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Obtaininganinitial obtaininganinitial plan

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Unformatted text preview: t = $1,250 It is better to hire and fire MATHEMATICAL METHODS MATHEMATICAL METHODS THE TRANSPORTATION THE TRANSPORTATION METHOD THE TRANSPORTATION THE TRANSPORTATION METHOD The transportation problems involve finding the lowest­cost plan for distributing G/S from a number of sources (supply points) to a number of destinations (demand points). We use the transportation method as a way to obtain aggregate plans that would match capacity with demand and ending inventory requirements at minimum costs. THE TRANSPORTATION THE TRANSPORTATION METHOD The transportation method starts with the development of a feasible solution, which is then sequentially tested and improved until an optimal solution is obtained. The major steps in the process are: 1. 2. 3. Obtaining an initial solution/plan Testing for optimality (Stepping stone Method, MODI) Improving sub­optimal solutions We will discuss step 1 that is often optimal or near optimal, as for the last two steps they will not be discussed. OBTAINING AN INITIAL OBTAINING AN INITIAL PLAN The method requires that the total supply is equal to the total demand (S = D) – Balanced transportation problem – Capacity (Supply) > Demand We need to add an extra column entitled “Excess” or “Unused Capacity” to the Transportation table. – Capacity (Supply) < Demand We need to add an extra row entitled “Shortages” or “Lost sales” to the Transportation table. TRANSPORTATION TABLE (Excess or Unused Capacity) Production Periods 1 Beginning Inventory 1 Regular Overtime 2 Regular Overtime 3 Regular Overtime End Excess Capacity Inv Sales Periods 2 3 4 TRANSPORTATION TABLE (Shortages or Lost Sales) Production Periods 1 Beginning Inventory 1 Regular Overtime 2 Regular Overtime 3 Regular Overtime 4 Regular Overtime Shortages Demand E nd Inv Sales Periods 2 3 4 Capacity EXAMPLE 4 : PRODUCTION OF PENCILS Demand for pencils for the next four months is : 560,000 , 960,000 , 1,140,000 and 700,000, respectively. The production capacity at RT is 600 boxes (of 1,000 pencils each) for the first month, and 800 boxes for each of the other months. OT costs $25 per box more than the regular production cost. The cost of RM is $50 per box. The overtime capacity is 150 boxes during the first month and 200 boxes per mon...
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