In order to smooth its production scheduling, a footwear company has decided to use a simple version
In order to smooth its production scheduling, a footwear company has decided to use a simple version of a linear cost model for aggregate planning. The model is: vi = Unit production cost for product i in each period, ci = Inventory-carrying cost per unit of product i in each period, r = Cost per man-hour of regular labor, o = Cost per man-hour of overtime labor, dit = Demand for product i in period t, ki = Man-hours required to produce one unit of product i, (rm) = Total man-hours of regular labor available in each period, p = Fraction of labor man-hours available as overtime, T = Time horizon in periods, N = Total number of products. The decision variables are: Xit = Units of product i to be produced in period t, Iit = Units of product i to be left over as inventory at the end of period t, Wt = Man-hours of regular labor used during period (fixed work force), Ot = Man-hours of overtime labor used during period t. The company has two major products, boots and shoes, whose production it wants to schedule for the next three periods. It costs $10 to make a pair of boots and $5 to make a pair of shoes. The company estimates that it costs $2 to maintain a pair of boots as inventory through the end of a period and half this amount for shoes. Average wage rates, including benefits, are three dollars an hour with overtime paying double. The company prefers a constant labor force and estimates that regular time will make 2000 man-hours available per period. Workers are willing to increase their work time up to 25% for overtime compensation. The demand for boots and shoes for the three periods is estimated as: a) Set up the model using 1 man-hour and 1 2 man-hour as the effort required to produce a pair of boots and shoes, respectively. b) Write the dual problem. c) Define the physical meaning of the dual objective function and the dual constraints. Apr 24 2022 07:41 AM
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