed by either (1) imposing (often overly restrictive) constraints a priori to guarantee feasibility from the outset possibly eliminating more economic schedule alternatives from consideration or (2) heuristic enumeration procedures where trial solutions are evaluated for feasibility a posteriori but the escape from infeasibility often poses algorithmic difficulties. In this paper, the focus is on providing a workable production sequence through a posteriori tests. Mathematical programming approaches are defined which include alternative formulations to better address the stockout concern. Goal programming procedures are proposed which provide a mechanism to directly examine the tradeoffs between scheduling efficiency and delivery performance.economic lot size, math programming, goal programming, capacity and stockout constraints

The objective of this study was to compare the quality characteristics of current plant-based protein ground beef alternatives (GBA) to ground beef (GB) patties of varying fat percentages. Fifteen different production lots (n = 15 / fat level) of 1.36 kg GB chubs of three different fat levels (10%, 20%, and 27%) were collected from retail markets in the Manhattan, KS area. Additionally, GBA products including a foodservice GBA (FGBA), a retail GBA (RGBA), and a traditional soy-protein based GBA (TGBA) currently available through commercial channels were collected. Consumers (n = 120) evaluated sample appearance, juiciness, tenderness, overall flavor liking, beef flavor liking, texture liking, and overall liking. Additionally, samples were evaluated for color, texture profile, shear force, pressed juiciness percentage (PJP), pH, and fat and moisture percentage. All three GB samples rated higher (P < 0.05) than the three GBA samples for appearance liking, overall flavor liking, beef flavor liking, and overall liking by consumers. Similar results were found with trained sensory panelists, which rated the GBA as less (P < 0.05) juicy, softer (P < 0.05), and lower (P < 0.05) for beef flavor and odor intensity and higher (P < 0.05) for off-flavor intensity than the GB. Moreover, the GBA had less (P < 0.05) change in shape through cooking and a lower (P < 0.05) percentage of cooking loss and cooking time than the GB. Also, the GBA all had lower (P < 0.05) shear force and PJP values than the GB. The color of the GBA differed (P < 0.05) from the GB, with the GB samples being more (P < 0.05) red in the raw state. These results indicate that the GBA provide different eating and quality experiences than GB and should thus be considered as different products by consumers and retailers.

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In a recent article in this journal Krajewski, Ritzman, and McKenzie [Krajewski, L. J., L. P. Ritzman, P. McKenzie. 1980. Shift scheduling in banking operations: A case application. Interfaces 10 (2, April).] described a linear programming approach for shift scheduling of encoder operations in commercial banks. Their methodology uses a one-week time horizon, thereby recognizing the need to satisfy personnel considerations while responding to substantial day-to-day volume fluctuations. As part of the sensitivity analysis, they performed a series of runs to determine the sensitivity of machine requirements to changes in the weekly volume of check arrivals. One set of runs used expected check arrivals while another set used a “worst case” series of check arrivals. With a minimal change in their formulation, the optimal number of machines for any volume of check arrivals could be determined directly.