Problem:
As an illustration, we will suppose that the Juarez ski plant can actually operate at as much as 150% of its stated capacity during the August - November period by placing its workforce on over-time. We will also assume that the company policy is to use this plant exclusively to service the Phoenix warehouse. Moreover, we will assume that Juarez can make up to 100 pairs of skis monthly at a cost of $60 per pair using regular labor, for an additional $20 per pair, Juarez can make 50 additional pairs of skis per month using overtime labor. Finally, we will assume that the factory can store extra skis for later distribution at a cost of $1 per pair per month
August 100 pairs
September 150
October 200
November 100
550 pair
There are eight plants, each representing the month and type of production (R =regular) (o = Overtime). There are four warehouses 0 one for each monthly demand, plus one dummy warehouse (total capacity exceeds total demand).
The transportation problem format may be used for certain production-scheduling problems where the nature of the physical items themselves, not just the timing, is to be decided. This approach might be used in an assembly operation, where various components are joined together into final products. Supply constraints exist for the components, and these must all be allocated to final products to meet demand constraints. All other production factors must be assumed in plentiful supply, so that there are no labor or machine time constraints, for example. ( The coefficients of the x's must always be 1, and all constraints must involve simple addition with the x's.)
Suppose the information changes: use the following information for this scheduling problem. Suppose that updated order information indicates that there will be 250 pairs for October and 200 pairs for November. We can also subcontract 50 pairs/month at a cost of $90/pair. Finally, we have discovered that we have 100 pairs on hand. (Our inventory control person said "oops." Our CEO pretended she was Donald Trump and said "you're fired!") Formulate (or set up) the production schedule using the appropriate technique.