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Inventory models

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Inventory models

  1. 1. Engineering Management 19/12/2013 MD MOUDUD HASAN LECTURER AIE, HSTU DINAJPUR An inventory problem exists when it is necessary to stock physical goods or commodities for the purpose of satisfying demand over a specified time horizon(finite or infinite). Almost every business must stock goods to ensure smooth and efficient running of its operation. Decisions regarding how much and when to order are typical of every inventory problem. M M HASAN, Lecturer, AIE, HSTU, DINAJPUR 1
  2. 2. Engineering Management 19/12/2013 1. Economic factors: a) Setup cost: • Fixed charge associated with the placement of an order • Independent of the quantity ordered b) Purchase price: • Parameter is of special interest when quantity discounts or price breaks can be secured c) Selling price: • Unit selling price may be constant or variable depending on whether quantity discount is allowed. d) Holding cost: • The cost of carrying inventory in storage • It includes the interest on invested capital, storage, handling cost, depreciation cost, etc. e. Shortage cost: • The penalty cost incurred as a result of running out of stock when the commodity is needed. • Include costs due to loss in customers goodwill and potential loss in income. 2. Demand: a) Deterministic demand : • It is assumed that the quantities needed over subsequent periods of time are known with certainty. b) Probabilistic demand: • The requirements over a certain period of time are not known with certainty • Requirements pattern can be described by a known probability distribution M M HASAN, Lecturer, AIE, HSTU, DINAJPUR 2
  3. 3. Engineering Management 19/12/2013 3. Ordering Cycle: a) Continuous review • A record of the inventory level is updated continuously until a certain lower limit is reached at which point a new order is placed. b) Periodic review • Orders are placed usually at equally spaced intervals of time. 4. Delivery Lags or Lead Times: • Time between the placement of an order and its receipt is called delivery lag or lead time. 5. Stock Replenishment: • The actual replenishment of stock may occur instantaneously or uniformly. 6. Time Horizon: • The time horizon defines the period over which the inventory level will be controlled. 7. Number of supply Echelons: • An inventory system may consist of several stocking points. 8. Number of items: • An inventory system may involve more than one item. M M HASAN, Lecturer, AIE, HSTU, DINAJPUR 3
  4. 4. Engineering Management 19/12/2013 The simplest type of inventory model occurs when demand is constant over time with instantaneous replenishment and no shortages. Typical situations to which this model may apply are- 1. Use of light bulbs in a building. 2. Use of clerical supplies, such as paper, pads, and pencils, in an office. 3. Use of certain industrial supplies such as bolts and nuts. etc. M M HASAN, Lecturer, AIE, HSTU, DINAJPUR 4
  5. 5. Engineering Management 19/12/2013 Let, K= Setup cost per unit time h= Holding cost per unit inventory per unit time β= Demand per unit time Y= Inventory level TCU= Total cost per unit time to=Y/β TCU as a function of Y can be written as TCU (Y) = (Setup cost/ unit time)+(holding cost/unit time) = + ℎ × TCU(Y)= + For minimum cost,
  6. 6. = 0 so that, − + = 0 ⟹ = ⟹ ∗ = This is called as wilson’s economic lot size for single item static model. M M HASAN, Lecturer, AIE, HSTU, DINAJPUR 5
  7. 7. Engineering Management 19/12/2013 Total inventory cost, ∗ = 2ℎ • Assumptions in single item static model: I. Single item II. Deterministic demand III. Instantaneous replenishment IV. Zero delivery lag V. Uniform demand per unit time. The purchasing price per unit depends on the quantity purchased. This usually occurs in the form of discrete price breaks or quantity discounts. In such cases, the purchasing price should be considered in the inventory model. Consider the inventory model with instantaneous stock replenishment and no shortage. Let, C1= cost per unit for yq C2= cost per unit for y≥q The total cost per unit time for yq is = 1 + + ℎ 2 M M HASAN, Lecturer, AIE, HSTU, DINAJPUR 6
  8. 8. Engineering Management 19/12/2013 • The total cost per unit time for y≥q is = 2 + + ℎ 2 • Let Ym be the quantity at which the minimum values of TCU1 and TCU2 occur. = 2 ℎ Define y=q1(ym) such that TCU1 (ym) = TCU2(q1) M M HASAN, Lecturer, AIE, HSTU, DINAJPUR 7
  9. 9. Engineering Management 19/12/2013 Total cost per unit ⋇ = 2 , ≤ , $ 1 , ≥ $ q1 q1 ()* +⋇ = ()*, +- , . ≤ +- ()* +⋇ = ()*, . , +- . ./ ()* +⋇ = ()*/ +- , . ≥ ./ +- q1 M M HASAN, Lecturer, AIE, HSTU, DINAJPUR 8
  10. 10. Engineering Management 19/12/2013 The daily demand for a commodity is approximately 100 unit. Every time an order is placed, a fixed cost Tk. 100 is incurred. The daily holding cost per unit inventory is TK. 0.02. if the lead time is 12 days . Determine the willson’s economic lot size and the reorder point. Solution: Given, Demand, β= 100 unit/day Setup cost, K= 100 Tk/order Holding cost, h= 0.02 Tk/unit/day Lead time= 12 days We know, Economic lot size, ∗ = Required, i. Economic lot size =? ii. Reorder point=? = ×00×00 0.0 = 1000 2345 Ordering time, 5∗ = ∗ = 1000 100 = 10 678 Effective Lead time= 12-10=2 days Demand for effective lead time= 2β = 2 x 100 =200 unit Reorder point= 200 unit 10 days 1000 unit Reorder point Lead time 12 days 200 unit M M HASAN, Lecturer, AIE, HSTU, DINAJPUR 9
  11. 11. Engineering Management 19/12/2013 Consider the inventory model with the following information. Demand, β= 5 unit/day Setup cost, K= 10 Tk/order Holding cost, h= 1 Tk/unit/day C1=2, 0q15 C2= 1, q≥15 We know, First compute, $ = = ×0×9 = 10 2345 Since ym q, it is necessary to check whether q is less than q1. The value of q1 is computed from TCU1 (ym) = TCU2(q1) 1 + $ + ℎ 2 $ = 2 + + ℎ 2 ⟹ 5 × 2 + 10 × 5 10 + 1 2 × 10 = 5 × 1 + 10 × 5 + 1 2 ⟹ 2 − 30 + 100 = 0 ⟹ = 30 ± 900 − 400 2 ⟹ = 26.18 AB 3.82 By definition, q1 is selected as the larger value. Since q1 q, it follows that y*=q=15 Tota lcos tper uni,t()* +⋇ = ()*, . , +- . ./ =P × / + /Q×P /P + / , × /P = 15.83 M M HASAN, Lecturer, AIE, HSTU, DINAJPUR 10

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